subject:(path integral)

1. 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

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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)

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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 (6^th 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 (16^th Edition):

Sandström, Martin. “Path Integrals and Quantum Mechanics.” 2015. Thesis, Umeå University. Accessed December 08, 2019. 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 (7^th Edition):

Sandström, Martin. “Path Integrals and Quantum Mechanics.” 2015. Web. 08 Dec 2019.

Vancouver:

Sandström M. Path Integrals and Quantum Mechanics. [Internet] [Thesis]. Umeå University; 2015. [cited 2019 Dec 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

2. 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

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Advisors/Committee Members: Chauhan, R S, Upadhyaya, K S.

Subjects/Keywords: path integral duality

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APA (6^th 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 (16^th Edition):

Chauhan, Arjun. “Some investigations in hypotheses of path integral duality;.” 2014. Thesis, V. B. S. Purvanchal University. Accessed December 08, 2019. 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 (7^th Edition):

Chauhan, Arjun. “Some investigations in hypotheses of path integral duality;.” 2014. Web. 08 Dec 2019.

Vancouver:

Chauhan A. Some investigations in hypotheses of path integral duality;. [Internet] [Thesis]. V. B. S. Purvanchal University; 2014. [cited 2019 Dec 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 Illinois – Urbana-Champaign

3. Wang, Fei. Quantum-classical and semiclassical path integral methods for condensed phase dynamics.

Degree: PhD, Chemistry, 2018, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/102468

► Chemical dynamics are essentially quantum mechanical processes. A great variety of chemical processes such as electron transfer and energy relaxation occur in condensed phase, reactants… (more)

▼ Chemical dynamics are essentially quantum mechanical processes. A great variety of chemical processes such as electron transfer and energy relaxation occur in condensed phase, reactants and products embedding in a non-reactive solution/environment. Therefore, quantum dynamics in condensed phase is the study of the behavior of the quantum system coupled to an interacting bath. The development of robust methodologies and efficient computational tools for condensed phase dynamics remains central to theoretical chemistry. Since the full quantum treatment only limits to a system with a few degrees of freedom, the partition of the entire system into a subsystem for which quantum mechanical description is necessary and the bath which can be modeled by the less expensive classical dynamics, is a common strategy. Due to the decoherence nature of the bath on the system, the quantum dynamics of the system is often described by the density matrix. Path integral formulation of the density matrix provides a versatile tool for studying quantum dynamics in condensed phase. Unlike the Schro ̈dinger equation in which the wavefunction is central, Feynman’s path integral formulation is trajectory based, and therefore offers a natural connection between quantum mechanics and classical mechanics. This work will investigate path integral formulation in treating a quantum system coupled to anharmonic environment and the semiclassical formulation of path integral. A big achievement in using Feynman’s path integral to study condensed phase dynamics is the development of quantum-classical path integral (QCPI) methodology. Taking advantage that the non-reactive environment can be modeled accurately by classical mechanics, a great reduction of computational cost is achieved. Previous studies have been largely focusing on a quantum system interacting with harmonic environment, mainly because the analytical expressions of harmonic oscillator can be obtained. In this work, we extend the QCPI method to anharmonic environment by making numerically accurate approximations. Semiclassical approach reduces all the possible quantum paths into one or several classical trajectories, therefore automatically eliminates the exponential growth of paths with time evolution. The distinct forward and backward trajectories in the density matrix allows quantum interference. This work explores the semiclassical-system classical-bath formulation of path integral. The stationary phase condition makes the phase smooth and makes Monte Carlo sampling very efficient with respect to the bath initial phase space distribution. The continuous coordinate formulation offers a potential utility of the method to treating multi-level systems. Advisors/Committee Members: Makri, Nancy (advisor), Makri, Nancy (Committee Chair), Gruebele, Martin (committee member), Pogorelov, Taras (committee member), Stone, Michael (committee member).

Subjects/Keywords: path integral; semiclassical; condensed phase dynamics

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APA (6^th Edition):

Wang, F. (2018). Quantum-classical and semiclassical path integral methods for condensed phase dynamics. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/102468

Chicago Manual of Style (16^th Edition):

Wang, Fei. “Quantum-classical and semiclassical path integral methods for condensed phase dynamics.” 2018. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed December 08, 2019. http://hdl.handle.net/2142/102468.

