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You searched for +publisher:"University of North Texas" +contributor:("Kobe, Donald H."). Showing records 1 – 3 of 3 total matches.

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University of North Texas

1. Zheng, Yindong. Chaos and Momentum Diffusion of the Classical and Quantum Kicked Rotor.

Degree: 2005, University of North Texas

The de Broglie-Bohm (BB) approach to quantum mechanics gives trajectories similar to classical trajectories except that they are also determined by a quantum potential. The quantum potential is a "fictitious potential" in the sense that it is part of the quantum kinetic energy. We use quantum trajectories to treat quantum chaos in a manner similar to classical chaos. For the kicked rotor, which is a bounded system, we use the Benettin et al. method to calculate both classical and quantum Lyapunov exponents as a function of control parameter K and find chaos in both cases. Within the chaotic sea we find in both cases nonchaotic stability regions for K equal to multiples of π. For even multiples of π the stability regions are associated with classical accelerator mode islands and for odd multiples of π they are associated with new oscillator modes. We examine the structure of these regions. Momentum diffusion of the quantum kicked rotor is studied with both BB and standard quantum mechanics (SQM). A general analytical expression is given for the momentum diffusion at quantum resonance of both BB and SQM. We obtain agreement between the two approaches in numerical experiments. For the case of nonresonance the quantum potential is not zero and must be included as part of the quantum kinetic energy for agreement. The numerical data for momentum diffusion of classical kicked rotor is well fit by a power law DNβ in the number of kicks N. In the anomalous momentum diffusion regions due to accelerator modes the exponent β(K) is slightly less than quadratic, except for a slight dip, in agreement with an upper bound (K2/2)N2. The corresponding coefficient D(K) in these regions has three distinct sections, most likely due to accelerator modes with period greater than one. We also show that the local Lyapunov exponent of the classical kicked rotor has a plateau for a duration that depends on the initial separation and then decreases asymptotically as O(t-1lnt), where t is the time. This behavior is consistent with an upper bound that is determined analytically. Advisors/Committee Members: Kobe, Donald H., Grigolini, Paolo, Kowalski, Jacek M., Krokhin, Arkadii.

Subjects/Keywords: Quantum chaos.; Momentum (Mechanics); Quantum theory.; quantum chaos; atom optics kicked rotor; Lyapunov exponents; quantum potential; momentum diffusion

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

APA (6th Edition):

Zheng, Y. (2005). Chaos and Momentum Diffusion of the Classical and Quantum Kicked Rotor. (Thesis). University of North Texas. Retrieved from https://digital.library.unt.edu/ark:/67531/metadc4824/

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

Chicago Manual of Style (16th Edition):

Zheng, Yindong. “Chaos and Momentum Diffusion of the Classical and Quantum Kicked Rotor.” 2005. Thesis, University of North Texas. Accessed October 17, 2019. https://digital.library.unt.edu/ark:/67531/metadc4824/.

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

MLA Handbook (7th Edition):

Zheng, Yindong. “Chaos and Momentum Diffusion of the Classical and Quantum Kicked Rotor.” 2005. Web. 17 Oct 2019.

Vancouver:

Zheng Y. Chaos and Momentum Diffusion of the Classical and Quantum Kicked Rotor. [Internet] [Thesis]. University of North Texas; 2005. [cited 2019 Oct 17]. Available from: https://digital.library.unt.edu/ark:/67531/metadc4824/.

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

Council of Science Editors:

Zheng Y. Chaos and Momentum Diffusion of the Classical and Quantum Kicked Rotor. [Thesis]. University of North Texas; 2005. Available from: https://digital.library.unt.edu/ark:/67531/metadc4824/

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


University of North Texas

2. Campisi, Michele. Microscopic Foundations of Thermodynamics and Generalized Statistical Ensembles.

Degree: 2008, University of North Texas

This dissertation aims at addressing two important theoretical questions which are still debated in the statistical mechanical community. The first question has to do with the outstanding problem of how to reconcile time-reversal asymmetric macroscopic laws with the time-reversal symmetric laws of microscopic dynamics. This problem is addressed by developing a novel mechanical approach inspired by the work of Helmholtz on monocyclic systems and the Heat Theorem, i.e., the Helmholtz Theorem. By following a line of investigation initiated by Boltzmann, a Generalized Helmholtz Theorem is stated and proved. This theorem provides us with a good microscopic analogue of thermodynamic entropy. This is the volume entropy, namely the logarithm of the volume of phase space enclosed by the constant energy hyper-surface. By using quantum mechanics only, it is shown that such entropy can only increase. This can be seen as a novel rigorous proof of the Second Law of Thermodynamics that sheds new light onto the arrow of time problem. The volume entropy behaves in a thermodynamic-like way independent of the number of degrees of freedom of the system, indicating that a whole thermodynamic-like world exists at the microscopic level. It is also shown that breaking of ergodicity leads to microcanonical phase transitions associated with nonanalyticities of volume entropy. The second part of the dissertation deals with the problem of the foundations of generalized ensembles in statistical mechanics. The starting point is Boltzmann's work on statistical ensembles and its relation with the Heat Theorem. We first focus on the nonextensive thermostatistics of Tsallis and the associated deformed exponential ensembles. These ensembles are analyzed in detail and proved (a) to comply with the requirements posed by the Heat Theorem, and (b) to interpolate between canonical and microcanonical ensembles. Further they are showed to describe finite systems in contact with finite heat baths. Their mechanical and information-theoretic foundation, are highlighted. Finally, a wide class of generalized ensembles is introduced, all of which reproduce the Heat Theorem. This class, named the class of dual orthodes, contains microcanonical, canonical, Tsallis and Gaussian ensembles as special cases. Advisors/Committee Members: Kobe, Donald H., Deering, William D., Weathers, Duncan L., Kowalski, Jacek M..

