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Topics in classical and quantum integrability
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Title
Topics in classical and quantum integrability
Name
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Scaramazza
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Jasen A.
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1990-
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Jasen A. Scaramazza
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author
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Yuzbashyan
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Emil A
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Emil A Yuzbashyan
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Advisory Committee
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chair
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Lebowitz
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Joel L
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Joel L Lebowitz
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Advisory Committee
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co-chair
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Zamick
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Larry
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Larry Zamick
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Advisory Committee
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internal member
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Gershenson
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Michael
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Michael Gershenson
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Advisory Committee
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internal member
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Ling
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Hong Y
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Hong Y Ling
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Advisory Committee
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Rutgers University
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School of Graduate Studies
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theses
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2019
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2019-05
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English
Abstract
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This Thesis is an amalgamation of research I conducted as a physics graduate student at Rutgers University. Each chapter stands independently of the others with its own introduction and set of references, though Chapters 4 and 5 treat the same subject and may be read in succession. The chapters are presented roughly in reverse chronological order, so that the first chapters are my most recent work.
The common threads of this research program are the statistical and dynamical properties of many body systems, both in and out of equilibrium. Save for Chapter 6, the works are strongly associated with physical models called integrable, whose Hamiltonians have a comparatively large number of conservation laws with respect to generic models. Using numerical and analytical techniques, we shall explore the effects of integrability on a diverse set of phenomena including far-from-equilibrium steady states in Chapter 2, heat conductivity in Chapter 3, and Hamiltonian level statistics in Chapters 4-5. We also characterize these phenomena for systems that are not quite integrable, but are in certain ways close to integrable.
The chapters in this Thesis are based on the following works:
J. A. Scaramazza, P. Smacchia, and E. A. Yuzbashyan, Consequences of integrability breaking in quench dynamics of pairing Hamiltonians, Accepted by Phys. Rev. B Jan. 2019.
J. L. Lebowitz and J. A. Scaramazza, Ballistic Transport in the classical Toda chain with harmonic pinning, arXiv:1801.07153 (2018).
A. Dhar, A. Kundu, J. L. Lebowitz and J. A. Scaramazza, Transport properties of the classical Toda chain: effect of a pinning potential, arXiv:1812.11770 (2018). Submitted to J. Stat. Phys. Jan. 2019.
E. A. Yuzbashyan, B. S. Shastry and J. A. Scaramazza, Rotationally invariant ensembles of integrable matrices, Phys. Rev. E 93, 052114 (2016).
J. A. Scaramazza, B. S. Shastry and E. A. Yuzbashyan, Integrable matrix theory: Level statistics, Phys. Rev. E 94, 032106 (2016).
J. L. Lebowitz and J. A. Scaramazza, A note on Lee-Yang zeros in the negative half-plane, J. Phys.: Condens. Matter 28, 414004 (2016).
The common threads of this research program are the statistical and dynamical properties of many body systems, both in and out of equilibrium. Save for Chapter 6, the works are strongly associated with physical models called integrable, whose Hamiltonians have a comparatively large number of conservation laws with respect to generic models. Using numerical and analytical techniques, we shall explore the effects of integrability on a diverse set of phenomena including far-from-equilibrium steady states in Chapter 2, heat conductivity in Chapter 3, and Hamiltonian level statistics in Chapters 4-5. We also characterize these phenomena for systems that are not quite integrable, but are in certain ways close to integrable.
The chapters in this Thesis are based on the following works:
J. A. Scaramazza, P. Smacchia, and E. A. Yuzbashyan, Consequences of integrability breaking in quench dynamics of pairing Hamiltonians, Accepted by Phys. Rev. B Jan. 2019.
J. L. Lebowitz and J. A. Scaramazza, Ballistic Transport in the classical Toda chain with harmonic pinning, arXiv:1801.07153 (2018).
A. Dhar, A. Kundu, J. L. Lebowitz and J. A. Scaramazza, Transport properties of the classical Toda chain: effect of a pinning potential, arXiv:1812.11770 (2018). Submitted to J. Stat. Phys. Jan. 2019.
E. A. Yuzbashyan, B. S. Shastry and J. A. Scaramazza, Rotationally invariant ensembles of integrable matrices, Phys. Rev. E 93, 052114 (2016).
J. A. Scaramazza, B. S. Shastry and E. A. Yuzbashyan, Integrable matrix theory: Level statistics, Phys. Rev. E 94, 032106 (2016).
J. L. Lebowitz and J. A. Scaramazza, A note on Lee-Yang zeros in the negative half-plane, J. Phys.: Condens. Matter 28, 414004 (2016).
Subject
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Topic
Condensed matter physics
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Physics and Astronomy
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Rutgers University Electronic Theses and Dissertations
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Ph.D.
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Includes bibliographical references
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School of Graduate Studies Electronic Theses and Dissertations
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ETD doctoral
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Rights
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The author owns the copyright to this work.
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Name
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Scaramazza
GivenName
Jasen
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A.
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2019-03-17 11:30:28
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Jasen Scaramazza
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Rutgers University. School of Graduate Studies
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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