MLA Handbook (7^th Edition):

Wang, Fei. “Quantum-classical and semiclassical path integral methods for condensed phase dynamics.” 2018. Web. 08 Dec 2019.

Vancouver:

Wang F. Quantum-classical and semiclassical path integral methods for condensed phase dynamics. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2018. [cited 2019 Dec 08]. Available from: http://hdl.handle.net/2142/102468.

Council of Science Editors:

Wang F. Quantum-classical and semiclassical path integral methods for condensed phase dynamics. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2018. Available from: http://hdl.handle.net/2142/102468

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)

Subjects/Keywords: Physics; cold atoms; path integral; superconductor

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APA (6^th 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 (16^th Edition):

Kim, Tom. “Path integral formalism of Bose Einstein condensation and superconductivity.” 2019. Thesis, University of California – Merced. Accessed December 08, 2019. 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 (7^th Edition):

Kim, Tom. “Path integral formalism of Bose Einstein condensation and superconductivity.” 2019. Web. 08 Dec 2019.

Vancouver:

Kim T. Path integral formalism of Bose Einstein condensation and superconductivity. [Internet] [Thesis]. University of California – Merced; 2019. [cited 2019 Dec 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 (6^th 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 (16^th Edition):

Walters, Peter Lawton. “Path integral methods for accurate simulation of condensed phase reactions.” 2016. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed December 08, 2019. http://hdl.handle.net/2142/90579.

MLA Handbook (7^th Edition):

Walters, Peter Lawton. “Path integral methods for accurate simulation of condensed phase reactions.” 2016. Web. 08 Dec 2019.

Vancouver:

Walters PL. Path integral methods for accurate simulation of condensed phase reactions. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2016. [cited 2019 Dec 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 (6^th 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 (16^th Edition):

Ing, Christopher. “Path integral Langevin dynamics of complex molecular systems: from low-temperature quantum clusters to biomolecules.” 2011. Thesis, University of Waterloo. Accessed December 08, 2019. 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 (7^th Edition):

Ing, Christopher. “Path integral Langevin dynamics of complex molecular systems: from low-temperature quantum clusters to biomolecules.” 2011. Web. 08 Dec 2019.

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 2019 Dec 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)

Subjects/Keywords: Most likely path; Path integral; Quantum measurement; Stochastic process

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th 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 (16^th Edition):

Chantasri, Areeya (1984 - ). “Stochastic path integral formalism for continuous quantum measurement.” 2016. Doctoral Dissertation, University of Rochester. Accessed December 08, 2019. http://hdl.handle.net/1802/31479.

MLA Handbook (7^th Edition):

Chantasri, Areeya (1984 - ). “Stochastic path integral formalism for continuous quantum measurement.” 2016. Web. 08 Dec 2019.

Vancouver:

Chantasri A(-). Stochastic path integral formalism for continuous quantum measurement. [Internet] [Doctoral dissertation]. University of Rochester; 2016. [cited 2019 Dec 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 (6^th 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 (16^th Edition):

Nathanson, Ekaterina Sergeyevna. “Path integration with non-positive distributions and applications to the Schrödinger equation.” 2014. Doctoral Dissertation, University of Iowa. Accessed December 08, 2019. https://ir.uiowa.edu/etd/1370.

MLA Handbook (7^th Edition):

Nathanson, Ekaterina Sergeyevna. “Path integration with non-positive distributions and applications to the Schrödinger equation.” 2014. Web. 08 Dec 2019.

Vancouver:

Nathanson ES. Path integration with non-positive distributions and applications to the Schrödinger equation. [Internet] [Doctoral dissertation]. University of Iowa; 2014. [cited 2019 Dec 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/

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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)

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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 (6^th 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 (16^th Edition):

Poma, Adolfo. “Coarse-graining and quantum-classical adaptive coupling in soft matter.” 2011. Doctoral Dissertation, Johannes Gutenberg Universität Mainz. Accessed December 08, 2019. http://ubm.opus.hbz-nrw.de/volltexte/2011/2776/.

