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Penn State University
1.
Henderson, Adam Dade.
Loop Quantum Cosmology: A Window Into the Path Integral Representation of Quantum Gravity
.
Degree: 2011, Penn State University
URL: https://submit-etda.libraries.psu.edu/catalog/12472 
► In this dissertation we present sum of histories formulations of loop quantum cosmology. These are considered for exactly soluble LQC expressed in a Schrodinger form…
(more)
▼ In this dissertation we present sum of histories formulations of loop quantum cosmology.
These are considered for exactly soluble LQC expressed in a Schrodinger
form with time provided by a scalar field where we are interested in transition
amplitudes and as a constrained system where we are interested in the physical
inner product defined by group averaging. As loop quantum cosmology is based on
the new quantum mechanics motivated from the representation of loop quantum
gravity the sum over histories have many distinct features from standard Feynman
path integrals. The sum over histories is given by an discrete sum over histories
which change configuration only finitely many times. The resulting sum over histories
have strong similarities to the current spin foam models while being derived
from a well-controlled canonical quantization. Thus we are able to probe many of
the open questions of spin foam models as well as provide new insights and avenues
of research.
Advisors/Committee Members: Abhay Vasant Ashtekar, Dissertation Advisor/Co-Advisor, Abhay Vasant Ashtekar, Committee Chair/Co-Chair, Paul Sommers, Committee Member, Victor Nistor, Committee Member, Dezhe Jin, Committee Member.
Subjects/Keywords: Quantum Gravity; Path Integral
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APA (6th Edition):
Henderson, A. D. (2011). Loop Quantum Cosmology: A Window Into the Path Integral Representation of Quantum Gravity
. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/12472
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Henderson, Adam Dade. “Loop Quantum Cosmology: A Window Into the Path Integral Representation of Quantum Gravity
.” 2011. Thesis, Penn State University. Accessed March 08, 2021.
https://submit-etda.libraries.psu.edu/catalog/12472.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Henderson, Adam Dade. “Loop Quantum Cosmology: A Window Into the Path Integral Representation of Quantum Gravity
.” 2011. Web. 08 Mar 2021.
Vancouver:
Henderson AD. Loop Quantum Cosmology: A Window Into the Path Integral Representation of Quantum Gravity
. [Internet] [Thesis]. Penn State University; 2011. [cited 2021 Mar 08].
Available from: https://submit-etda.libraries.psu.edu/catalog/12472.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Henderson AD. Loop Quantum Cosmology: A Window Into the Path Integral Representation of Quantum Gravity
. [Thesis]. Penn State University; 2011. Available from: https://submit-etda.libraries.psu.edu/catalog/12472
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
2.
Sandström, Martin.
Path Integrals and Quantum Mechanics.
Degree: Physics, 2015, Umeå University
URL: http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-110026
► In this thesis we are investigating a different formalism of non-relativistic quantum mechanics called the path integral formalism. It is a generalization of the…
(more)
▼ In this thesis we are investigating a different formalism of non-relativistic quantum mechanics called the path integral formalism. It is a generalization of the classical least action principle. The introduction to this subject begins with the construction of the path integral in terms of the idea of probability amplitudes whose absolute square gives the probability of finding a system in a particular state. Then we show that if the Lagrangian is a quadratic form one needs only to calculate the classical action besides from a time-dependent normalization constant to find the explicit expression of the path integral. We look in to the subject of two kinds of slit-experiments: The square slit, the single- and the double-Gaussian slit. Also, the propagator for constrained paths is calculated and applied to the Aharonov-Bohm effect, which shows that the vector potential defined in classical electrodynamics have a physical meaning in quantum mechanics. It is also shown that the path integral formulation is equivalent to the Schrödinger description of quantum mechanics, by deriving the Schrödinger equation from the path integral. Further applications of the path integral are discussed.
I detta fördjupningsarbete undersöker vi en annan formalism av icke-relativistisk kvantmekanik kallad banintegral formalismen. Det är en generalisering av den klassiska verkansprincipen. Introduktionen till detta ämne börjar med konstruktionen av banintegralen i termer av sannolikhetsamplituder vars absolutbelopp i kvadrat ger sannolikheten av att finna ett system i ett särskilt tillstånd. Sedan visar vi att om Lagrangianen är av kvadratisk form så krävs endast en beräkning av den klassiska verkan förutom en tidsberoende normaliseringskonstant för att finna ett uttryck för banintegralen. Vi ser på två olika typer av spaltproblem: Den kantinga spalten, enkel- och dubbel Gaussisk spalt. Vi beräknar dessutom propagatorn för banor med restriktioner och applicerar detta på Aharonov-Bohm effekten, som visar att den klassiska vektorpotentialen som definierad i klassisk elektrodynamik har en fysikalisk mening i kvantmekaniken. Vi visar också ekvivalensen av banintegralformalismen med Schrödingerekvationen genom att härleda Schrödingerekvationen från banintegralen. Andra applikationer av banintegralen diskuteras.
Subjects/Keywords: quantum; path integral; aharonov-bohm
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APA (6th Edition):
Sandström, M. (2015). Path Integrals and Quantum Mechanics. (Thesis). Umeå University. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-110026
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Sandström, Martin. “Path Integrals and Quantum Mechanics.” 2015. Thesis, Umeå University. Accessed March 08, 2021.
http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-110026.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Sandström, Martin. “Path Integrals and Quantum Mechanics.” 2015. Web. 08 Mar 2021.
Vancouver:
Sandström M. Path Integrals and Quantum Mechanics. [Internet] [Thesis]. Umeå University; 2015. [cited 2021 Mar 08].
Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-110026.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Sandström M. Path Integrals and Quantum Mechanics. [Thesis]. Umeå University; 2015. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-110026
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
3.
Chauhan, Arjun.
Some investigations in hypotheses of path integral
duality;.
Degree: 2014, V. B. S. Purvanchal University
URL: http://shodhganga.inflibnet.ac.in/handle/10603/36482
Subjects/Keywords: path integral duality
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APA (6th Edition):
Chauhan, A. (2014). Some investigations in hypotheses of path integral
duality;. (Thesis). V. B. S. Purvanchal University. Retrieved from http://shodhganga.inflibnet.ac.in/handle/10603/36482
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Chauhan, Arjun. “Some investigations in hypotheses of path integral
duality;.” 2014. Thesis, V. B. S. Purvanchal University. Accessed March 08, 2021.
http://shodhganga.inflibnet.ac.in/handle/10603/36482.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Chauhan, Arjun. “Some investigations in hypotheses of path integral
duality;.” 2014. Web. 08 Mar 2021.
Vancouver:
Chauhan A. Some investigations in hypotheses of path integral
duality;. [Internet] [Thesis]. V. B. S. Purvanchal University; 2014. [cited 2021 Mar 08].
Available from: http://shodhganga.inflibnet.ac.in/handle/10603/36482.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Chauhan A. Some investigations in hypotheses of path integral
duality;. [Thesis]. V. B. S. Purvanchal University; 2014. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/36482
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of California – Merced
4.
Kim, Tom.
Path integral formalism of Bose Einstein condensation and superconductivity.
Degree: Physics, 2019, University of California – Merced
URL: http://www.escholarship.org/uc/item/5kk698mc
► I set up the path integral formalism to study interacting bosonic gases, binary boson-fermion mixtures, and fermionic superconductors. The large-N theory is applied to bosonic…
(more)
▼ I set up the path integral formalism to study interacting bosonic gases, binary boson-fermion mixtures, and fermionic superconductors. The large-N theory is applied to bosonic interactions. The corresponding auxiliary field theory is applied to fermionic interactions. Using the thermodynamic quantities obtained by evaluating the path integral, I map out the phase boundaries. For fermionic superconductors, the path integral method reproduces well-known methods that were developed previously.
Subjects/Keywords: Physics; cold atoms; path integral; superconductor
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APA (6th Edition):
Kim, T. (2019). Path integral formalism of Bose Einstein condensation and superconductivity. (Thesis). University of California – Merced. Retrieved from http://www.escholarship.org/uc/item/5kk698mc
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Kim, Tom. “Path integral formalism of Bose Einstein condensation and superconductivity.” 2019. Thesis, University of California – Merced. Accessed March 08, 2021.
http://www.escholarship.org/uc/item/5kk698mc.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Kim, Tom. “Path integral formalism of Bose Einstein condensation and superconductivity.” 2019. Web. 08 Mar 2021.
Vancouver:
Kim T. Path integral formalism of Bose Einstein condensation and superconductivity. [Internet] [Thesis]. University of California – Merced; 2019. [cited 2021 Mar 08].
Available from: http://www.escholarship.org/uc/item/5kk698mc.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Kim T. Path integral formalism of Bose Einstein condensation and superconductivity. [Thesis]. University of California – Merced; 2019. Available from: http://www.escholarship.org/uc/item/5kk698mc
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Illinois – Urbana-Champaign
5.
Walters, Peter Lawton.
Path integral methods for accurate simulation of condensed phase reactions.
Degree: PhD, Chemistry, 2016, University of Illinois – Urbana-Champaign
URL: http://hdl.handle.net/2142/90579
► Simulating a realistic condensed phase reaction (e.g., charge transfer in solution) is a notoriously demanding task. These reactions often involve thousands of strongly coupled atoms.…
(more)
▼ Simulating a realistic condensed phase reaction (e.g., charge transfer in solution) is a notoriously demanding task. These reactions often involve thousands of strongly coupled atoms. This coupling is complex and extremely non-trivial. Additionally, despite the rapid movement of the atoms themselves, these reactions are usually very slow. A vast majority of chemistry and biology takes place in condensed environments. A method that can accurately simulate these reactions would be invaluable. To that end, we focus on improving the efficiency of a pair of preexisting
path integral methods.
The first method we discuss treats the entire problem quantum mechanically. While extremely accurate, the computational cost of quantum simulations grows exponentially with the size of the system. To help prevent this, we use an efficient spatial grid as the starting point for an iterative Monte Carlo calculation. Although good methods can mitigate exponential cost, they are still limited to simulations containing only a few atoms.
The second method uses a quantum-classical approximation. In these approximations, the majority of the system is simulated using (cheep) classical methods; the (expensive) quantum calculations are reserved for the excessively quantum portions of the system, which tend to be small. The quantum-classical
path integral (QCPI) approach handles the interaction between the quantum and classical portions of the system rigorously. By only reducing part of the total system, this QCPI approach introduces nonlocal temporal effects into the simulation. This nonlocality can only be treated by standard iterative-QCPI algorithms, if the coupling between the quantum and classical portions is weak or the simulation time is short. We introduce a scheme that can reduce the effective span of the temporal nonlocality. We employ our new accelerated-QCPI approach to perform an exceedingly accurate simulation of the ferrocene-ferrocenium charge transfer reaction in liquid hexane.
Advisors/Committee Members: Makri, Nancy (advisor), Makri, Nancy (Committee Chair), Hirata, So (committee member), Gruebele, Martin (committee member), Heath, Michael (committee member).
Subjects/Keywords: Quantum Dynamics; Path Integral; Charge Transfer
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APA (6th Edition):
Walters, P. L. (2016). Path integral methods for accurate simulation of condensed phase reactions. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/90579
Chicago Manual of Style (16th Edition):
Walters, Peter Lawton. “Path integral methods for accurate simulation of condensed phase reactions.” 2016. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed March 08, 2021.
http://hdl.handle.net/2142/90579.
MLA Handbook (7th Edition):
Walters, Peter Lawton. “Path integral methods for accurate simulation of condensed phase reactions.” 2016. Web. 08 Mar 2021.
