Coherence and decoherence processes of a harmonic oscillator coupled with finite temperature field: exact eigenbasis solution of Kossakowski-Linblad's equation

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dc.contributor.advisorPetrosky, Tomio Y.en
dc.creatorTay, Buang Annen
dc.date.accessioned2008-08-28T22:38:17Zen
dc.date.accessioned2017-05-11T22:17:03Z
dc.date.available2008-08-28T22:38:17Zen
dc.date.available2017-05-11T22:17:03Z
dc.date.issued2004en
dc.descriptiontexten
dc.description.abstractThe eigenvalue problem of Kossakowski-Linblad’s kinetic equation associated with the reduced density matrix of a harmonic oscillator interacting with a thermal bath in equilibrium is solved. The solution gives rise to a complete orthogonal eigenbasis endowed with Hilbert space structure that has a weighted norm. We find that the eigenfunctions at finite temperature can be obtained from the eigenfunction at zero temperature through a hyperbolic rotation on the position variables. This transformation enables the extension of the simple harmonic oscillator density matrix to that of a finite temperature. We further investigate the decay of these extended states under our dissipative kinetic equation. Furthermore, the Hilbert space structure enables the proof of a H-theorem in this system. We apply the eigenbasis expansion of an initial state to analyze decohorence as well as coherence processes. We find that coherence process occurs at a longer time scale compared to decoherence process. The time scales of both processes are estimated with the eigenbasis expansion. In the same way we analyze the evolution of the coherent state. We show that in addition to the ordinary decay time, we found another time scale which is defined by the time when the motion of the peak of the coherent state become comparative to the width of the coherent state. In contrast to the ordinary decay time this new relaxation time depends on the initial value of the momentum of the oscillator. We also find that our eigenbasis is applicable to a class of non-linear interactions, with a slight extension of the form of transport coefficients due to the non-linear interactions.
dc.description.departmentPhysicsen
dc.format.mediumelectronicen
dc.identifierb60875343en
dc.identifier.oclc69372836en
dc.identifier.proqst3145809en
dc.identifier.urihttp://hdl.handle.net/2152/2218en
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.lcshKossakowski-Limblad's problemen
dc.subject.lcshEigenvaluesen
dc.subject.lcshEigenfunctionsen
dc.subject.lcshHarmonic oscillatorsen
dc.subject.lcshCoherent statesen
dc.subject.lcshDensity matricesen
dc.titleCoherence and decoherence processes of a harmonic oscillator coupled with finite temperature field: exact eigenbasis solution of Kossakowski-Linblad's equationen
dc.type.genreThesisen

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