MLA Handbook (7^th Edition):

Poma, Adolfo. “Coarse-graining and quantum-classical adaptive coupling in soft matter.” 2011. Web. 08 Dec 2019.

Vancouver:

Poma A. Coarse-graining and quantum-classical adaptive coupling in soft matter. [Internet] [Doctoral dissertation]. Johannes Gutenberg Universität Mainz; 2011. [cited 2019 Dec 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/

10. Henderson, Adam Dade. Loop Quantum Cosmology: A Window Into the Path Integral Representation of Quantum Gravity.

Degree: PhD, Physics, 2011, Penn State University

URL: https://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)

Subjects/Keywords: Quantum Gravity; Path Integral

…Hamiltonian formulation of classical mechanics. Second, is path integral or sum over histories… …path integral paradigm, which has led to a very enticing picture for quantum gravity. 1.3… …operator and obtaining the physical Hilbert space by working within the path integral approach to… …latter route is often used in quantum 6 field theory where a path integral is used to define… …path integral paradigm gives a distinct route to quantum gravity as defined by a sum over all…

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APA (6^th Edition):

Henderson, A. D. (2011). Loop Quantum Cosmology: A Window Into the Path Integral Representation of Quantum Gravity. (Doctoral Dissertation). Penn State University. Retrieved from https://etda.libraries.psu.edu/catalog/12472

Chicago Manual of Style (16^th Edition):

Henderson, Adam Dade. “Loop Quantum Cosmology: A Window Into the Path Integral Representation of Quantum Gravity.” 2011. Doctoral Dissertation, Penn State University. Accessed December 08, 2019. https://etda.libraries.psu.edu/catalog/12472.

MLA Handbook (7^th Edition):

Henderson, Adam Dade. “Loop Quantum Cosmology: A Window Into the Path Integral Representation of Quantum Gravity.” 2011. Web. 08 Dec 2019.

Vancouver:

Henderson AD. Loop Quantum Cosmology: A Window Into the Path Integral Representation of Quantum Gravity. [Internet] [Doctoral dissertation]. Penn State University; 2011. [cited 2019 Dec 08]. Available from: https://etda.libraries.psu.edu/catalog/12472.

Council of Science Editors:

Henderson AD. Loop Quantum Cosmology: A Window Into the Path Integral Representation of Quantum Gravity. [Doctoral Dissertation]. Penn State University; 2011. Available from: https://etda.libraries.psu.edu/catalog/12472

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 (6^th 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 (16^th Edition):

Walker, James Nicholas. “Inference methods for First Few Hundred Studies.” 2016. Thesis, University of Adelaide. Accessed December 08, 2019. 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 (7^th Edition):

Walker, James Nicholas. “Inference methods for First Few Hundred Studies.” 2016. Web. 08 Dec 2019.

Vancouver:

Walker JN. Inference methods for First Few Hundred Studies. [Internet] [Thesis]. University of Adelaide; 2016. [cited 2019 Dec 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 Oregon

12. Mackrory, Jonathan. The Worldline Method for Electromagnetic Casimir Energies.

Degree: 2017, University of Oregon

URL: http://hdl.handle.net/1794/22664

► The Casimir effect refers to the primarily attractive force between material bodies due to quantum fluctuations in the electromagnetic field. The Casimir effect is difficult… (more)