Vancouver:
Walters PL. Path integral methods for accurate simulation of condensed phase reactions. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2016. [cited 2021 Mar 08].
Available from: http://hdl.handle.net/2142/90579.
Council of Science Editors:
Walters PL. Path integral methods for accurate simulation of condensed phase reactions. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2016. Available from: http://hdl.handle.net/2142/90579
University of Waterloo
6.
Ing, Christopher.
Path integral Langevin dynamics of complex molecular systems: from low-temperature quantum clusters to biomolecules.
Degree: 2011, University of Waterloo
URL: http://hdl.handle.net/10012/6202
► This thesis presents an implementation of path integral molecular dynamics (PIMD) for sampling equilibrium and dynamical properties within the molecular modelling toolkit (MMTK) [J. Comp.…
(more)
▼ This thesis presents an implementation of path integral molecular dynamics (PIMD) for sampling equilibrium and dynamical properties within the molecular modelling toolkit (MMTK) [J. Comp. Chem. 21, 79 (2000)], an open source Python package. Rigorous simulation using this code serves to benchmark this implementation as well as the robust- ness of the path integral Langevin equation as a thermostat [J. Chem. Phys. 133, 124104 (2010)].
PIMD is used to calculate equilibrium properties for clusters of HeN-CO2 at low- temperatures, with comparison to experimental and exact results. We characterize the convergence of structural and energetic properties as a function of path-integral discretiza- tion error. The radial and angular distribution of these clusters is studied as a function of size in the absence of rotation and bosonic exchange. These distributions are subsequently used to calculate vibrational shifts of CO2. This result is compared to high-accuracy path integral Monte Carlo simulations which include rotational and exchange effects. These sim- ulations indicate that the neglect of rotational degrees of freedom leads to an unphysical localization of helium atoms and incorrect vibrational shifts when compared to experiment.
Approximate real-time quantum dynamics is presented for doped helium clusters using the ring-polymer molecular dynamics (RPMD) method. The accuracy of RPMD is tested
iii
for low-temperature simulations and compared to exact results. Preliminary calculation of the dynamics of the helium solvated CO2 dopant with respect to the center of mass of the cluster is presented. The effect of a cartesian integrator versus a normal-mode integrator for quantum dynamics is addressed.
The path integral ground-state method is applied in order to calculate T = 0 properties. A convergence study of the ground-state energy of the quantum harmonic oscillator with respect to sampling time and path discretization is shown. As a final application of this implementation, a sugar in a periodic water box is simulated at T = 300K. The calculation of rotamer populations and a dipole autocorrelation indicate negligible change with the inclusion of quantum effects.
This work offers a comprehensive foundation from which to base future PIMD centered research.
Subjects/Keywords: path integral; molecular dynamics; helium cluster; ring polymer molecular dynamics; path integral ground state; quantum
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APA (6th Edition):
Ing, C. (2011). Path integral Langevin dynamics of complex molecular systems: from low-temperature quantum clusters to biomolecules. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/6202
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Ing, Christopher. “Path integral Langevin dynamics of complex molecular systems: from low-temperature quantum clusters to biomolecules.” 2011. Thesis, University of Waterloo. Accessed March 08, 2021.
http://hdl.handle.net/10012/6202.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Ing, Christopher. “Path integral Langevin dynamics of complex molecular systems: from low-temperature quantum clusters to biomolecules.” 2011. Web. 08 Mar 2021.
Vancouver:
Ing C. Path integral Langevin dynamics of complex molecular systems: from low-temperature quantum clusters to biomolecules. [Internet] [Thesis]. University of Waterloo; 2011. [cited 2021 Mar 08].
Available from: http://hdl.handle.net/10012/6202.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Ing C. Path integral Langevin dynamics of complex molecular systems: from low-temperature quantum clusters to biomolecules. [Thesis]. University of Waterloo; 2011. Available from: http://hdl.handle.net/10012/6202
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Rochester
7.
Chantasri, Areeya (1984 - ).
Stochastic path integral formalism for continuous quantum
measurement.
Degree: PhD, 2016, University of Rochester
URL: http://hdl.handle.net/1802/31479
► We present a stochastic path integral formalism to study statistical behaviour of a quantum system under weak continuous measurement. The path integral is constructed from…
(more)
▼ We present a stochastic path integral formalism to
study statistical behaviour of a
quantum system under weak
continuous measurement. The path integral is constructed
from
joint probability density functions of measurement outcomes and
quantum state trajectories. The optimal dynamics, such as the most
likely path,
is obtained by extremizing the action of the
stochastic path integral. We also
explore advantages of having the
full joint probability distribution of quantum
trajectories by
applying exact functional methods as well as developing a
perturbative
approach to investigate the statistical behaviour of
continuous quantum
measurement. Examples are given for qubits
measured in the {\hat σ}z basis and qubits
undergoing
fluorescence, where their most likely evolutions, average
trajectories,
variances, and multi-time correlation functions are
investigated. Moreover, we
verify the theoretical prediction for
the most likely paths with experimental data
from superconducting
transmon qubits coupled to microwave cavities. We present
the
experiment in two different cases: one is a single transmon qubit
continuously
measured in time, and another is two qubits that are
jointly measured and spatially
separated in two microwave
cavities. We show that the qubits' trajectories
can be accurately
tracked, and the qubits' state statistics and optimal dynamics
can
be predicted using our stochastic path integral and action
principle approach.
Subjects/Keywords: Most likely path; Path integral; Quantum measurement; Stochastic process
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APA (6th Edition):
Chantasri, A. (. -. ). (2016). Stochastic path integral formalism for continuous quantum
measurement. (Doctoral Dissertation). University of Rochester. Retrieved from http://hdl.handle.net/1802/31479
Chicago Manual of Style (16th Edition):
Chantasri, Areeya (1984 - ). “Stochastic path integral formalism for continuous quantum
measurement.” 2016. Doctoral Dissertation, University of Rochester. Accessed March 08, 2021.
http://hdl.handle.net/1802/31479.
MLA Handbook (7th Edition):
Chantasri, Areeya (1984 - ). “Stochastic path integral formalism for continuous quantum
measurement.” 2016. Web. 08 Mar 2021.
Vancouver:
Chantasri A(-). Stochastic path integral formalism for continuous quantum
measurement. [Internet] [Doctoral dissertation]. University of Rochester; 2016. [cited 2021 Mar 08].
Available from: http://hdl.handle.net/1802/31479.
Council of Science Editors:
Chantasri A(-). Stochastic path integral formalism for continuous quantum
measurement. [Doctoral Dissertation]. University of Rochester; 2016. Available from: http://hdl.handle.net/1802/31479
University of Iowa
8.
Nathanson, Ekaterina Sergeyevna.
Path integration with non-positive distributions and applications to the Schrödinger equation.
Degree: PhD, Mathematics, 2014, University of Iowa
URL: https://ir.uiowa.edu/etd/1370
► In 1948, Richard Feynman published the first paper on his new approach to non-relativistic quantum mechanics. Before Feynman's work there were two mathematical formulations…
(more)
▼ In 1948, Richard Feynman published the first paper on his new approach to non-relativistic quantum mechanics. Before Feynman's work there were two mathematical formulations of quantum mechanics. Schrödinger's formulation was based on PDE (the Schrödinger equation) and states representation by wave functions, so it was in the framework of analysis and differential equations. The other formulation was Heisenberg's matrix algebra. Initially, they were thought to be competing. The proponents of one claimed that the other was “ wrong. ” Within a couple of years, John von Neumann had proved that they are equivalent. Although Feynman's theory was not fundamentally new, it nonetheless offered an entirely fresh and different perspective: via a precise formulation of Bohr's correspondence principle, it made quantum mechanics similar to classical mechanics in a precise sense. In addition, Feynman's approach made it possible to explain physical experiments, and, via diagrams, link them directly to computations. What resulted was a very powerful device for computing energies and scattering amplitudes - the famous Feynman's diagrams. In his formulation, Feynman aimed at representing the solution to the non-relativistic Schrödinger equation in the form of an “ average ” over histories or paths of a particle. This solution is commonly known as the Feynman
path integral. It plays an important role in the theory but appears as a postulate based on intuition coming from physics rather than a justified mathematical object. This is why Feynman's vision has caught the attention of many mathematicians as well as physicists. The papers of Gelfand, Cameron, and Nelson are among the first, and more substantial, attempts to supply Feynman's theory with a rigorous mathematical foundation. These attempts were followed by many others, but unfortunately all of them were not quite satisfactory. The difficulty comes from a need to define a measure on an infinite-dimensional space of continuous functions that represent all possible paths of a particle. This Feynman's measure has to produce an
integral with the properties requested by Feynman. In particular, the expression for the Feynman measure has to involve the non-absolutely integrable Fresnel integrands. The non-absolute integrability of the Fresnel integrands makes the measure fail to be positive and to have the countably additive property. Thus, a well-defined measure in the case of the Feynman
path integral does not exist. Extensive research has been done on the methods of relating the Feynman
path integral to the
integral with respect to the Wiener measure. The method of analytic continuation in mass defines the Feynman
path integral as a certain limit of the Wiener integrals. Unfortunately, this method can be used as definition for only almost all values of the mass parameter in the Schrödinger equation. For physicists, this is not a satisfactory result and needs to be improved. In this work we examine those questions which originally led to the…
Advisors/Committee Members: Jørgensen, Palle E. T., 1947- (supervisor).
Subjects/Keywords: Distributions on Path-Space; Feynman Path Integral; Feynman's measure; Functional Analysis; Henstock Integral; Stochastic Analysis; Mathematics
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APA (6th Edition):
Nathanson, E. S. (2014). Path integration with non-positive distributions and applications to the Schrödinger equation. (Doctoral Dissertation). University of Iowa. Retrieved from https://ir.uiowa.edu/etd/1370
Chicago Manual of Style (16th Edition):
Nathanson, Ekaterina Sergeyevna. “Path integration with non-positive distributions and applications to the Schrödinger equation.” 2014. Doctoral Dissertation, University of Iowa. Accessed March 08, 2021.
https://ir.uiowa.edu/etd/1370.
MLA Handbook (7th Edition):
Nathanson, Ekaterina Sergeyevna. “Path integration with non-positive distributions and applications to the Schrödinger equation.” 2014. Web. 08 Mar 2021.
Vancouver:
Nathanson ES. Path integration with non-positive distributions and applications to the Schrödinger equation. [Internet] [Doctoral dissertation]. University of Iowa; 2014. [cited 2021 Mar 08].
Available from: https://ir.uiowa.edu/etd/1370.
Council of Science Editors:
Nathanson ES. Path integration with non-positive distributions and applications to the Schrödinger equation. [Doctoral Dissertation]. University of Iowa; 2014. Available from: https://ir.uiowa.edu/etd/1370
Johannes Gutenberg Universität Mainz
9.
Poma, Adolfo.
Coarse-graining and quantum-classical adaptive coupling in soft matter.