Subjects/Keywords: finite heat bath; Heat theorem; microcanonical AMSE transition; second law; Thermodynamics.; Statistical mechanics.

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

APA (6th Edition):

Campisi, M. (2008). Microscopic Foundations of Thermodynamics and Generalized Statistical Ensembles. (Thesis). University of North Texas. Retrieved from https://digital.library.unt.edu/ark:/67531/metadc6128/

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

Chicago Manual of Style (16th Edition):

Campisi, Michele. “Microscopic Foundations of Thermodynamics and Generalized Statistical Ensembles.” 2008. Thesis, University of North Texas. Accessed October 17, 2019. https://digital.library.unt.edu/ark:/67531/metadc6128/.

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

MLA Handbook (7th Edition):

Campisi, Michele. “Microscopic Foundations of Thermodynamics and Generalized Statistical Ensembles.” 2008. Web. 17 Oct 2019.

Vancouver:

Campisi M. Microscopic Foundations of Thermodynamics and Generalized Statistical Ensembles. [Internet] [Thesis]. University of North Texas; 2008. [cited 2019 Oct 17]. Available from: https://digital.library.unt.edu/ark:/67531/metadc6128/.

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

Council of Science Editors:

Campisi M. Microscopic Foundations of Thermodynamics and Generalized Statistical Ensembles. [Thesis]. University of North Texas; 2008. Available from: https://digital.library.unt.edu/ark:/67531/metadc6128/

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


University of North Texas

3. Bagci, Gokhan Baris. The Nonadditive Generalization of Klimontovich's S-Theorem for Open Systems and Boltzmann's Orthodes.

Degree: 2008, University of North Texas

We show that the nonadditive open systems can be studied in a consistent manner by using a generalized version of S-theorem. This new generalized S-theorem can further be considered as an indication of self-organization in nonadditive open systems as prescribed by Haken. The nonadditive S-theorem is then illustrated by using the modified Van der Pol oscillator. Finally, Tsallis entropy as an equilibrium entropy is studied by using Boltzmann's method of orthodes. This part of dissertation shows that Tsallis ensemble is on equal footing with the microcanonical, canonical and grand canonical ensembles. However, the associated entropy turns out to be Renyi entropy. Advisors/Committee Members: Kobe, Donald H., Deering, William D., Kowalski, Jacek M., Ordonez, Carlos A..

Subjects/Keywords: Nonadditivity; entropy; orthode; System analysis.; Statistical mechanics.

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

APA (6th Edition):

Bagci, G. B. (2008). The Nonadditive Generalization of Klimontovich's S-Theorem for Open Systems and Boltzmann's Orthodes. (Thesis). University of North Texas. Retrieved from https://digital.library.unt.edu/ark:/67531/metadc9124/

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

Chicago Manual of Style (16th Edition):

Bagci, Gokhan Baris. “The Nonadditive Generalization of Klimontovich's S-Theorem for Open Systems and Boltzmann's Orthodes.” 2008. Thesis, University of North Texas. Accessed October 17, 2019. https://digital.library.unt.edu/ark:/67531/metadc9124/.

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

MLA Handbook (7th Edition):

Bagci, Gokhan Baris. “The Nonadditive Generalization of Klimontovich's S-Theorem for Open Systems and Boltzmann's Orthodes.” 2008. Web. 17 Oct 2019.

Vancouver:

Bagci GB. The Nonadditive Generalization of Klimontovich's S-Theorem for Open Systems and Boltzmann's Orthodes. [Internet] [Thesis]. University of North Texas; 2008. [cited 2019 Oct 17]. Available from: https://digital.library.unt.edu/ark:/67531/metadc9124/.

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

Council of Science Editors:

Bagci GB. The Nonadditive Generalization of Klimontovich's S-Theorem for Open Systems and Boltzmann's Orthodes. [Thesis]. University of North Texas; 2008. Available from: https://digital.library.unt.edu/ark:/67531/metadc9124/

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

.