Alexandria Digital Research Library

Thermalization and its breakdown in isolated quantum systems

Author:
Garrison, James Robert
Degree Grantor:
University of California, Santa Barbara. Physics
Degree Supervisor:
Matthew P. A. Fisher
Place of Publication:
[Santa Barbara, Calif.]
Publisher:
University of California, Santa Barbara
Creation Date:
2016
Issued Date:
2016
Topics:
Condensed matter physics and Theoretical physics
Keywords:
Quantum mechanics
Eigenstate thermalization hypothesis
Statistical mechanics
Thermalization
Genres:
Dissertations, Academic and Online resources
Dissertation:
Ph.D.--University of California, Santa Barbara, 2016
Description:

A very fundamental problem in quantum statistical mechanics involves whether---and how---an isolated quantum system will reach thermal equilibrium after waiting a long time. In quantum systems that do thermalize, the long-time expectation value of any "reasonable" operator will match its predicted value in the canonical ensemble. The Eigenstate Thermalization Hypothesis (ETH) posits that this thermalization occurs at the level of each individual energy eigenstate; in fact, any single eigenstate in a microcanonical energy window will predict the expectation values of such operators exactly. In the first part of this dissertation, we identify, for a generic model system, precisely which operators satisfy ETH, as well as limits to the information contained in a single eigenstate. Remarkably, our results strongly suggest that a single eigenstate can contain information about energy densities---and therefore temperatures---far away from the energy density of the eigenstate.

Additionally, we study the possible breakdown of quantum thermalization in a model of itinerant electrons on a one-dimensional chain, with both spin and charge degrees of freedom. This model exhibits peculiar properties in the entanglement entropy, the apparent scaling of which is modified from a "volume law" to an "area law" after performing a partial, site-wise measurement on the system. These properties and others suggest that this model realizes a new, non-thermal phase of matter, known as a Quantum Disentangled Liquid (QDL). The putative existence of this phase has striking implications for the foundations of quantum statistical mechanics.

Physical Description:
1 online resource (159 pages)
Format:
Text
Collection(s):
UCSB electronic theses and dissertations
ARK:
ark:/48907/f3gt5n8r
ISBN:
9781369147346
Catalog System Number:
990046968400203776
Rights:
Inc.icon only.dark In Copyright
Copyright Holder:
James Garrison
File Description
Access: Public access
Garrison_ucsb_0035D_13084.pdf pdf (Portable Document Format)