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dc.contributor.advisorTomsovic, Steven L
dc.creatorLi, Jizhou
dc.date.accessioned2019-08-21T17:57:03Z
dc.date.available2019-08-21T17:57:03Z
dc.date.issued2018
dc.identifier.urihttp://hdl.handle.net/2376/16363
dc.descriptionThesis (Ph.D.), Physics, Washington State Universityen_US
dc.description.abstractRare sets of classical orbits, such as the heteroclinic and periodic orbits, play central roles in various semiclassical sum rules, in which they sum up in interference-like ways to determine spectral quantities of quantum systems. The interferences between them are governed by the orbits’ classical actions and Maslov indices. In particular, the classical actions as the phase factors, are scaled by h. Therefore, even small errors in the actions will significantly compromise the accuracy of semiclassical calculations. Due to the “butterfly effect”, numerical determinations of orbits (thus their actions) become exponentially difficult with increasing orbit lengths, hindering the calculation of the system’s spectra on finer scales. In this study, we present new approaches for determining the classical actions of heteroclinic and periodic orbits using phase-space invariant structures, such as the stable and unstable manifolds, and the areas they enclose. These manifolds can be grown in fast and numerically stable ways, which completely bypass the exponential divergence inherent in chaotic systems. By relating orbits to phase-space areas, we also provide analytic expressions for universal action relations between classical orbits, which lead to corrections of the cycle expansion, and a novel scheme of expressing the exponentially proliferating set of homoclinic orbit actions in terms of a sub-algebraically growing set of phase-space areas, which represents a major reduction on the information input for semiclassical methods.en_US
dc.description.sponsorshipWashington State University, Physicsen_US
dc.languageEnglish
dc.rightsIn copyright
dc.rightsPublicly accessible
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectPhysics
dc.subjectChaos
dc.subjectClassical actions
dc.subjectHomoclinic orbit
dc.subjectNonlinear dynamics
dc.subjectPeriodic orbit
dc.subjectQuantum chaos
dc.titleANALYTIC RELATIONS BETWEEN CLASSICAL ORBITS IN CHAOTIC SYSTEMS, AND THEIR IMPLICATIONS FOR QUANTUM CHAOS
dc.typeElectronic Thesis or Dissertation


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