Quantum chaos and electron transport properties in a quantum waveguide

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dc.contributor.advisorReichl, L. E.en
dc.creatorLee, Hoshik, 1975-en
dc.date.accessioned2008-08-29T00:18:55Zen
dc.date.accessioned2017-05-11T22:19:27Z
dc.date.available2008-08-29T00:18:55Zen
dc.date.available2017-05-11T22:19:27Z
dc.date.issued2008-05en
dc.descriptiontexten
dc.description.abstractWe numerically investigate electron transport properties in an electron waveguide which can be constructed in 2DEG of the heterostructure of GaAs and AlGaAs. We apply R-matrix theory to solve a Schrödinger equation and construct a S-matrix, and we then calculate conductance of an electron waveguide. We study single impurity scattering in a waveguide. A [delta]-function model as a single impurity is very attractive, but it has been known that [delta]-function potential does not give a convergent result in two or higher space dimensions. However, we find that it can be used as a single impurity in a waveguide with the truncation of the number of modes. We also compute conductance for a finite size impurity by using R-matrix theory. We propose an appropriate criteria for determining the cut-off mode for a [delta]-function impurity that reproduces the conductance of a waveguide when a finite impurity presents. We find quantum scattering echoes in a ripple waveguide. A ripple waveguide (or cavity) is widely used for quantum chaos studies because it is easy to control a particle's dynamics. Moreover we can obtain an exact expression of Hamiltonian matrix with for the waveguide using a simple coordinate transformation. Having an exact Hamiltonian matrix reduces computation time significantly. It saves a lot of computational needs. We identify three families of resonance which correspond to three different classical phase space structures. Quasi bound states of one of those resonances reside on a hetero-clinic tangle formed by unstable manifolds and stable manifolds in the phase space of a corresponding classical system. Resonances due to these states appear in the conductance in a nearly periodic manner as a function of energy. Period from energy frequency gives a good agreement with a prediction of the classical theory. We also demonstrate wavepacket dynamics in a ripple waveguide. We find quantum echoes in the transmitted probability of a wavepacket. The period of echoes also agrees with the classical predictions. We also compute the electron transmission probability through a multi-ripple electron waveguide. We find an effect analogous to the Dicke effect in the multi-ripple electron waveguide. We show that one of the S-matrix poles, that of the super-radiant resonance state, withdraws further from the real axis as each ripple is added. The lifetime of the super-radiant state, for N quantum dots, decreases as [1/N] . This behavior of the lifetime of the super-radiant state is a signature of the Dicke effect.en
dc.description.departmentPhysicsen
dc.format.mediumelectronicen
dc.identifierb70670249en
dc.identifier.oclc243863152en
dc.identifier.urihttp://hdl.handle.net/2152/3914en
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.lcshScattering (Physics)--Mathematical modelsen
dc.subject.lcshElectron transport--Mathematical modelsen
dc.subject.lcshWave guidesen
dc.subject.lcshQuantum chaosen
dc.subject.lcshMatrix mechanicsen
dc.titleQuantum chaos and electron transport properties in a quantum waveguideen
dc.type.genreThesisen

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