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CC BY V4.0, Open Access
Dissertation
QUANTUM STATISTICAL PHYSICS OF WEAKLY COUPLED CHAOTIC SYSTEMS: PERTURBATION THEORY, ENTANGLEMENT, QUANTUM COHERENCE, EQUILIBRATION, AND THERMALIZATION
Washington State University
Doctor of Philosophy (PhD), Washington State University
05/2024
DOI:
https://doi.org/10.7273/000006541
Abstract
A bipartite system whose subsystems are quantum chaotic and coupled via an entangling interaction with a tunable strength is a paradigmatic model to explore nonequilibrium phenomena. Using this generic model various interesting problems are explored in this thesis research.
Conventional entanglement measures for bipartite systems can be expressed in terms of Schmidt eigenvalues. A perturbation theory for computing the Schmidt eigenvalues and associated eigenvectors of Floquet and Hamiltonian systems can be derived in the spirit of standard Rayleigh-Schrödinger approach, including a regularization to handle small Schmidt eigenvalue denominators.
It is found that the quantum coherence of the initial state relative to the preferred subsystem eigenbases — quantified by the off-diagonal elements of the subsystem density matrices — acts as a resource for equilibration and thermalization as embodied by the entanglement generated when time evolved. Based on the entangling interaction strength, four distinct perturbation regimes can be conceived: ultraweak, weak, intermediate, and strong. In addition, hinging on the quantum coherence endowed by an initial state, various initial state ensembles are considered. A universal timescale involving the interaction strength valid for any initial state is identified, enabling one to cast the theory in a universal form. For initial states with vanishing coherence, it was found that the average entanglement generated is negligibly small for weak regimes, and system fails to equilibrate. However, in the limit of maximal initial state coherence, the average entanglement generated becomes maximal, and the system thermalizes, even when the interaction between the subsystems is ultraweak. This is a remarkable result, given that the eigenstates are not all thermal-like, providing an alternative path to thermalization than from the famous eigenstate thermalization hypothesis. In addition, in the ultraweak regime, the initial states with maximal coherence show a dominant quadratic-in-time entanglement growth, in contrast to widely observed linear-in-time behavior.
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Details
- Title
- QUANTUM STATISTICAL PHYSICS OF WEAKLY COUPLED CHAOTIC SYSTEMS
- Creators
- Jethin Pulikkottil Jacob
- Contributors
- Steven L Tomsovic (Chair)Peter W Engels (Committee Member)Michael McNeil Forbes (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Physics and Astronomy, Department of
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Publisher
- Washington State University
- Number of pages
- 224
- Identifiers
- 99901121437201842
- Language
- English
- Resource Type
- Dissertation