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dc.contributor.advisorMorrison, Philip J.en
dc.creatorHagstrom, George Isaacen
dc.date.accessioned2011-10-28T17:51:40Zen
dc.date.available2011-10-28T17:51:40Zen
dc.date.issued2011-08en
dc.date.submittedAugust 2011en
dc.identifier.urihttp://hdl.handle.net/2152/ETD-UT-2011-08-3753en
dc.descriptiontexten
dc.description.abstractVarious properties of linear infinite-dimensional Hamiltonian systems are studied. The structural stability of the Vlasov-Poisson equation linearized around a homogeneous stable equilibrium [mathematical symbol] is investigated in a Banach space setting. It is found that when perturbations of [mathematical symbols] are allowed to live in the space [mathematical symbols], every equilibrium is structurally unstable. When perturbations are restricted to area preserving rearrangements of [mathematical symbol], structural stability exists if and only if there is negative signature in the continuous spectrum. This analogizes Krein's theorem for linear finite-dimensional Hamiltonian systems. The techniques used to prove this theorem are applied to other aspects of the linearized Vlasov-Poisson equation, in particular the energy of discrete modes which are embedded within the continuous spectrum. In the second part, an integral transformation that exactly diagonalizes the Caldeira-Leggett model is presented. The resulting form of the Hamiltonian, derived using canonical transformations, is shown to be identical to that of the linearized Vlasov-Poisson equation. The damping mechanism in the Caldeira-Leggett model is identified with the Landau damping of a plasma. The correspondence between the two systems suggests the presence of an echo effect in the Caldeira-Leggett model. Generalizations of the Caldeira-Leggett model with negative energy are studied and interpreted in the context of Krein's theorem.en
dc.format.mimetypeapplication/pdfen
dc.language.isoengen
dc.subjectInfinite-dimensional Hamiltonian systemsen
dc.subjectKrein-Moser theoremen
dc.subjectLandau dampingen
dc.subjectCaldeira-Leggett modelen
dc.subjectHilbert transformen
dc.subjectVlasov-Poisson equationen
dc.titleInfinite-dimensional Hamiltonian systems with continuous spectra : perturbation theory, normal forms, and Landau dampingen
dc.date.updated2011-10-28T17:51:47Zen
dc.identifier.slug2152/ETD-UT-2011-08-3753en
dc.contributor.committeeMemberHazeltine, Richard D.en
dc.contributor.committeeMemberHorton, Wendellen
dc.contributor.committeeMemberGamba, Irene M.en
dc.contributor.committeeMemberde la Llave, Rafaelen
dc.description.departmentPhysicsen
dc.type.genrethesisen
thesis.degree.departmentPhysicsen
thesis.degree.disciplinePhysicsen
thesis.degree.grantorUniversity of Texas at Austinen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen


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