▼ The Casimir effect refers to the primarily attractive force between material bodies due to quantum fluctuations in the electromagnetic field. The Casimir effect is difficult to calculate in general, since it is sensitive to the exact shapes of the bodies and involves contributions from all frequencies. As a result, calculating the Casimir effect between general bodies usually requires a numerical approach. The worldline method computes Casimir energies by creating an ensemble of space-time paths corresponding to a virtual particle interacting with the bodies. This method was originally developed for a scalar fields coupled to an idealized background potential, rather than the vector electromagnetic field interacting with media. This thesis presents work on extending the worldline method to account for the material properties of the interacting bodies, and the polarizations of electromagnetism. This thesis starts by covering background material on path integrals, and quantizing the electromagnetic field in media. The electromagnetic field is decomposed in terms of two scalar fields for planar bodies, where these scalar fields correspond to the transverse-electric and transverse-magnetic polarizations of the electromagnetic field. The worldline path integrals are developed for both polarizations, and solved analytically. Next, numerical methods are developed and tested in the context of planar bodies. The starting positions, and scale of the paths, and shape of the paths are sampled via Monte Carlo methods. The transverse-magnetic path integral also requires specialized methods for estimating derivatives, and path construction. The analytical and numerical results for both worldline path integrals are in agreement with known solutions. Finally, specialized methods are developed for computing derivatives of the worldline Casimir-energy path integrals, allowing for efficient numerical computations of Casimir forces and torques. Advisors/Committee Members: Steck, Daniel (advisor).

Subjects/Keywords: Casimir effect; Path Integral methods; Quantum Electrodynamics; Worldline formalism

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APA (6^th Edition):

Mackrory, J. (2017). The Worldline Method for Electromagnetic Casimir Energies. (Thesis). University of Oregon. Retrieved from http://hdl.handle.net/1794/22664

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Mackrory, Jonathan. “The Worldline Method for Electromagnetic Casimir Energies.” 2017. Thesis, University of Oregon. Accessed December 08, 2019. http://hdl.handle.net/1794/22664.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Mackrory, Jonathan. “The Worldline Method for Electromagnetic Casimir Energies.” 2017. Web. 08 Dec 2019.

Vancouver:

Mackrory J. The Worldline Method for Electromagnetic Casimir Energies. [Internet] [Thesis]. University of Oregon; 2017. [cited 2019 Dec 08]. Available from: http://hdl.handle.net/1794/22664.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Mackrory J. The Worldline Method for Electromagnetic Casimir Energies. [Thesis]. University of Oregon; 2017. Available from: http://hdl.handle.net/1794/22664

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)

Subjects/Keywords: quantum; statistical mechanics; path integral; rotation; centroid; state projection

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APA (6^th 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 (16^th Edition):

Orr, Lindsay A. “Developments in the Centroid Phase Space Formulation of Quantum Statistical Mechanics.” 2016. Thesis, University of Waterloo. Accessed December 08, 2019. 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 (7^th Edition):

Orr, Lindsay A. “Developments in the Centroid Phase Space Formulation of Quantum Statistical Mechanics.” 2016. Web. 08 Dec 2019.

Vancouver:

Orr LA. Developments in the Centroid Phase Space Formulation of Quantum Statistical Mechanics. [Internet] [Thesis]. University of Waterloo; 2016. [cited 2019 Dec 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

University of St. Andrews

14. 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)

Subjects/Keywords: Majorana; Magnetism; Quantum field theory; Ising; Path integral; Random phase approximation

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APA (6^th 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 (16^th Edition):

Bennett, Edmund. “Exotic order in magnetic systems from Majorana fermions .” 2016. Thesis, University of St. Andrews. Accessed December 08, 2019. 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 (7^th Edition):

Bennett, Edmund. “Exotic order in magnetic systems from Majorana fermions .” 2016. Web. 08 Dec 2019.

Vancouver:

Bennett E. Exotic order in magnetic systems from Majorana fermions . [Internet] [Thesis]. University of St. Andrews; 2016. [cited 2019 Dec 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

Clemson University

15. 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 (6^th 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 (16^th Edition):

Dickson, Bradley. “PATH INTEGRAL FORMULATION OF LANGEINV DYNAMICS WITH APPLICATIONS TO RARE-EVENT SYSTEMS.” 2006. Doctoral Dissertation, Clemson University. Accessed December 08, 2019. https://tigerprints.clemson.edu/all_dissertations/24.

MLA Handbook (7^th Edition):

Dickson, Bradley. “PATH INTEGRAL FORMULATION OF LANGEINV DYNAMICS WITH APPLICATIONS TO RARE-EVENT SYSTEMS.” 2006. Web. 08 Dec 2019.