Degree: 2011, Johannes Gutenberg Universität Mainz
URL: http://ubm.opus.hbz-nrw.de/volltexte/2011/2776/
► Die vorliegende Arbeit untersucht den Zusammenhang zwischen Skalen in Systemen weicher Materie, der für Multiskalen-Simulationen eine wichtige Rolle spielt. Zu diesem Zweck wurde eine Methode…
(more)
▼ Die vorliegende Arbeit untersucht den Zusammenhang zwischen Skalen in Systemen weicher Materie, der für Multiskalen-Simulationen eine wichtige Rolle spielt. Zu diesem Zweck wurde eine Methode entwickelt, die die Approximation der Separierbarkeit von Variablen für die Molekulardynamik und ähnliche Anwendungen bewertet. Der zweite und größere Teil dieser Arbeit beschäftigt sich mit der konzeptionellen und technischen Erweiterung des Adaptive Resolution Scheme'' (AdResS), einer Methode zur gleichzeitigen Simulation von Systemen mit mehreren Auflösungsebenen. Diese Methode wurde auf Systeme erweitert, in denen klassische und quantenmechanische Effekte eine Rolle spielen.rnrnDie oben genannte erste Methode benötigt nur die analytische Form der Potentiale, wie sie die meisten Molekulardynamik-Programme zur Verfügung stellen. Die Anwendung der Methode auf ein spezielles Problem gibt bei erfolgreichem Ausgang einen numerischen Hinweis auf die Gültigkeit der Variablenseparation. Bei nicht erfolgreichem Ausgang garantiert sie, dass keine Separation der Variablen möglich ist. Die Methode wird exemplarisch auf ein zweiatomiges Molekül auf einer Oberfläche und für die zweidimensionale Version des Rotational Isomer State (RIS) Modells einer Polymerkette angewandt.rnrnDer zweite Teil der Arbeit behandelt die Entwicklung eines Algorithmus zur adaptiven Simulation von Systemen, in denen Quanteneffekte berücksichtigt werden. Die Quantennatur von Atomen wird dabei in der Pfadintegral-Methode durch einen klassischen Polymerring repräsentiert. Die adaptive Pfadintegral-Methode wird zunächst für einatomige Flüssigkeiten und tetraedrische Moleküle unter normalen thermodynamischen Bedingungen getestet. Schließlich wird die Stabilität der Methode durch ihre Anwendung auf flüssigen para-Wasserstoff bei niedrigen Temperaturen geprüft.
This thesis investigates the connection between the length scales in soft matter systems, which is very important in the field of multiscale modeling. For this purpose a method was developed to evaluate the approximation of separation of variables in molecular dynamics and related fields. A second issue, and the main part of this thesis, concerns the conceptual and technical extension of the "Adaptive Resolution Scheme" (AdResS), a method that allows the simulation of a system with concurrent scales, to situations where quantum effects play a role.rnrnThe first method mentioned above requires only the analytical form of the potential as provided in most of the molecular dynamics programs. The outcome of the application to a particular problem gives, in the case of a positive assessment, a numerical indication about the validity of the separation of variables and in the negative case the evaluation guarantees strictly that no separation will be possible. This method is then applied to a diatomic molecule on a flat surface and the 2D version of the Rotational Isomer State (RIS) model of a polymer chain.rnrnThe second part of this thesis is about the development of an algorithm to perform an adaptive resolution…
Subjects/Keywords: Pfadintegral, Moleküldynamik, Statistische Mechanik; Path Integral, Molecular Dynamics, Statistical Mechanics; Physics
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APA (6th Edition):
Poma, A. (2011). Coarse-graining and quantum-classical adaptive coupling in soft matter. (Doctoral Dissertation). Johannes Gutenberg Universität Mainz. Retrieved from http://ubm.opus.hbz-nrw.de/volltexte/2011/2776/
Chicago Manual of Style (16th Edition):
Poma, Adolfo. “Coarse-graining and quantum-classical adaptive coupling in soft matter.” 2011. Doctoral Dissertation, Johannes Gutenberg Universität Mainz. Accessed March 08, 2021.
http://ubm.opus.hbz-nrw.de/volltexte/2011/2776/.
MLA Handbook (7th Edition):
Poma, Adolfo. “Coarse-graining and quantum-classical adaptive coupling in soft matter.” 2011. Web. 08 Mar 2021.
Vancouver:
Poma A. Coarse-graining and quantum-classical adaptive coupling in soft matter. [Internet] [Doctoral dissertation]. Johannes Gutenberg Universität Mainz; 2011. [cited 2021 Mar 08].
Available from: http://ubm.opus.hbz-nrw.de/volltexte/2011/2776/.
Council of Science Editors:
Poma A. Coarse-graining and quantum-classical adaptive coupling in soft matter. [Doctoral Dissertation]. Johannes Gutenberg Universität Mainz; 2011. Available from: http://ubm.opus.hbz-nrw.de/volltexte/2011/2776/
University of Waterloo
10.
Bishop, Kevin.
Quantum mechanical free energy calculations using path integral molecular dynamics.
Degree: 2019, University of Waterloo
URL: http://hdl.handle.net/10012/15349
► Free energy calculations are one of the most powerful tools within modern theoretical chemistry and are often used to make comparisons with experimental results. Existing…
(more)
▼ Free energy calculations are one of the most powerful tools within modern theoretical chemistry and are often used to make comparisons with experimental results. Existing free energy calculations are typically performed for classical molecular dynamics simulations but there are certain systems where nuclear quantum effects play an integral role. Specifically, systems with light atoms or low temperatures are the most influenced by such nuclear quantum effects and the development of Feynman path integrals [1] has been effective in accurately describing the quantum nature of these nuclei [2–8]. The primary objective of this thesis is the development of a pair of methodologies to calculate free energies utilizing path integral molecular dynamics to account for nuclear quantum effects.
Prior to the development of these free energy methodologies, this thesis presents a communication interface between the OpenMM and MMTK software packages that has been previously published [9]. This interface allows for users of MMTK to take advantage of the performance of OpenMM without major modifications to existing simulation scripts. Notably, the serial OpenMM integrator is shown to provide a 3x performance gain in comparison to a standard MMTK simulation while the GPU implementations of OpenMM provide over a 400x performance gain for larger systems with periodic boundary conditions.
The first path integral free energy methodology of this thesis combines the existing um- brella sampling technique [10,11] with path integral molecular dynamics. This methodology has been previously published and proposes that the umbrella sampling biasing potential only needs to be applied to a single path integral bead [12]. Furthermore, this proposed methodology is successfully benchmarked for a pair of Lennard-Jones dimer systems before being applied to the more difficult water dimer. The free energy profiles obtained from simulation are then used to calculate a free energy difference of -12.90 ± 0.05 kJ/mol for the MB-Pol potential in comparison to the experimental dissociation energy of -13.2 ± 0.12 kJ/mol [13].
The second path integral free energy methodology introduces a constraint within the path integral molecular dynamics simulations as opposed to an umbrella sampling restraint. Specifically, this methodology applies a constraint to an individual path integral bead in a manner that is similar to the concept of thermodynamic integration for classical simulations [14]. Formal estimators for the derivative of the free energy have been developed by Iouchtchenko et al. [15] and the results presented in this thesis analyze the effectiveness of these estimators for molecular dynamics simulations of Lennard-Jones and water dimers. Additionally, a new estimator is developed and the resulting free energy profiles are used to evaluate a free energy difference for the water dimer of -13.03 ± 0.14 kJ/mol, which is within the errors of the experimental dissociation energy [13].
Overall, this thesis provides a theoretical framework to study the…
Subjects/Keywords: free energy; path integral; molecular dynamics; nuclear quantum effects; statistical mechanics
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APA (6th Edition):
Bishop, K. (2019). Quantum mechanical free energy calculations using path integral molecular dynamics. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/15349
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Bishop, Kevin. “Quantum mechanical free energy calculations using path integral molecular dynamics.” 2019. Thesis, University of Waterloo. Accessed March 08, 2021.
http://hdl.handle.net/10012/15349.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Bishop, Kevin. “Quantum mechanical free energy calculations using path integral molecular dynamics.” 2019. Web. 08 Mar 2021.
Vancouver:
Bishop K. Quantum mechanical free energy calculations using path integral molecular dynamics. [Internet] [Thesis]. University of Waterloo; 2019. [cited 2021 Mar 08].
Available from: http://hdl.handle.net/10012/15349.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Bishop K. Quantum mechanical free energy calculations using path integral molecular dynamics. [Thesis]. University of Waterloo; 2019. Available from: http://hdl.handle.net/10012/15349
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Adelaide
11.
Walker, James Nicholas.
Inference methods for First Few Hundred Studies.
Degree: 2016, University of Adelaide
URL: http://hdl.handle.net/2440/99525
► Infectious diseases are a threat to the health of populations around the world. During the early stages of a novel infectious disease outbreak, intensive data…
(more)
▼ Infectious diseases are a threat to the health of populations around the world. During the early stages of a novel infectious disease outbreak, intensive data collection may be conducted on the first few hundred symptomatic individuals in what is referred to as a First Few Hundred (FF100) Study. This data is used to assess the potential impact of a pandemic in terms of its transmissibility and clinical severity; these are used to inform a response that is proportionate to the level of risk posed by the disease. Transmissibility is not only determined by the infectiousness of a disease; it is also determined by how individuals interact with one another in a population. Household epidemic models allow for interactions at a household level and interactions at a population level. Hence, they account for some of the inherent structure in a population. Furthermore, data in FF100 studies are collected from all individuals within an infectious individuals' household, hence these models are appropriate when considering FF100 Study data. This thesis develops new statistical methods, based upon continuous-time Markov chain epidemic models, to estimate the transmissibility of a disease in a population of households. In particular, we use Bayesian inference to estimate posterior distributions for the rate of infection between households. The large state space of household models means that conventional methods for calculating likelihoods for Markov chain models are infeasible for this problem and hence motivates the development of the new methods presented in this thesis. These are based on the assumption that between household infections only occur between an infectious household and a household of susceptible individuals. This is a reasonable assumption for the beginning of an outbreak in a large population and allows us to consider the dynamics of infection within households, following the import of infection, independently of each other. Under the assumption of no secondary introductions into households, the force of infection of newly infected households and hence the likelihood for the number of newly infected households over a day can be calculated as a convolution of the force of infection within each household. Two types of methods for evaluating the likelihood are developed: the first method calculates the expected force of infection; and, the second method calculates the distribution of the force of infection. The expectation method utilises matrix exponential methods on the small, household process. The distribution method utilises recursive methods to calculate the Laplace transform of the force of infection within households, and then numerically inverts the Laplace transform of the distribution corresponding to the product of individual households forces of infection. These methods are compared for accuracy - in terms of point estimates and posterior distributions - and numerical efficiency.
Advisors/Committee Members: Ross, Joshua (advisor), Black, Andrew (advisor), School of Mathematical Sciences (school).
Subjects/Keywords: Bayesian Inference methods; Markovian household epidemic model; path integral
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APA (6th Edition):
Walker, J. N. (2016). Inference methods for First Few Hundred Studies. (Thesis). University of Adelaide. Retrieved from http://hdl.handle.net/2440/99525
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Walker, James Nicholas. “Inference methods for First Few Hundred Studies.” 2016. Thesis, University of Adelaide. Accessed March 08, 2021.
http://hdl.handle.net/2440/99525.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Walker, James Nicholas. “Inference methods for First Few Hundred Studies.” 2016. Web. 08 Mar 2021.
Vancouver:
Walker JN. Inference methods for First Few Hundred Studies. [Internet] [Thesis]. University of Adelaide; 2016. [cited 2021 Mar 08].
Available from: http://hdl.handle.net/2440/99525.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Walker JN. Inference methods for First Few Hundred Studies. [Thesis]. University of Adelaide; 2016. Available from: http://hdl.handle.net/2440/99525
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of St. Andrews
12.
Bennett, Edmund.
Exotic order in magnetic systems from Majorana fermions
.
