Investigations of transport phenomena and dynamical relaxation in closed quantum systems
| Autor: | Khodja, Abdellah |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
transport coefficients
Boltzmann equation eigenstate thermalization hypothesis 33.28 - Transportvorgänge irreversible Thermodynamik 33.23 - Quantenphysik 33.10 - Theoretische Physik: Allgemeines 33.66 - Amorpher Zustand Gläser 72.15.Cz - Electrical and thermal conduction in amorphous and liquid metals and alloys 72.25.Rb - Spin relaxation and scattering ddc:530 |
| Druh dokumentu: | Doctoral Thesis |
| Popis: | The 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. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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