Vancouver:

Dickson B. PATH INTEGRAL FORMULATION OF LANGEINV DYNAMICS WITH APPLICATIONS TO RARE-EVENT SYSTEMS. [Internet] [Doctoral dissertation]. Clemson University; 2006. [cited 2019 Dec 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

16. 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

新制・課程博士

甲第19121号

情博第567号

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 (6^th 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 (16^th 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 December 08, 2019. 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 (7^th 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 Dec 2019.

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 2019 Dec 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

17. 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 (6^th 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 (16^th Edition):

Ito, Yu. “Rough path theory via fractional calculus .” 2015. Thesis, Kyoto University. Accessed December 08, 2019. 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 (7^th Edition):

Ito, Yu. “Rough path theory via fractional calculus .” 2015. Web. 08 Dec 2019.

Vancouver:

Ito Y. Rough path theory via fractional calculus . [Internet] [Thesis]. Kyoto University; 2015. [cited 2019 Dec 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

18. 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)

Subjects/Keywords: Chemistry; Theoretical physics; Electron Correlation; Orbital Optimization; Path Integral Monte Carlo; Spin Contamination; Vibrational Anharmonicity

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APA (6^th 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 (16^th Edition):

Stuck, David. “The Importance of Zeroth-Order Approximations in Molecular Quantum Mechanics.” 2015. Thesis, University of California – Berkeley. Accessed December 08, 2019. 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 (7^th Edition):

Stuck, David. “The Importance of Zeroth-Order Approximations in Molecular Quantum Mechanics.” 2015. Web. 08 Dec 2019.

Vancouver:

Stuck D. The Importance of Zeroth-Order Approximations in Molecular Quantum Mechanics. [Internet] [Thesis]. University of California – Berkeley; 2015. [cited 2019 Dec 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

Clemson University

19. 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 · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th 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 (16^th Edition):

Kilgo, Paul Michael. “Radiative Transfer Using Path Integrals for Multiple Scattering in Participating Media.” 2016. Doctoral Dissertation, Clemson University. Accessed December 08, 2019. https://tigerprints.clemson.edu/all_dissertations/2301.

MLA Handbook (7^th Edition):

Kilgo, Paul Michael. “Radiative Transfer Using Path Integrals for Multiple Scattering in Participating Media.” 2016. Web. 08 Dec 2019.

Vancouver:

Kilgo PM. Radiative Transfer Using Path Integrals for Multiple Scattering in Participating Media. [Internet] [Doctoral dissertation]. Clemson University; 2016. [cited 2019 Dec 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

Karlstad University

20. 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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APA (6^th 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 (16^th Edition):

Svensson, Anders. “Path Integral for the Hydrogen Atom : Solutions in two and three dimensions.” 2016. Thesis, Karlstad University. Accessed December 08, 2019. 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 (7^th Edition):

Svensson, Anders. “Path Integral for the Hydrogen Atom : Solutions in two and three dimensions.” 2016. Web. 08 Dec 2019.

Vancouver:

Svensson A. Path Integral for the Hydrogen Atom : Solutions in two and three dimensions. [Internet] [Thesis]. Karlstad University; 2016. [cited 2019 Dec 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

21. 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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APA (6^th 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 (16^th Edition):

XIN, DU. “Path integral modelling of interest rates, options and commodities.” 2015. Thesis, National University of Singapore. Accessed December 08, 2019. 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 (7^th Edition):

XIN, DU. “Path integral modelling of interest rates, options and commodities.” 2015. Web. 08 Dec 2019.

Vancouver:

XIN D. Path integral modelling of interest rates, options and commodities. [Internet] [Thesis]. National University of Singapore; 2015. [cited 2019 Dec 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

22. 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 (6^th 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 (16^th Edition):

MIAO, YU. “FUTURES AND SPOT COMMODITY PRICES, OPTIONS, AND FORWARD INTEREST RATES: MODEL AND EMPIRICAL ANALYSIS.” 2017. Thesis, National University of Singapore. Accessed December 08, 2019. 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 (7^th Edition):

MIAO, YU. “FUTURES AND SPOT COMMODITY PRICES, OPTIONS, AND FORWARD INTEREST RATES: MODEL AND EMPIRICAL ANALYSIS.” 2017. Web. 08 Dec 2019.