Degree: 2016, University of St. Andrews
URL: http://hdl.handle.net/10023/9437
► This thesis explores the theoretical representation of localised electrons in magnetic systems, using Majorana fermions. A motivation is provided for the Majorana fermion representation, which…
(more)
▼ This thesis explores the theoretical representation of localised electrons in magnetic systems, using Majorana fermions. A motivation is provided for the Majorana fermion representation, which is then developed and applied as a mean-field theory and in the
path-
integral formalism to the Ising model in transversal-field (TFIM) in one, two and three dimensions, on an orthonormal lattice. In one dimension the development of domain walls precludes long-range order in discrete systems; this is as free energy savings due to entropy outweigh the energetic cost of a domain wall. An argument due to Peierls exists in 2D which allows the formation of domains of ordered spins amidst a disordered background, however, which may be extended to 3D. The forms of the couplings to the bosons used in the Random Phase Analysis (RPA) are considered and an explanation for the non-existence of the phases calculated in this thesis is discussed, in terms of spare degrees of freedom in the Majorana representation. This thesis contains the first known application of Majorana fermions at the RPA level.
Advisors/Committee Members: Hooley, Chris (advisor).
Subjects/Keywords: Majorana;
Magnetism;
Quantum field theory;
Ising;
Path integral;
Random phase approximation
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APA (6th Edition):
Bennett, E. (2016). Exotic order in magnetic systems from Majorana fermions
. (Thesis). University of St. Andrews. Retrieved from http://hdl.handle.net/10023/9437
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Bennett, Edmund. “Exotic order in magnetic systems from Majorana fermions
.” 2016. Thesis, University of St. Andrews. Accessed March 08, 2021.
http://hdl.handle.net/10023/9437.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Bennett, Edmund. “Exotic order in magnetic systems from Majorana fermions
.” 2016. Web. 08 Mar 2021.
Vancouver:
Bennett E. Exotic order in magnetic systems from Majorana fermions
. [Internet] [Thesis]. University of St. Andrews; 2016. [cited 2021 Mar 08].
Available from: http://hdl.handle.net/10023/9437.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Bennett E. Exotic order in magnetic systems from Majorana fermions
. [Thesis]. University of St. Andrews; 2016. Available from: http://hdl.handle.net/10023/9437
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Waterloo
13.
Orr, Lindsay A.
Developments in the Centroid Phase Space Formulation of Quantum Statistical Mechanics.
Degree: 2016, University of Waterloo
URL: http://hdl.handle.net/10012/10221
► The centroid formalism provides a phase space representation of quantum statistical mechanics based on the Feynman path integral. Real time quantum correlation functions can be…
(more)
▼ The centroid formalism provides a phase space representation of quantum statistical mechanics based on the Feynman path integral. Real time quantum correlation functions can be exactly calculated using the centroid formalism, though this requires diagonalizing the system Hamiltonian which is intractable for large collections of molecules. A computational method for computing real time correlation functions called centroid molecular dynamics (CMD) has been formulated to circumvent this issue though the results are approximations. The centroid formalism had previously only been able to treat systems moving in Euclidean space. This is insufficient to capture rotational motion and intramolecular torsions, which may be viewed as motion in a constrained subspace of the Euclidean space. Herein we present a method for incorporating this type of motion into the centroid formalism and test the validity by examining the motion of a particle on a ring. Past work has also seen the centroid formalism extended to pairs of particles obeying Bose-Einstein and Fermi-Dirac statistics by way of a projection operator. In this work we examine the case where this projection operator projects onto an individual quantum state. This will allow the centroid formalism, and hence CMD, to be extended to microcanonical ensembles. Results are shown for the quantum harmonic oscillator, quartic well system and double well system.
Subjects/Keywords: quantum; statistical mechanics; path integral; rotation; centroid; state projection
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APA ·
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Export
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APA (6th Edition):
Orr, L. A. (2016). Developments in the Centroid Phase Space Formulation of Quantum Statistical Mechanics. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/10221
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Orr, Lindsay A. “Developments in the Centroid Phase Space Formulation of Quantum Statistical Mechanics.” 2016. Thesis, University of Waterloo. Accessed March 08, 2021.
http://hdl.handle.net/10012/10221.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Orr, Lindsay A. “Developments in the Centroid Phase Space Formulation of Quantum Statistical Mechanics.” 2016. Web. 08 Mar 2021.
Vancouver:
Orr LA. Developments in the Centroid Phase Space Formulation of Quantum Statistical Mechanics. [Internet] [Thesis]. University of Waterloo; 2016. [cited 2021 Mar 08].
Available from: http://hdl.handle.net/10012/10221.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Orr LA. Developments in the Centroid Phase Space Formulation of Quantum Statistical Mechanics. [Thesis]. University of Waterloo; 2016. Available from: http://hdl.handle.net/10012/10221
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Boston University
14.
Provazza, Justin.
Modeling nonadiabatic dynamical processes in molecular aggregates.
Degree: PhD, Chemistry, 2020, Boston University
URL: http://hdl.handle.net/2144/42021
► A fundamental understanding of ultrafast nonequilibrium dynamical processes in molecular aggregates is crucially important for the design of nanodevices that utilize quantum mechanical effects. However,…
(more)
▼ A fundamental understanding of ultrafast nonequilibrium dynamical processes in molecular aggregates is crucially important for the design of nanodevices that utilize quantum mechanical effects. However, understanding the coupled electron-phonon dynamics of such high-dimensional systems remains a challenging issue. As a result of the ever-growing computational power that is available, realistic parameterization of model Hamiltonians and implementation of sophisticated quantum dynamics algorithms have become indispensable tools for gaining insight into these processes.
The focus of this dissertation is the development and implementation of approximate
path integral-based methods to compute the time-evolution as well as linear and nonlinear spectroscopic signals of molecular aggregates following photo-excitation. The developments and applications presented here are geared toward gaining a better understanding of the role that electron-phonon coupling plays in framing ultrafast excitation energy transfer networks in photosynthetic light-harvesting complexes.
The ultrafast excitation energy transfer dynamics that occurs upon photo-excitation of a network of electronically coupled chromophores is remarkably sensitive to the strength of electronic coupling as well as the frequencies and coupling strengths that characterize electron-phonon interactions. Based on approximations to the diabatic representation of molecular Hamiltonians, energetic models of condensed phase molecular aggregates can be parameterized from a first principles description. Often times, computational parameterization of these models reveals comparable magnitudes for intermolecular electronic couplings and electron-phonon couplings, negating the applicability of popular perturbative algorithms (such as those based on Forster or Redfield theory) for describing their time-evolution. Moreover, non-perturbative exact methods (e.g. stochastic Schrodinger equations and the Hierarchical Equations of Motion) are generally inefficient for all but a few specific limiting forms of electron-phonon coupling, or make assumptions about autocorrelation timescales of the vibrational environment. Because of the failure of the energetic parameters determined through recent ab initio studies of natural molecular aggregates to abide by the rather restrictive requirements for efficient application of the above-mentioned methods, the development of approximate non-perturbative algorithms for predicting nonequilibrium dynamical properties of such systems is a central theme in this dissertation.
Following a general introductory section describing the basic concepts that are fundamental to the remainder of the thesis, the derivation of
path integral dynamics methods is presented. These include a cartesian phase space
path integral derivation of the truncated Wigner approximation as applied to the Meyer-Miller-Stock-Thoss mapping model for describing vibronic systems as well as a novel derivation of the Partially Linearized Density Matrix algorithm, highlighting its emergence…
Advisors/Committee Members: Coker, David F. (advisor).
Subjects/Keywords: Computational chemistry; Algorithm; Density matrix; Path integral; Quantum dynamics; Spectroscopy
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APA ·
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APA (6th Edition):
Provazza, J. (2020). Modeling nonadiabatic dynamical processes in molecular aggregates. (Doctoral Dissertation). Boston University. Retrieved from http://hdl.handle.net/2144/42021
Chicago Manual of Style (16th Edition):
Provazza, Justin. “Modeling nonadiabatic dynamical processes in molecular aggregates.” 2020. Doctoral Dissertation, Boston University. Accessed March 08, 2021.
http://hdl.handle.net/2144/42021.
MLA Handbook (7th Edition):
Provazza, Justin. “Modeling nonadiabatic dynamical processes in molecular aggregates.” 2020. Web. 08 Mar 2021.
Vancouver:
Provazza J. Modeling nonadiabatic dynamical processes in molecular aggregates. [Internet] [Doctoral dissertation]. Boston University; 2020. [cited 2021 Mar 08].
Available from: http://hdl.handle.net/2144/42021.
Council of Science Editors:
Provazza J. Modeling nonadiabatic dynamical processes in molecular aggregates. [Doctoral Dissertation]. Boston University; 2020. Available from: http://hdl.handle.net/2144/42021
University of Waterloo
15.
Lou, Xichen.
Hybrid Path Integral Monte Carlo/Molecular Dynamics Approach for the Simulation of Rigid Rotating and Translating Molecules.
Degree: 2020, University of Waterloo
URL: http://hdl.handle.net/10012/15546
► The path integral formulation of quantum statistical mechanics [1] is widely used for formulating the partition function and diverse thermodynamic properties. The basic objective of…
(more)
▼ The path integral formulation of quantum statistical mechanics [1] is widely used for formulating the partition function and diverse thermodynamic properties. The basic objective of this thesis is to present the benchmark calculations and develop new methods to study the quantum rotating and translating system.
Prior to the development of a new method, we perform benchmark calculations on newly implemented Path Integral Monte Carlo code in the Molecular Modelling Toolkit software package [2] against exact diagonalization calculation on Hydrogen Fluoride in an electric field. An energy convergence study proved the validity of the new integrated Path Integral Monte Carlo code within statistical error. Then, we benchmark our PIMC code against the direct Classical Monte Carlo (dCMC) calculations to study the interacting quantum rotors at finite temperature. Then, the application of the direct Classical Monte Carlo code for a 1D water chain system at different temperature and various lattice spacing is performed. Two phase transitions and three specific phase regions have been observed from the calculations.
Then, we combine our well-established Path Integral Molecular Dynamics code [3, 4] with the Path Integral Monte Carlo code to develop a novel hybrid Path Integral Molecular Dynamics/Path Integral Monte Carlo program for quantum system simulation including rotation and translation. This proposed methodology is successfully benchmarked for CO 2 He system at a large tau region.
The second Path Integral Monte Carlo methodology introduces a cluster-update algorithm applying on quantum rotational system. This methodology has been previously applied to lattice spin system [5, 6] and hard sphere continuum system [7]. This is the first time to discuss and develop a cluster-update method on quantum rotors. A primary cluster-update Path Integral Monte Carlo algorithm and related test is presented. The preliminary results for the test of Hydrogen Fluoride molecules with dipole-dipole interaction shows an existing problem within our code, and the problem is fully discussed in this thesis for future study.
Overall, this thesis focuses on the development of new methodologies to study quantum molecules. Noted that all methodologies require more tests and benchmark calculations to prove its validity. In spite of that, this discussion of a novel methodology and application will lead to an exciting further study.
Subjects/Keywords: Path Integral Monte Carlo, Path Integral Molecular Dynamics, molecular simulation, quantum rotors; cluster-update algorithm; Quantum statistics; Monte Carlo method; Path integrals
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APA ·
Chicago ·
MLA ·
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CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Lou, X. (2020). Hybrid Path Integral Monte Carlo/Molecular Dynamics Approach for the Simulation of Rigid Rotating and Translating Molecules. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/15546
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Lou, Xichen. “Hybrid Path Integral Monte Carlo/Molecular Dynamics Approach for the Simulation of Rigid Rotating and Translating Molecules.” 2020. Thesis, University of Waterloo. Accessed March 08, 2021.
http://hdl.handle.net/10012/15546.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Lou, Xichen. “Hybrid Path Integral Monte Carlo/Molecular Dynamics Approach for the Simulation of Rigid Rotating and Translating Molecules.” 2020. Web. 08 Mar 2021.
