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FIDELITY:
A QUANTUM INFORMATION-THEORETIC APPROACH TO PROBLEMS IN
CONDENSED MATTER PHYSICS AND QUANTUM CHAOS
by
Noah Tobias Jacobson
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(PHYSICS)
August 2011
Copyright 2011 Noah Tobias Jacobson
Object Description
| Title | Fidelity: A quantum information-theoretic approach to problems in condensed matter physics and quantum chaos |
| Author | Jacobson, Noah Tobias |
| Author email | ntj@usc.edu;tobyjacobson@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Physics |
| School | College of Letters, Arts And Sciences |
| Date defended/completed | 2011-05-09 |
| Date submitted | 2011-07-26 |
| Date approved | 2011-07-26 |
| Restricted until | 2011-07-26 |
| Date published | 2011-07-26 |
| Advisor (committee chair) | Zanardi, Paolo |
| Advisor (committee member) |
Haas, Stephan Lidar, Daniel Brun, Todd Jonckheere, Edmond |
| Abstract | In this dissertation, we address several problems in condensed matter physics, statistical mechanics, and quantum chaos from the perspective of the quantum information-theoretic notion of state distinguishability, as measured though evaluation of the appropriate fidelity measure. ❧ We find that the fidelity susceptibility, a measure for the response of the fidelity to infinitesimal changes of the Hamiltonian parameters, serves as a useful tool for studying the effects of disorder on quantum phase transitions. We study in detail the phase diagram of the well-known one-dimensional random quantum XY chain. Through an analysis of the fidelity susceptibility’s finite-size scaling and statistics for this model, we find that the fidelity approach reflects large variation between average and typical behavior, may detect the presence of Griffiths phases, and indicates the modifications to the phase diagram due to disorder. ❧ For this same model, though without disorder, we evaluate the dynamics following a sudden Hamiltonian quench using the Loschmidt echo, a form of the fidelity that compares the initial state with the time-evolved state. Through a central limit theorem-type argument we find that the long-time statistics of the Loschmidt echo takes one of two universal forms, even at finite temperature, depending on the system’s proximity to the quantum critical lines. ❧ Finally, for a canonical model exhibiting quantum chaos, the hydrogen atom in a uniform external magnetic field, we evaluate the operator fidelity susceptibility (OFS) between unitary operators generating the dynamics. We find that the part of the OFS which corresponds to the variation of the Hamiltonian eigenvectors serves to indicate the transition from the regular perturbative and n-mixing regimes to the quantum chaotic regime. |
| Keyword | fidelity; quantum phase transition; quantum chaos; Loschmidt echo; disorder; equilibration |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m |
| Rights | Jacobson, Noah Tobias |
| Access conditions | The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given. |
| Repository name | University of Southern California Digital Library |
| Repository address | USC Digital Library, University of Southern California, University Park Campus MC 7002, 106 University Village, Los Angeles, California 90089-7002, USA |
| Repository email | cisadmin@usc.edu |
| Archival file | uscthesesreloadpub_Volume71/etd-JacobsonNo-176.pdf |
Description
| Title | Page 1 |
| Full text | FIDELITY: A QUANTUM INFORMATION-THEORETIC APPROACH TO PROBLEMS IN CONDENSED MATTER PHYSICS AND QUANTUM CHAOS by Noah Tobias Jacobson A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (PHYSICS) August 2011 Copyright 2011 Noah Tobias Jacobson |
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