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 2019 Dec 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 Waterloo

23. 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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APA (6^th 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 (16^th Edition):

Faruk, Nabil. “Quantum effects in molecular systems.” 2014. Thesis, University of Waterloo. Accessed December 08, 2019. 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 (7^th Edition):

Faruk, Nabil. “Quantum effects in molecular systems.” 2014. Web. 08 Dec 2019.

Vancouver:

Faruk N. Quantum effects in molecular systems. [Internet] [Thesis]. University of Waterloo; 2014. [cited 2019 Dec 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

University of Waterloo

24. 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)

Subjects/Keywords: Parahydrogen; Clusters; Pseudopotential; Centroid variables; Path integral; Feynman; Centroid Molecular Dynamics; Structural properties; Deconvolution

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APA (6^th 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 (16^th 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 December 08, 2019. 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 (7^th Edition):

Yang, Jing. “A Feynman Path Centroid Effective Potential Approach for the Study of Low Temperature Parahydrogen Clusters and Droplets.” 2012. Web. 08 Dec 2019.

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 2019 Dec 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

University of Waterloo

25. 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 (6^th 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 (16^th 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 December 08, 2019. 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 (7^th Edition):

Schmidt, Matthew D G. “Path integral ground state approaches for the study of weakly bound clusters and confined molecules.” 2018. Web. 08 Dec 2019.

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 2019 Dec 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

University of Oxford

26. 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)

Subjects/Keywords: 530.12; ab initio path integral molecular dynamics; density functional theory; PIMD; Constant pressure simulations; AIPIMD

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APA (6^th 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 (16^th Edition):

More, Joshua N. “Algorithms and computer code for ab initio path integral molecular dynamics simulations.” 2015. Doctoral Dissertation, University of Oxford. Accessed December 08, 2019. 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 (7^th Edition):

More, Joshua N. “Algorithms and computer code for ab initio path integral molecular dynamics simulations.” 2015. Web. 08 Dec 2019.

Vancouver:

More JN. Algorithms and computer code for ab initio path integral molecular dynamics simulations. [Internet] [Doctoral dissertation]. University of Oxford; 2015. [cited 2019 Dec 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

Freie Universität Berlin

27. 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 (6^th 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 (16^th Edition):

Agarwal, Animesh. “Pfadintegral-Molekulardynamikmethoden in der Simulation offener Systeme.” 2016. Thesis, Freie Universität Berlin. Accessed December 08, 2019. 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 (7^th Edition):

Agarwal, Animesh. “Pfadintegral-Molekulardynamikmethoden in der Simulation offener Systeme.” 2016. Web. 08 Dec 2019.

Vancouver:

Agarwal A. Pfadintegral-Molekulardynamikmethoden in der Simulation offener Systeme. [Internet] [Thesis]. Freie Universität Berlin; 2016. [cited 2019 Dec 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

Indian Institute of Science

28. Janakiraman, Deepika. Path Integral Approach to Levy Flights and Hindered Rotations.

Degree: 2013, Indian Institute of Science

URL: http://etd.iisc.ernet.in/2005/3396 ; http://etd.iisc.ernet.in/abstracts/4262/G25859-Abs.pdf

► 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.

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 (6^th Edition):

Janakiraman, D. (2013). Path Integral Approach to Levy Flights and Hindered Rotations. (Thesis). Indian Institute of Science. Retrieved from http://etd.iisc.ernet.in/2005/3396 ; http://etd.iisc.ernet.in/abstracts/4262/G25859-Abs.pdf

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Janakiraman, Deepika. “Path Integral Approach to Levy Flights and Hindered Rotations.” 2013. Thesis, Indian Institute of Science. Accessed December 08, 2019. http://etd.iisc.ernet.in/2005/3396 ; http://etd.iisc.ernet.in/abstracts/4262/G25859-Abs.pdf.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Janakiraman, Deepika. “Path Integral Approach to Levy Flights and Hindered Rotations.” 2013. Web. 08 Dec 2019.

