Persistent Link:
http://hdl.handle.net/10150/282102
Title:
Chaotic dynamics in classical and quantum mechanical systems
Author:
Han, Pin, 1967-
Issue Date:
1996
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
This dissertation describes mainly researches on the chaotic properties of some classical and quantum mechanical systems. New phenomena like the three-dimensional uniform stochastic web and multiply riddled behavior are presented with numerical results. In the introduction, a short history and basic principles about chaotic dynamical systems are reviewed, which include the concepts of Lyapunov exponents and Poincare sections. In Chapter 2, we first discuss the Hamiltonian system, followed by the perturbation and KAM theory, then introduce Arnold diffusion and the existence of stochastic webs. We close this chapter with a system which can generate a three-dimensional uniform stochastic web. In Chapter 3, the relationship between deterministic chaos and quantum mechanics is studied. A quantum mechanical system called the tetrahedral array of Josephson junctions in which the deterministic chaos can exist is presented. At the end, we generalize such systems to any dimension and expect that chaos should survive in a higher dimensional case. In Chapter 4, in addition to the introduction of the riddled behavior, three examples in which multiply riddled behavior can occur are given and illustrated by graphs. The generalization of these systems is also made and we still expect that multiply riddled behavior will exist in these generalized systems containing more degrees of freedom.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Physics, General.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Physics
Degree Grantor:
University of Arizona
Advisor:
Parmenter, Robert H.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleChaotic dynamics in classical and quantum mechanical systemsen_US
dc.creatorHan, Pin, 1967-en_US
dc.contributor.authorHan, Pin, 1967-en_US
dc.date.issued1996en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThis dissertation describes mainly researches on the chaotic properties of some classical and quantum mechanical systems. New phenomena like the three-dimensional uniform stochastic web and multiply riddled behavior are presented with numerical results. In the introduction, a short history and basic principles about chaotic dynamical systems are reviewed, which include the concepts of Lyapunov exponents and Poincare sections. In Chapter 2, we first discuss the Hamiltonian system, followed by the perturbation and KAM theory, then introduce Arnold diffusion and the existence of stochastic webs. We close this chapter with a system which can generate a three-dimensional uniform stochastic web. In Chapter 3, the relationship between deterministic chaos and quantum mechanics is studied. A quantum mechanical system called the tetrahedral array of Josephson junctions in which the deterministic chaos can exist is presented. At the end, we generalize such systems to any dimension and expect that chaos should survive in a higher dimensional case. In Chapter 4, in addition to the introduction of the riddled behavior, three examples in which multiply riddled behavior can occur are given and illustrated by graphs. The generalization of these systems is also made and we still expect that multiply riddled behavior will exist in these generalized systems containing more degrees of freedom.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectPhysics, General.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplinePhysicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorParmenter, Robert H.en_US
dc.identifier.proquest9626550en_US
dc.identifier.bibrecord.b33956911en_US
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