Vancouver:
Lou X. Hybrid Path Integral Monte Carlo/Molecular Dynamics Approach for the Simulation of Rigid Rotating and Translating Molecules. [Internet] [Thesis]. University of Waterloo; 2020. [cited 2021 Mar 08].
Available from: http://hdl.handle.net/10012/15546.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Lou X. Hybrid Path Integral Monte Carlo/Molecular Dynamics Approach for the Simulation of Rigid Rotating and Translating Molecules. [Thesis]. University of Waterloo; 2020. Available from: http://hdl.handle.net/10012/15546
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Clemson University
16.
Dickson, Bradley.
PATH INTEGRAL FORMULATION OF LANGEINV DYNAMICS WITH APPLICATIONS TO RARE-EVENT SYSTEMS.
Degree: PhD, Chemistry, 2006, Clemson University
URL: https://tigerprints.clemson.edu/all_dissertations/24
► In the last decade great efforts have been made to efficiently study the behaviors of rare-event systems. The methods and theories developed in pursuit of…
(more)
▼ In the last decade great efforts have been made to efficiently study the behaviors of rare-event systems. The methods and theories developed in pursuit of this goal are far from unified and are instead applied on a case-by-case basis where one makes a best educated guess as to which approach may afford the greatest chance of studying the rare-event system in question. The work contained here is directed at further development of one of these sets of methods and theories. Specifically, a new theory of dynamics in the Langevin
path space is developed with emphasis on generating and sampling Langevin trajectories that exhibit rare transitions. The quest to formulate
path dynamics or
path sampling is not new. Rather, this work offers a new formulation of an old idea while keeping in mind two key issues: first, whatever theory and methods are developed they should be accessible to those simply seeking methods and easy to implement, since the goal is application to complex, large dimensional systems. Second, the rigorous limits of the problem should never be overlooked and one`s intuition should always be held in check by these limits of rigor. Past formulations of techniques that employ a Langevin measure to either uncover very probable paths or to define
path-wise dynamics tend to rely too heavily on intuition, allowing one to unknowingly overstep the rigorous limit of what can be done or said. With this in mind, a new Langevin
path probability is derived once it is established that the more common representation can only be written without justification. The new Langevin measure is then used to demonstrate consequences related to applications that are not limited to a special function space; the space of functions that solve the given dynamical equation. This is simply a demonstration of uniqueness for Langevin`s equation. Because working in the configuration or phase space is a familiar thing,
path sampling and
path dynamics are usually formulated on one of those spaces. Since the first part of this work revolves around the idea that the domain of Langevin trajectories is in neither of those spaces, an alternate formulation of dynamics in the Langevin
path space is given. In this formulation the intuition developed by the regular dynamics in phase space is pushed aside for a different perspective. This forces the domain of the
path dynamics to stay on the random force space, the independant variable of the Langevin trajectory. Once the
path dynamics are formulated the scheme is demonstrated on a test potential and then used to close a fullerene at low temperature. This work is unique amoung the literature in that it avoids forcing physical intuition from one problem on the study of another. In the end, the tools developed here are easy to understand and straightforward to implement. A number of the difficulties of the usual
path sampling formulations are even avoided. For instance, one is not required to have access to a reactive trajectory…
Advisors/Committee Members: Stuart, Steven J.
Subjects/Keywords: path integral; Langevin equation; path sampling; Physical Chemistry
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APA (6th Edition):
Dickson, B. (2006). PATH INTEGRAL FORMULATION OF LANGEINV DYNAMICS WITH APPLICATIONS TO RARE-EVENT SYSTEMS. (Doctoral Dissertation). Clemson University. Retrieved from https://tigerprints.clemson.edu/all_dissertations/24
Chicago Manual of Style (16th Edition):
Dickson, Bradley. “PATH INTEGRAL FORMULATION OF LANGEINV DYNAMICS WITH APPLICATIONS TO RARE-EVENT SYSTEMS.” 2006. Doctoral Dissertation, Clemson University. Accessed March 08, 2021.
https://tigerprints.clemson.edu/all_dissertations/24.
MLA Handbook (7th Edition):
Dickson, Bradley. “PATH INTEGRAL FORMULATION OF LANGEINV DYNAMICS WITH APPLICATIONS TO RARE-EVENT SYSTEMS.” 2006. Web. 08 Mar 2021.
Vancouver:
Dickson B. PATH INTEGRAL FORMULATION OF LANGEINV DYNAMICS WITH APPLICATIONS TO RARE-EVENT SYSTEMS. [Internet] [Doctoral dissertation]. Clemson University; 2006. [cited 2021 Mar 08].
Available from: https://tigerprints.clemson.edu/all_dissertations/24.
Council of Science Editors:
Dickson B. PATH INTEGRAL FORMULATION OF LANGEINV DYNAMICS WITH APPLICATIONS TO RARE-EVENT SYSTEMS. [Doctoral Dissertation]. Clemson University; 2006. Available from: https://tigerprints.clemson.edu/all_dissertations/24
Kyoto University / 京都大学
17.
Ito, Yu.
Rough path theory via fractional calculus : 非整数階微積分によるラフパス理論.
Degree: 博士(情報学), 2015, Kyoto University / 京都大学
URL: http://hdl.handle.net/2433/199445
;
http://dx.doi.org/10.14989/doctor.k19121
Subjects/Keywords: Stieltjes integral; Integral equation; Differential equation; Fractional derivative; Rough path; Controlled path
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APA ·
Chicago ·
MLA ·
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APA (6th Edition):
Ito, Y. (2015). Rough path theory via fractional calculus : 非整数階微積分によるラフパス理論. (Thesis). Kyoto University / 京都大学. Retrieved from http://hdl.handle.net/2433/199445 ; http://dx.doi.org/10.14989/doctor.k19121
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Ito, Yu. “Rough path theory via fractional calculus : 非整数階微積分によるラフパス理論.” 2015. Thesis, Kyoto University / 京都大学. Accessed March 08, 2021.
http://hdl.handle.net/2433/199445 ; http://dx.doi.org/10.14989/doctor.k19121.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Ito, Yu. “Rough path theory via fractional calculus : 非整数階微積分によるラフパス理論.” 2015. Web. 08 Mar 2021.
Vancouver:
Ito Y. Rough path theory via fractional calculus : 非整数階微積分によるラフパス理論. [Internet] [Thesis]. Kyoto University / 京都大学; 2015. [cited 2021 Mar 08].
Available from: http://hdl.handle.net/2433/199445 ; http://dx.doi.org/10.14989/doctor.k19121.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Ito Y. Rough path theory via fractional calculus : 非整数階微積分によるラフパス理論. [Thesis]. Kyoto University / 京都大学; 2015. Available from: http://hdl.handle.net/2433/199445 ; http://dx.doi.org/10.14989/doctor.k19121
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
18.
Ito, Yu.
Rough path theory via fractional calculus
.
Degree: 2015, Kyoto University
URL: http://hdl.handle.net/2433/199445
Subjects/Keywords: Stieltjes integral;
Integral equation;
Differential equation;
Fractional derivative;
Rough path;
Controlled path
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Ito, Y. (2015). Rough path theory via fractional calculus
. (Thesis). Kyoto University. Retrieved from http://hdl.handle.net/2433/199445
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Ito, Yu. “Rough path theory via fractional calculus
.” 2015. Thesis, Kyoto University. Accessed March 08, 2021.
http://hdl.handle.net/2433/199445.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Ito, Yu. “Rough path theory via fractional calculus
.” 2015. Web. 08 Mar 2021.
Vancouver:
Ito Y. Rough path theory via fractional calculus
. [Internet] [Thesis]. Kyoto University; 2015. [cited 2021 Mar 08].
Available from: http://hdl.handle.net/2433/199445.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Ito Y. Rough path theory via fractional calculus
. [Thesis]. Kyoto University; 2015. Available from: http://hdl.handle.net/2433/199445
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of California – Berkeley
19.
Stuck, David.
The Importance of Zeroth-Order Approximations in Molecular Quantum Mechanics.
Degree: Chemistry, 2015, University of California – Berkeley
URL: http://www.escholarship.org/uc/item/82w6491p
► The work herein is concerned with developing computational models to understand molecules. The underlying theme of this research is the reassessment of zeroth-order approximations for…
(more)
▼ The work herein is concerned with developing computational models to understand molecules. The underlying theme of this research is the reassessment of zeroth-order approximations for higher-level methods. For second-order Moller-Plesset theory (MP2), qualitative failures of the Hartree-Fock orbitals in the form of spin contamination can lead to catastrophic errors in the second order energies. By working with orbitals optimized in the presence of correlations, orbital-optimized MP2 can fix the spin contamination problem that plague radicals, aromatics, and transition metal complexes. In path integral Monte Carlo for vibrational energies, the zeroth-order propagator is typically chosen to be the most general possible, the free particle propagator; we chose to be informed by the molecular structure we have already attained and apply a propagator based on the harmonic modes of the molecule, improving sampling efficiency and our Trotter approximation.
Subjects/Keywords: Chemistry; Theoretical physics; Electron Correlation; Orbital Optimization; Path Integral Monte Carlo; Spin Contamination; Vibrational Anharmonicity
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APA (6th Edition):
Stuck, D. (2015). The Importance of Zeroth-Order Approximations in Molecular Quantum Mechanics. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/82w6491p
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Stuck, David. “The Importance of Zeroth-Order Approximations in Molecular Quantum Mechanics.” 2015. Thesis, University of California – Berkeley. Accessed March 08, 2021.
http://www.escholarship.org/uc/item/82w6491p.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Stuck, David. “The Importance of Zeroth-Order Approximations in Molecular Quantum Mechanics.” 2015. Web. 08 Mar 2021.
Vancouver:
Stuck D. The Importance of Zeroth-Order Approximations in Molecular Quantum Mechanics. [Internet] [Thesis]. University of California – Berkeley; 2015. [cited 2021 Mar 08].
Available from: http://www.escholarship.org/uc/item/82w6491p.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Stuck D. The Importance of Zeroth-Order Approximations in Molecular Quantum Mechanics. [Thesis]. University of California – Berkeley; 2015. Available from: http://www.escholarship.org/uc/item/82w6491p
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Waterloo
20.
Faruk, Nabil.
Quantum effects in molecular systems.
Degree: 2014, University of Waterloo
URL: http://hdl.handle.net/10012/8645
► This thesis presents two different approaches and applications where nuclear dynamics are treated quantum mechanically in order to obtain more accurate theoretical predictions of molecular…
(more)
▼ This thesis presents two different approaches and applications where nuclear dynamics are treated quantum mechanically in order to obtain more accurate theoretical predictions of molecular properties. In our first application, we report a first-principles prediction of the Raman shifts of parahydrogen (pH2) clusters of sizes N=4-19 and 33, based on path integral ground-state simulations with an ab initio potential energy surface. The Raman shifts are calculated, using perturbation theory, as the average of the difference-potential energy surface between the potential energy surfaces for vibrationally-excited and ground-state parahydrogen monomers. The radial distribution of the clusters is used as a weight function in this average. Very good overall agreement with experiment [1] is achieved for p(H2)2-8,13,33. A number of different pair potentials are employed for the calculation of the radial distribution functions. We find that the Raman shifts are sensitive to slight variations in the radial distribution functions. In our second application, we discuss the development of Path Integral Molecular Dynamics (PIMD) methodology, which our group has previously incorporated into the Molecular Modeling Toolkit (MMTK) [2] to account for nuclear quantum effects. This thesis is to provide a proof-of-concept for our software tools and PIMD method through the gas phase investigation of methyl beta-D-arabinofuranoside, which is a sugar residue in the cell wall of tuberculosis bacteria and is thought to provide bacterial resistance to drugs. We observe the effect of nuclear quantum sampling on the sugar's dihedral angle distributions at different temperatures, which we then relate to nuclear magnetic resonance proton-proton coupling constants via Karplus equations. We also determine the sugar's energy convergence with path integral sampling and the energy behaviour with temperature. We find that quantum effects are non-negligible even at biological temperatures, although some challenges remain in converging our coupling constant predictions. Finally, we discuss and benchmark our extension with the Open Molecular Mechanics (OpenMM) program [3] to enable graphics processing unit-accelerated solution phase simulations for future work.