Vancouver:

Janakiraman D. Path Integral Approach to Levy Flights and Hindered Rotations. [Internet] [Thesis]. Indian Institute of Science; 2013. [cited 2019 Dec 08]. Available from: http://etd.iisc.ernet.in/2005/3396 ; http://etd.iisc.ernet.in/abstracts/4262/G25859-Abs.pdf.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Janakiraman D. Path Integral Approach to Levy Flights and Hindered Rotations. [Thesis]. Indian Institute of Science; 2013. Available from: http://etd.iisc.ernet.in/2005/3396 ; http://etd.iisc.ernet.in/abstracts/4262/G25859-Abs.pdf

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Texas A&M University

29. Jeong, Jaehoon. Analytical time domain electromagnetic field propagators and closed-form solutions for transmission lines.

Degree: 2009, Texas A&M University

URL: http://hdl.handle.net/1969.1/ETD-TAMU-1105

► An analytical solution for the coupled telegrapher?s equations in terms of the voltage and current on a homogeneous lossy transmission line and multiconductor transmission line… (more)

Subjects/Keywords: Propagator; Time domain analysis; Lossy circuits; Nonuniform transmission line; Coupled transmission lines; Multiconductor transmission lines; Green's function; Maxwell's equations; Path Integral

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Jeong, J. (2009). Analytical time domain electromagnetic field propagators and closed-form solutions for transmission lines. (Thesis). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/ETD-TAMU-1105

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Jeong, Jaehoon. “Analytical time domain electromagnetic field propagators and closed-form solutions for transmission lines.” 2009. Thesis, Texas A&M University. Accessed December 08, 2019. http://hdl.handle.net/1969.1/ETD-TAMU-1105.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Jeong, Jaehoon. “Analytical time domain electromagnetic field propagators and closed-form solutions for transmission lines.” 2009. Web. 08 Dec 2019.

Vancouver:

Jeong J. Analytical time domain electromagnetic field propagators and closed-form solutions for transmission lines. [Internet] [Thesis]. Texas A&M University; 2009. [cited 2019 Dec 08]. Available from: http://hdl.handle.net/1969.1/ETD-TAMU-1105.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Jeong J. Analytical time domain electromagnetic field propagators and closed-form solutions for transmission lines. [Thesis]. Texas A&M University; 2009. Available from: http://hdl.handle.net/1969.1/ETD-TAMU-1105

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Vermont

30. Himberg, Benjamin Evert. Accelerating Quantum Monte Carlo via Graphics Processing Units.

Degree: MS, Physics, 2017, University of Vermont

URL: https://scholarworks.uvm.edu/graddis/728

► An exact quantum Monte Carlo algorithm for interacting particles in the spatial continuum is extended to exploit the massive parallelism offered by graphics processing… (more)

Subjects/Keywords: Calogero-Sutherland model; Exactly solvable; Graphics Processing Units; One-dimensional models; Path Integral Monte Carlo; Condensed Matter Physics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Himberg, B. E. (2017). Accelerating Quantum Monte Carlo via Graphics Processing Units. (Thesis). University of Vermont. Retrieved from https://scholarworks.uvm.edu/graddis/728

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Himberg, Benjamin Evert. “Accelerating Quantum Monte Carlo via Graphics Processing Units.” 2017. Thesis, University of Vermont. Accessed December 08, 2019. https://scholarworks.uvm.edu/graddis/728.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Himberg, Benjamin Evert. “Accelerating Quantum Monte Carlo via Graphics Processing Units.” 2017. Web. 08 Dec 2019.

Vancouver:

Himberg BE. Accelerating Quantum Monte Carlo via Graphics Processing Units. [Internet] [Thesis]. University of Vermont; 2017. [cited 2019 Dec 08]. Available from: https://scholarworks.uvm.edu/graddis/728.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Himberg BE. Accelerating Quantum Monte Carlo via Graphics Processing Units. [Thesis]. University of Vermont; 2017. Available from: https://scholarworks.uvm.edu/graddis/728

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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Open Access Theses and Dissertations