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Investigations of transport phenomena and dynamical relaxation in closed quantum systems

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https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2015031713128
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dc.contributor.advisorProf. Dr. Jochen Gemmer
dc.creatorKhodja, Abdellah
dc.date.accessioned2015-03-17T10:52:45Z
dc.date.available2015-03-17T10:52:45Z
dc.date.issued2015-03-17T10:52:45Z
dc.identifier.urihttps://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2015031713128-
dc.description.abstractThe first part of the present Phd thesis is devoted to transport investigations in disordered quantum systems. We aim at quantitatively determining transport parameters like conductivity, mean free path, etc., for simple models of spatially disordered and/or percolated quantum systems in the limit of high temperatures and low fillings using linear response theory. We find the transport behavior for some models to be in accord with a Boltzmann equation, i.e., long mean free paths, exponentially decaying currents although there are no band-structures to start from, while this does not apply to other models even though they are also almost completely delocalized. The second part of the present PhD thesis addresses the issue of initial state independence (ISI) in closed quantum system. The relevance of the eigenstate thermalization hypothesis (ETH) for the emergence of ISI equilibration is to some extent addressed. To this end, we investigate the Heisenberg spin-ladder and check the validity of the ETH for the energy difference operator by examining the scaling behavior of the corresponding ETH-fluctuations, which we compute using an innovative numerical method based on typicality related arguments. While, the ETH turns out to hold for the generic non-integrable models and may therefore serve as the key mechanism for ISI for this cases, it does not hold for the integrable Heisenberg-chain. However, close analysis on the dynamic of substantially out-of-equilibrium initial states indicates the occurrence of ISI equillibration in the thermodynamic limit regardless of whether the ETH is violated. Thus, we introduce a new parameter $v$, which we propose as an alternative of the ETH to indicate ISI equillibration in cases, in which the ETH does not strictly apply.eng
dc.rightsNamensnennung 3.0 Unported-
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/-
dc.subjecttransport coefficientseng
dc.subjectBoltzmann equationeng
dc.subjecteigenstate thermalization hypothesiseng
dc.subject.ddc530 - Physik
dc.titleInvestigations of transport phenomena and dynamical relaxation in closed quantum systemseng
dc.typeDissertation oder Habilitation [doctoralThesis]-
thesis.locationOsnabrück-
thesis.institutionUniversität-
thesis.typeDissertation [thesis.doctoral]-
thesis.date2015-03-10-
dc.contributor.refereeProf. Dr. Phillip Maaß
dc.subject.bk33.28 - Transportvorgänge, irreversible Thermodynamik
dc.subject.bk33.23 - Quantenphysik
dc.subject.bk33.10 - Theoretische Physik: Allgemeines
dc.subject.bk33.66 - Amorpher Zustand, Gläser
dc.subject.pacs72.15.Cz - Electrical and thermal conduction in amorphous and liquid metals and alloys
dc.subject.pacs72.25.Rb - Spin relaxation and scattering
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