Subjects/Keywords: Quantum mechanics; Molecular dynamics; Carbohydrate; Basis set; Path integral; Parahydrogen; Raman spectra
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Manager
APA (6th Edition):
Faruk, N. (2014). Quantum effects in molecular systems. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/8645
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Faruk, Nabil. “Quantum effects in molecular systems.” 2014. Thesis, University of Waterloo. Accessed March 08, 2021.
http://hdl.handle.net/10012/8645.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Faruk, Nabil. “Quantum effects in molecular systems.” 2014. Web. 08 Mar 2021.
Vancouver:
Faruk N. Quantum effects in molecular systems. [Internet] [Thesis]. University of Waterloo; 2014. [cited 2021 Mar 08].
Available from: http://hdl.handle.net/10012/8645.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Faruk N. Quantum effects in molecular systems. [Thesis]. University of Waterloo; 2014. Available from: http://hdl.handle.net/10012/8645
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Freie Universität Berlin
21.
Agarwal, Animesh.
Pfadintegral-Molekulardynamikmethoden in der Simulation offener Systeme.
Degree: 2016, Freie Universität Berlin
URL: http://dx.doi.org/10.17169/refubium-6354
► Mit der von Richard Feynman entwickelte Pfadintegral (PI)-Formulierung können Kern-Quanteneffekte, die durch die Delokalisierung leichter Atomkerne auftreten, mit den Methoden der Molekulardynamik (MD) behandelt werden.…
(more)
▼ Mit der von Richard Feynman entwickelte Pfadintegral (PI)-Formulierung
können Kern-Quanteneffekte, die durch die Delokalisierung leichter
Atomkerne auftreten, mit den Methoden der Molekulardynamik (MD) behandelt
werden. Allerdings ist PIMD aufgrund des hohen Rechenaufwands auf kleine
Systeme und kurze Zeitskalen beschränkt. In dieser Dissertation wird eine
Erweiterung der kürzlich entwickelten ``Grand Canonical AdResS''-Methode
(GC-AdResS) durch verschiedene PIMD-Algorithmen behandelt. Hierbei wird der
PI-Formalismus auf eine relativ kleine Region angewandt, die in eine grosses
Reservoir eingebettet ist, in dem die gleichen Moleküle in einem ``coarse-
grained''-Model behandelt werden. Um die strukturellen und dynamischen
Eigenschaften in dem Quantengleichgewicht zu berechnen, müssen zunächst
diese Eigenschaften für offener Systeme definiert werden. Hierzu zeigen
wir die Genauigkeit der GC-AdResS in Verbindung mit klassischen MD, indem wir
das chemische Überschusspotential berechnen. Wir zeigen die Entsprechung
zwischen dem Bergmann-Lebowitz (BL) Modell für offener Systeme und GC-
AdResS, und verwenden die Prinzipien des BL-Modells, um die Gleichgewichts-
Zeitkorrelationfunktionen für offener Systeme zu definieren. Diese
berechnen wir für flüssiges Wasserd und zu zeigen, dass GC-AdresS die
gleichen Ergebnisse wie MD bei vollständig atomistischer Auflösung
ergibt. In der Pfadintegral-Formulierung wird jedes Atom als Ring von
``fiktiven'' klassischen Partikeln repräsentiert. Somit können wir die
zuvor entwickelten theoretischen Konzepte anwenden, um die
Quanteneigenschaften von Wasser zu untersuchen. Hierzu kombinieren wir GC-
AdResS mit drei verschiedene PI-Methoden: PIMD, ``Ring-polymer'' MD (RPMD) und
``Centroid''-MD (CMD). Wir zeigen, dass die Ergebnisse aller drei Methoden mit
denen einer reinen PI-Simulation konsistent sind.
Advisors/Committee Members: [email protected] (contact), m (gender), Prof. Christof Schuette (firstReferee), Prof. Carsten Hartmann (furtherReferee).
Subjects/Keywords: Multiscale Simulations; Open Boundary Systems; Path Integral Molecular Dynamics; 500 Naturwissenschaften und Mathematik::530 Physik
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APA (6th Edition):
Agarwal, A. (2016). Pfadintegral-Molekulardynamikmethoden in der Simulation offener Systeme. (Thesis). Freie Universität Berlin. Retrieved from http://dx.doi.org/10.17169/refubium-6354
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Agarwal, Animesh. “Pfadintegral-Molekulardynamikmethoden in der Simulation offener Systeme.” 2016. Thesis, Freie Universität Berlin. Accessed March 08, 2021.
http://dx.doi.org/10.17169/refubium-6354.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Agarwal, Animesh. “Pfadintegral-Molekulardynamikmethoden in der Simulation offener Systeme.” 2016. Web. 08 Mar 2021.
Vancouver:
Agarwal A. Pfadintegral-Molekulardynamikmethoden in der Simulation offener Systeme. [Internet] [Thesis]. Freie Universität Berlin; 2016. [cited 2021 Mar 08].
Available from: http://dx.doi.org/10.17169/refubium-6354.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Agarwal A. Pfadintegral-Molekulardynamikmethoden in der Simulation offener Systeme. [Thesis]. Freie Universität Berlin; 2016. Available from: http://dx.doi.org/10.17169/refubium-6354
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Oxford
22.
More, Joshua N.
Algorithms and computer code for ab initio path integral molecular dynamics simulations.
Degree: PhD, 2015, University of Oxford
URL: https://ora.ox.ac.uk/objects/uuid:b8ca7471-21e3-4240-95b1-8775e5d6c08f
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.712047
► This thesis presents i-PI, a new path integral molecular dynamics code designed to capture nuclear quantum effects in ab initio electronic structure calculations of condensed…
(more)
▼ This thesis presents i-PI, a new path integral molecular dynamics code designed to capture nuclear quantum effects in ab initio electronic structure calculations of condensed phase systems. This software has an implementation of estimators used to calculate a wide range of static and dynamical properties and of state-of-the-art techniques used to increase the computational efficiency of path integral simulations. i-PI has been designed in a highly modular fashion, to ensure that it is as simple as possible to develop and implement new algorithms to keep up with the research frontier, and so that users can take maximum advantage of the numerous electronic structure programs which are freely available without needing to rewrite large amounts of code. Among the functionality of the i-PI code is a novel integrator for constant pressure dynamics, which is used to investigate the properties of liquid water at 750 K and 10 GPa, and efficient estimators for the calculation of single particle momentum distri- butions, which are used to study the properties of solid and liquid ammonia. These show respectively that i-PI can be used to make predictions about systems which are both difficult to study experimentally and highly non-classical in nature, and that it can illustrate the relative advantages and disadvantages of different theoretical methods and their ability to reproduce experimental data.
Subjects/Keywords: 530.12; ab initio path integral molecular dynamics; density functional theory; PIMD; Constant pressure simulations; AIPIMD
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to Zotero / EndNote / Reference
Manager
APA (6th Edition):
More, J. N. (2015). Algorithms and computer code for ab initio path integral molecular dynamics simulations. (Doctoral Dissertation). University of Oxford. Retrieved from https://ora.ox.ac.uk/objects/uuid:b8ca7471-21e3-4240-95b1-8775e5d6c08f ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.712047
Chicago Manual of Style (16th Edition):
More, Joshua N. “Algorithms and computer code for ab initio path integral molecular dynamics simulations.” 2015. Doctoral Dissertation, University of Oxford. Accessed March 08, 2021.
https://ora.ox.ac.uk/objects/uuid:b8ca7471-21e3-4240-95b1-8775e5d6c08f ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.712047.
MLA Handbook (7th Edition):
More, Joshua N. “Algorithms and computer code for ab initio path integral molecular dynamics simulations.” 2015. Web. 08 Mar 2021.
Vancouver:
More JN. Algorithms and computer code for ab initio path integral molecular dynamics simulations. [Internet] [Doctoral dissertation]. University of Oxford; 2015. [cited 2021 Mar 08].
Available from: https://ora.ox.ac.uk/objects/uuid:b8ca7471-21e3-4240-95b1-8775e5d6c08f ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.712047.
Council of Science Editors:
More JN. Algorithms and computer code for ab initio path integral molecular dynamics simulations. [Doctoral Dissertation]. University of Oxford; 2015. Available from: https://ora.ox.ac.uk/objects/uuid:b8ca7471-21e3-4240-95b1-8775e5d6c08f ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.712047
Karlstad University
23.
Svensson, Anders.
Path Integral for the Hydrogen Atom : Solutions in two and three dimensions.
Degree: Engineering and Physics, 2016, Karlstad University
URL: http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-44425
► The path integral formulation of quantum mechanics generalizes the action principle of classical mechanics. The Feynman path integral is, roughly speaking, a sum over…
(more)
▼ The path integral formulation of quantum mechanics generalizes the action principle of classical mechanics. The Feynman path integral is, roughly speaking, a sum over all possible paths that a particle can take between fixed endpoints, where each path contributes to the sum by a phase factor involving the action for the path. The resulting sum gives the probability amplitude of propagation between the two endpoints, a quantity called the propagator. Solutions of the Feynman path integral formula exist, however, only for a small number of simple systems, and modifications need to be made when dealing with more complicated systems involving singular potentials, including the Coulomb potential. We derive a generalized path integral formula, that can be used in these cases, for a quantity called the pseudo-propagator from which we obtain the fixed-energy amplitude, related to the propagator by a Fourier transform. The new path integral formula is then successfully solved for the Hydrogen atom in two and three dimensions, and we obtain integral representations for the fixed-energy amplitude.
Vägintegral-formuleringen av kvantmekanik generaliserar minsta-verkanprincipen från klassisk mekanik. Feynmans vägintegral kan ses som en summa över alla möjliga vägar en partikel kan ta mellan två givna ändpunkter A och B, där varje väg bidrar till summan med en fasfaktor innehållande den klassiska verkan för vägen. Den resulterande summan ger propagatorn, sannolikhetsamplituden att partikeln går från A till B. Feynmans vägintegral är dock bara lösbar för ett fåtal simpla system, och modifikationer behöver göras när det gäller mer komplexa system vars potentialer innehåller singulariteter, såsom Coulomb – potentialen. Vi härleder en generaliserad vägintegral-formel som kan användas i dessa fall, för en pseudo-propagator, från vilken vi erhåller fix-energi-amplituden som är relaterad till propagatorn via en Fourier-transform. Den nya vägintegral-formeln löses sedan med framgång för väteatomen i två och tre dimensioner, och vi erhåller integral-representationer för fix-energi-amplituden.
