Floquet theory and continued fractions for harmonically driven systems

dc.contributor.advisorReichl, L. E.en
dc.creatorMartinez Mantilla, Dario Fernandoen
dc.date.accessioned2008-08-28T21:33:52Zen
dc.date.available2008-08-28T21:33:52Zen
dc.date.issued2003en
dc.descriptiontexten
dc.description.abstractWe derive an exact solution using continued fractions for a quantum particle scattering from an oscillating delta-function potential. We study its transmission properties such as: Transmission zeros, transmission poles and threshold anomalies. Using the same technique and a translation matrix method, we study the problem of an infinite chain of oscillating deltas. We calculate its band structure and eigenstates and show explicitly the contribution to these eigenstates from the quasi-bound state of a single oscillating delta. We study the dynamics of the quasi-energy bands of the system as a function of the strength of the oscillation and show band quasi-periodicity and band collapse. We also define the Floquet-Green’s function for a time-periodic Hamiltonian and by a generalization of the method used for the two previous potentials we are able to derive an expression for the Floquet-Green’s function of any harmonically driven Hamiltonian. As an example of the application of this method we study a tight-binding Hamiltonian with harmonic time dependence.
dc.description.departmentPhysicsen
dc.format.mediumelectronicen
dc.identifierb57157170en
dc.identifier.oclc56799216en
dc.identifier.proqst3116382en
dc.identifier.urihttp://hdl.handle.net/2152/756en
dc.language.isoengen
dc.rightsCopyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.en
dc.subject.lcshFloquet theoryen
dc.subject.lcshContinued fractionsen
dc.subject.lcshQuantum theoryen
dc.titleFloquet theory and continued fractions for harmonically driven systemsen
dc.type.genreThesisen
thesis.degree.departmentPhysicsen
thesis.degree.disciplinePhysicsen
thesis.degree.grantorThe University of Texas at Austinen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen
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