Subjects/Keywords: physics; quantum mechanics; path integral; feynman; hydrogen atom; propagator; fysik; kvantmekanik; vägintegral; feynman; väteatom; propagator
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Manager
APA (6th Edition):
Svensson, A. (2016). Path Integral for the Hydrogen Atom : Solutions in two and three dimensions. (Thesis). Karlstad University. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-44425
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Svensson, Anders. “Path Integral for the Hydrogen Atom : Solutions in two and three dimensions.” 2016. Thesis, Karlstad University. Accessed March 08, 2021.
http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-44425.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Svensson, Anders. “Path Integral for the Hydrogen Atom : Solutions in two and three dimensions.” 2016. Web. 08 Mar 2021.
Vancouver:
Svensson A. Path Integral for the Hydrogen Atom : Solutions in two and three dimensions. [Internet] [Thesis]. Karlstad University; 2016. [cited 2021 Mar 08].
Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-44425.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Svensson A. Path Integral for the Hydrogen Atom : Solutions in two and three dimensions. [Thesis]. Karlstad University; 2016. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-44425
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
24.
DU XIN.
Path integral modelling of interest rates, options and commodities.
Degree: 2015, National University of Singapore
URL: http://scholarbank.nus.edu.sg/handle/10635/119774
Subjects/Keywords: Path Integral; Options; commodities; quantum finance
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Manager
APA (6th Edition):
XIN, D. (2015). Path integral modelling of interest rates, options and commodities. (Thesis). National University of Singapore. Retrieved from http://scholarbank.nus.edu.sg/handle/10635/119774
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
XIN, DU. “Path integral modelling of interest rates, options and commodities.” 2015. Thesis, National University of Singapore. Accessed March 08, 2021.
http://scholarbank.nus.edu.sg/handle/10635/119774.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
XIN, DU. “Path integral modelling of interest rates, options and commodities.” 2015. Web. 08 Mar 2021.
Vancouver:
XIN D. Path integral modelling of interest rates, options and commodities. [Internet] [Thesis]. National University of Singapore; 2015. [cited 2021 Mar 08].
Available from: http://scholarbank.nus.edu.sg/handle/10635/119774.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
XIN D. Path integral modelling of interest rates, options and commodities. [Thesis]. National University of Singapore; 2015. Available from: http://scholarbank.nus.edu.sg/handle/10635/119774
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
25.
YU MIAO.
FUTURES AND SPOT COMMODITY PRICES, OPTIONS, AND FORWARD INTEREST RATES: MODEL AND EMPIRICAL ANALYSIS.
Degree: 2017, National University of Singapore
URL: http://scholarbank.nus.edu.sg/handle/10635/137746
Subjects/Keywords: Quantum; Finance; Model; Derivatives; Path Integral
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APA (6th Edition):
MIAO, Y. (2017). FUTURES AND SPOT COMMODITY PRICES, OPTIONS, AND FORWARD INTEREST RATES: MODEL AND EMPIRICAL ANALYSIS. (Thesis). National University of Singapore. Retrieved from http://scholarbank.nus.edu.sg/handle/10635/137746
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
MIAO, YU. “FUTURES AND SPOT COMMODITY PRICES, OPTIONS, AND FORWARD INTEREST RATES: MODEL AND EMPIRICAL ANALYSIS.” 2017. Thesis, National University of Singapore. Accessed March 08, 2021.
http://scholarbank.nus.edu.sg/handle/10635/137746.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
MIAO, YU. “FUTURES AND SPOT COMMODITY PRICES, OPTIONS, AND FORWARD INTEREST RATES: MODEL AND EMPIRICAL ANALYSIS.” 2017. Web. 08 Mar 2021.
Vancouver:
MIAO Y. FUTURES AND SPOT COMMODITY PRICES, OPTIONS, AND FORWARD INTEREST RATES: MODEL AND EMPIRICAL ANALYSIS. [Internet] [Thesis]. National University of Singapore; 2017. [cited 2021 Mar 08].
Available from: http://scholarbank.nus.edu.sg/handle/10635/137746.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
MIAO Y. FUTURES AND SPOT COMMODITY PRICES, OPTIONS, AND FORWARD INTEREST RATES: MODEL AND EMPIRICAL ANALYSIS. [Thesis]. National University of Singapore; 2017. Available from: http://scholarbank.nus.edu.sg/handle/10635/137746
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Toronto
26.
Simine, Yelena.
Theory of Charge Transport through Vibrating Molecules.
Degree: PhD, 2015, University of Toronto
URL: http://hdl.handle.net/1807/69498
► In this Thesis we study several aspects of charge transport through single molecule junctions. Focusing on the interaction of the electrons with vibrations we devise…
(more)
▼ In this Thesis we study several aspects of charge transport through single
molecule junctions. Focusing on the interaction of the electrons with vibrations
we devise toy-models which capture the consequences of many-body
interactions for transport properties of the junction.
We begin with the study of heating, cooling and stability of the
molecular bridge.
First, the dynamics of the vibrational mode is followed using the master equation.
Using this approximate technique, we identify the regimes in which the electronic current is pumping energy
into the vibrational mode, or alternatively, absorbing energy from it.
An important conclusion of this study is that at large currents, the pumping of energy into vibrations may result in uncontrolled heating,
making the structure unstable; Alternatively,
at small biases, extraction of energy from vibrations is possible, resulting
in a cooling behavior. We extend the model to include a dissipative environment,
such as the vibrating backbone of the molecule
or the solvent, and demonstrate that dissipation may alleviate structural instability.
From the comparison of the behavior of a strongly anharmonic mode (two-level system) with a fully harmonic mode
a surprising conclusion is reached: the cooling/heating analysis in both cases produces qualitatively similar results.
Finally, we confirm the microscopic equivalent of the Second Law, the charge and energy Fluctuation Theorem, at the level of second order markovian master equation.
In order to study exactly the vibration assisted
electron transport through a donor-acceptor junction we develop a numerical scheme
based on the influence functional
path integral (INFPI) and quasi-adiabatic
path integral (QUAPI)
methods. With this tool, the results obtained with the perturbative kinetic master equation are confirmed validating the
approximations used there. We further extend the model to include direct electronic tunneling.
Encouraged by the similarity of transport behavior in harmonic and strongly
anharmonic junctions, we compare
the non-equilibrium Anderson-Holstein model of electron interacting
with a harmonic mode to its variant, in which the infinite ladder of the harmonic mode is truncated.
In this case, interestingly, the two models show significant differences:
strong vibrational anharmonicity does not allow for the
Franck-Condon blockade or current hysteresis effects
found in the harmonic model. Instead, it introduces a novel many-body
off-resonance blockade. We conclude with the study of electronic
decoherence due to the interaction with vibrations.
To this end, we consider three cases of electronic transport
through a molecular junction:
fully coherent (rigid molecule), fully dephased and purely inelastic.
We demonstrate that the three cases produce characteristic
energy profiles and may be distinguished from one another via the measurement
of the thermopower.
Advisors/Committee Members: Segal, Dvira, Chemistry.
Subjects/Keywords: charge transport; dissipation; influence functional path integral method; quantum master equation; quantum physics; 0494
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APA (6th Edition):
Simine, Y. (2015). Theory of Charge Transport through Vibrating Molecules. (Doctoral Dissertation). University of Toronto. Retrieved from http://hdl.handle.net/1807/69498
Chicago Manual of Style (16th Edition):
Simine, Yelena. “Theory of Charge Transport through Vibrating Molecules.” 2015. Doctoral Dissertation, University of Toronto. Accessed March 08, 2021.
http://hdl.handle.net/1807/69498.
MLA Handbook (7th Edition):
Simine, Yelena. “Theory of Charge Transport through Vibrating Molecules.” 2015. Web. 08 Mar 2021.
Vancouver:
Simine Y. Theory of Charge Transport through Vibrating Molecules. [Internet] [Doctoral dissertation]. University of Toronto; 2015. [cited 2021 Mar 08].
Available from: http://hdl.handle.net/1807/69498.
Council of Science Editors:
Simine Y. Theory of Charge Transport through Vibrating Molecules. [Doctoral Dissertation]. University of Toronto; 2015. Available from: http://hdl.handle.net/1807/69498
Clemson University
27.
Kilgo, Paul Michael.
Radiative Transfer Using Path Integrals for Multiple Scattering in Participating Media.
Degree: PhD, School of Computing, 2016, Clemson University
URL: https://tigerprints.clemson.edu/all_dissertations/2301
► The theory of light transport forms the basis by which many computer graphic renderers are implemented. The more general theory of radiative transfer has…
(more)
▼ The theory of light transport forms the basis by which many computer graphic renderers are implemented. The more general theory of radiative transfer has applications in the wider scientific community, including ocean and atmospheric science, medicine, and even geophysics. Accurately capturing multiple scattering physics of light transport is an issue of great concern. Multiple scattering is responsible for indirect lighting, which is desired for images where high realism is the goal. Additionally, multiple scattering is quite important for scientific applications as it is a routine phenomenon. Computationally, it is a difficult process to model. Many have developed solutions for hard surface scenes where it is assumed that light travels in straight paths, for example, scenes without participating media. However, multiple scattering for participating media is still an open question, especially in developing robust and general techniques for particularly difficult scenes.
Radiative transfer can be expressed mathematically as a Feynman
path integral (FPI), and we give background on how the transport kernel of the volume rendering equation can be written in terms of a FPI. To move this model into a numerical setting, we need numerical methods to solve the model. We start by focusing on the spatial and angular integrals of the volume rendering equation, and show a way to generate seed paths without regard as to if they are cast from the emitter or the sensor. Seed paths are converted into a discretized form, and we use an existing numerical method to tackle the FPI. A modified version of this technique shows how to reduce the running time from a quadratic to a linear expression. We then perform experimental analysis of the
path integral calculation. The entire numerical method is put to full scale test on a distributed computing platform to calculate beam spread functions and compare the results to experimental data.
The dissertation is laid out as follows. In Chapter 1, we introduce the basic concepts of light propagation for computer graphics, multiple scattering, and volume rendering. Chapter 2 offers background on the
subject of FPIs and some mathematical techniques used in their numerical integration for this work. Chapter 3 is a survey of radiative transfer and multiple scattering as it is studied in computer graphics and elsewhere. Chapter 4 is a full description of the current methodology. In Section 4.1 we describe sensor and emitter geometries used for our experiments. We propose a new algorithm for creating seed paths to use in the numerical integration of the FPI in Section 4.2. Section 4.3 introduces past work in the numerical integration, formalizes it, and improves upon its running time. Section 4.4 presents some analysis of the
path weighting. In Chapters 5 and 6 we run experiments using the numerical methods. The first characterizes the calculation of the
path integral itself using arbitrary spatial parameters, and shows repeatability and unbiased calculation given enough samples. In the…
Advisors/Committee Members: Dr. Jerry Tessendorf, Committee Chair, Dr. Joshua Levine, Dr. Brian Dean, Dr. Amy Apon.
Subjects/Keywords: computer graphics; multiple scattering; participating media; path integral; radiative transfer; Computer Sciences
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APA (6th Edition):
Kilgo, P. M. (2016). Radiative Transfer Using Path Integrals for Multiple Scattering in Participating Media. (Doctoral Dissertation). Clemson University. Retrieved from https://tigerprints.clemson.edu/all_dissertations/2301
Chicago Manual of Style (16th Edition):
Kilgo, Paul Michael. “Radiative Transfer Using Path Integrals for Multiple Scattering in Participating Media.” 2016. Doctoral Dissertation, Clemson University. Accessed March 08, 2021.
https://tigerprints.clemson.edu/all_dissertations/2301.
MLA Handbook (7th Edition):
Kilgo, Paul Michael. “Radiative Transfer Using Path Integrals for Multiple Scattering in Participating Media.” 2016. Web. 08 Mar 2021.
Vancouver:
Kilgo PM. Radiative Transfer Using Path Integrals for Multiple Scattering in Participating Media. [Internet] [Doctoral dissertation]. Clemson University; 2016. [cited 2021 Mar 08].
Available from: https://tigerprints.clemson.edu/all_dissertations/2301.
Council of Science Editors:
Kilgo PM. Radiative Transfer Using Path Integrals for Multiple Scattering in Participating Media. [Doctoral Dissertation]. Clemson University; 2016. Available from: https://tigerprints.clemson.edu/all_dissertations/2301
University of Waterloo
28.
Yang, Jing.
A Feynman Path Centroid Effective Potential Approach for the Study of Low Temperature Parahydrogen Clusters and Droplets.
Degree: 2012, University of Waterloo
URL: http://hdl.handle.net/10012/6861
► The quantum simulation of large molecular systems is a formidable task. We explore the use of effective potentials based on the Feynman path centroid variable…
(more)
▼ The quantum simulation of large molecular systems is a formidable task. We explore the use of effective potentials based on the Feynman path centroid variable in order to simulate large quantum clusters at a reduced computational cost. This centroid can be viewed as the “most” classical variable of a quantum system. Earlier work has shown that one can use a pairwise centroid pseudo-potential to simulate the quantum dynamics of hydrogen in the bulk phase at 25 K and 14 K [Chem. Phys. Lett. 249, 231, (1996)]. Bulk hydrogen, however, freezes below 14 K, so we focus on hydrogen clusters and nanodroplets in the very low temperature regime in order to study their structural behaviours. The calculation of the effective centroid potential is addressed along with its use in the context of molecular dynamics simulations. The effective pseudo-potential of a cluster is temperature dependent and shares similar behaviour as that in the bulk phase. Centroid structural properties in three dimensional space are presented and compared to the results of reference path-integral Monte Carlo simulations. The centroid pseudo-potential approach yields a great reduction in computation cost. With large cluster sizes, the approximate pseudo-potential results are in agreement with the exact reference calculations. An approach to deconvolute centroid structural properties in order to obtain real space results for hydrogen clusters of a wide range of sizes is also presented. The extension of the approach to the treatment of confined hydrogen is discussed, and concluding remarks are presented.
Subjects/Keywords: Parahydrogen; Clusters; Pseudopotential; Centroid variables; Path integral; Feynman; Centroid Molecular Dynamics; Structural properties; Deconvolution
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APA (6th Edition):
Yang, J. (2012). A Feynman Path Centroid Effective Potential Approach for the Study of Low Temperature Parahydrogen Clusters and Droplets. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/6861
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Yang, Jing. “A Feynman Path Centroid Effective Potential Approach for the Study of Low Temperature Parahydrogen Clusters and Droplets.” 2012. Thesis, University of Waterloo. Accessed March 08, 2021.
http://hdl.handle.net/10012/6861.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Yang, Jing. “A Feynman Path Centroid Effective Potential Approach for the Study of Low Temperature Parahydrogen Clusters and Droplets.” 2012. Web. 08 Mar 2021.
Vancouver:
Yang J. A Feynman Path Centroid Effective Potential Approach for the Study of Low Temperature Parahydrogen Clusters and Droplets. [Internet] [Thesis]. University of Waterloo; 2012. [cited 2021 Mar 08].
Available from: http://hdl.handle.net/10012/6861.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Yang J. A Feynman Path Centroid Effective Potential Approach for the Study of Low Temperature Parahydrogen Clusters and Droplets. [Thesis]. University of Waterloo; 2012. Available from: http://hdl.handle.net/10012/6861
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
29.
Schmidt, Matthew D.G.
Path integral ground state approaches for the study of weakly bound clusters and confined molecules.
Degree: 2018, University of Waterloo
URL: http://hdl.handle.net/10012/13902
► This thesis presents the study of weakly bound clusters in the ground state (or the zero-temperature limit) using path integral molecular dynamics. Specifically, we look…
(more)
▼ This thesis presents the study of weakly bound clusters in the ground state (or the zero-temperature limit) using path integral molecular dynamics. Specifically, we look individually at the quantum properties of small clusters of hydrogen and water molecules and confined hydrogen within water cages, known as clathrate hydrates, which serves as a more practical application. Clathrate hydrates have been extensively studied as a clean storage container for molecular hydrogen and there have been discrepancies on the hydrogen occupancy number between various theoretical and experimental studies. It has been shown that the occupancy number is sensitive to the potential energy surfaces and models of the hydrogen and water systems. A preliminary study of hydrogen contained in clathrates is performed using a traditional hydrogen pair potential and water-hydrogen interaction potential. Hydrogen occupancy and structural distributions are compared to literature values. Small clusters of the individual molecules themselves are then focused on. The molecular hydrogen pair potentials are evaluated by calculating the Raman vibrational shift, a property that is very sensitive to the interaction potential, and comparing to experimental measurements. These shifts are calculated using first order perturbation theory based on pair distribution functions generated from Langevin equation path integral ground state (LePIGS) simulations for all bosonic isotopologues. It is determined that the shifts calculated using the Hinde pair potential give better agreement to experimental results than the traditional hydrogen potentials that we have been using in the past. The perturbation theory approach is then compared with two exact methods to calculate the shifts. For the application of hydrogen clusters, it is determined that perturbation theory is the best choice when balancing accuracy and precision. In the literature, there has been a discrepancy in the shape of the chemical potential at low temperature and in the ground state. We calculate the ground state chemical potential using LePIGS and find agreement with other PIGS results. We then extend our LePIGS code to simulate flexible molecules by investigating the water dimer. Ground state energies, dissociation energies, and structural properties are calculated using two empirically based interaction potentials and one ab initio potential, MB-pol, that includes polarizability and many-body effects which has been shown to reproduce experimental dissociation energies. We further demonstrate that imaginary time correlation functions generated from LePIGS can be used to calculate accurate vibrational transition energies. This work serves as a demonstration of the effectiveness of the LePIGS method towards calculating ground state properties of small clusters and provides useful information on the interaction potentials that should be used for systems containing hydrogen or water, specifically hydrogen contained in a flexible clathrate hydrate. An analytic form of the 1-D Hinde pair potential for…
Subjects/Keywords: path integral; molecular dynamics; water; hydrogen; Raman; ground state; quantum; potential energy surface
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APA (6th Edition):
Schmidt, M. D. G. (2018). Path integral ground state approaches for the study of weakly bound clusters and confined molecules. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/13902
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Schmidt, Matthew D G. “Path integral ground state approaches for the study of weakly bound clusters and confined molecules.” 2018. Thesis, University of Waterloo. Accessed March 08, 2021.
http://hdl.handle.net/10012/13902.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Schmidt, Matthew D G. “Path integral ground state approaches for the study of weakly bound clusters and confined molecules.” 2018. Web. 08 Mar 2021.
Vancouver:
Schmidt MDG. Path integral ground state approaches for the study of weakly bound clusters and confined molecules. [Internet] [Thesis]. University of Waterloo; 2018. [cited 2021 Mar 08].
Available from: http://hdl.handle.net/10012/13902.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Schmidt MDG. Path integral ground state approaches for the study of weakly bound clusters and confined molecules. [Thesis]. University of Waterloo; 2018. Available from: http://hdl.handle.net/10012/13902
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Indian Institute of Science
30.
Janakiraman, Deepika.
Path Integral Approach to Levy Flights and Hindered Rotations.
Degree: PhD, Faculty of Science, 2018, Indian Institute of Science
URL: http://etd.iisc.ac.in/handle/2005/3396
► Path integral approaches have been widely used for long in both quantum mechanics as well as statistical mechanics. In addition to being a tool for…
(more)
▼ Path integral approaches have been widely used for long in both quantum mechanics as well as statistical mechanics. In addition to being a tool for obtaining the probability distributions of interest(wave functions in the case of quantum mechanics),these methods are very instructive and offer great insights into the problem. In this thesis,
path integrals are extensively employed to study some very interesting problems in both equilibrium and non-equilibrium statistical mechanics. In the non-equilibrium regime, we have studied, using a
path integral approach, a very interesting class of anomalous diffusion, viz. the L´evy flights. In equilibrium statistical mechanics, we have evaluated the partition function for a class of molecules referred to as the hindered rotors which have a barrier for internal rotation. Also, we have evaluated the exact quantum statistical mechanical propagator for a harmonic potential with a time-dependent force constant, valid under certain conditions.
Diffusion processes have attracted a great amount of scientific attention because of their presence in a wide range of phenomena. Brownian motion is the most widely known class of diffusion which is usually driven by thermal noise. However ,there are other classes of diffusion which cannot be classified as Brownian motion and therefore, fall under the category of Anomalous diffusion. As the name suggests, the properties of this class of diffusion are very different from those for usual Brownian motion. We are interested in a particular class of anomalous diffusion referred to as L´evy flights in which the step sizes taken by the particle during the random walk are obtained from what is known as a L´evy distribution. The diverging mean square displacement is a very typical feature for L´evy flights as opposed to a finite mean square displacement with a linear dependence on time in the case of Brownian motion. L´evy distributions are characterized by an index α where 0 <α ≤ 2. When α =2, the distribution becomes a Gaussian and when α=1, it reduces to a Cauchy/Lorentzian distribution.
In the overdamped limit of friction, the probability density or the propagator associated with L´evy flights can be described by a position space fractional Fokker-Planck equation(FFPE)[1–3]. Jespersen et al. [4]have solved the FFPE in the Fourier domain to obtain the propagator for free L´evy flight(absence of an external potential) and L´evy flights in linear and harmonic potentials. We use a
path integral technique to study L´evy flights. L´evy distributions rarely have a compact analytical expression in the position space. However, their Fourier transformations are rather simple and are given by e−D │p│α where D determines the width of the distribution. Due to the absence of a simple analytical expression, attempts in the past to study L´evy flights using
path integrals in the position space [5, 6] have not been very successful. In our approach, we have tried to make use of the elegant representation of the L´evy distribution in the Fourier space and…
Advisors/Committee Members: Sebastian, K L (advisor).
Subjects/Keywords: Path Integrals; Levy Noise; Levy Flight; Anomalous Diffusion; Hamiltonian Path Integral; Harmonic Oscillators - Path Integrals; Barrier Crossing - Path Integrals; Statistical Mechanics; Hindered Rotors; Friction (Levy Flights); Levy Flights - Path Integrals; Hindered Rotations; Quantum Mechanics
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APA ·
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MLA ·
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to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Janakiraman, D. (2018). Path Integral Approach to Levy Flights and Hindered Rotations. (Doctoral Dissertation). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/3396
Chicago Manual of Style (16th Edition):
Janakiraman, Deepika. “Path Integral Approach to Levy Flights and Hindered Rotations.” 2018. Doctoral Dissertation, Indian Institute of Science. Accessed March 08, 2021.
http://etd.iisc.ac.in/handle/2005/3396.
MLA Handbook (7th Edition):
Janakiraman, Deepika. “Path Integral Approach to Levy Flights and Hindered Rotations.” 2018. Web. 08 Mar 2021.
Vancouver:
Janakiraman D. Path Integral Approach to Levy Flights and Hindered Rotations. [Internet] [Doctoral dissertation]. Indian Institute of Science; 2018. [cited 2021 Mar 08].
Available from: http://etd.iisc.ac.in/handle/2005/3396.
Council of Science Editors:
Janakiraman D. Path Integral Approach to Levy Flights and Hindered Rotations. [Doctoral Dissertation]. Indian Institute of Science; 2018. Available from: http://etd.iisc.ac.in/handle/2005/3396
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Open Access Theses and Dissertations
