PMID: 22587163May 17, 2012Paper

Onset of chaos and relaxation in isolated systems of interacting spins: energy shell approach

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Lea F SantosF M Izrailev

Abstract

We study the onset of chaos and statistical relaxation in two isolated dynamical quantum systems of interacting spins 1/2, one of which is integrable and the other chaotic. Our approach to identifying the emergence of chaos is based on the level of delocalization of the eigenstates with respect to the energy shell, the latter being determined by the interaction strength between particles or quasiparticles. We also discuss how the onset of chaos may be anticipated by a careful analysis of the Hamiltonian matrices, even before diagonalization. We find that despite differences between the two models, their relaxation processes following a quench are very similar and can be described analytically with a theory previously developed for systems with two-body random interactions. Our results imply that global features of statistical relaxation depend on the degree of spread of the eigenstates within the energy shell and may happen to both integrable and nonintegrable systems.

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Citations

Nov 1, 2017·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·E J Torres-Herrera, Lea F Santos
Sep 17, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·H N DeotaManan Vyas
Oct 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Pablo R ZangaraLea F Santos
Feb 4, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Quntao Zhuang, Biao Wu
Feb 17, 2018·Physical Review. E·S RayS Sinha
Feb 20, 2019·Physical Review. E·Fausto Borgonovi, Felix M Izrailev
Nov 28, 2019·Physical Review. E·Emiliano M FortesDiego A Wisniacki
Oct 24, 2019·Physical Review. E·Arnd BäckerIvan M Khaymovich
Feb 14, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Wouter BeugelingMasudul Haque
May 17, 2017·Physical Review. E·Fausto BorgonoviFelix M Izrailev
Jul 18, 2018·Physical Review. E·Jiaozi Wang, Wen-Ge Wang
Dec 25, 2019·Physical Review. E·Eric G ArraisFabricio Toscano
Feb 14, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ignacio García-MataDiego A Wisniacki
Sep 19, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tatsuhiko N Ikeda, Masahito Ueda
Sep 27, 2018·Physical Review. E·Wouter BeugelingMasudul Haque
Feb 20, 2019·Physical Review. E·Fausto BorgonoviLea F Santos
Feb 20, 2019·Physical Review. E·Alberto D Verga
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Jul 16, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·E J Torres-Herrera, Lea F Santos
Mar 4, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·B V FineA S de Wijn
Nov 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·E J Torres-Herrera, Lea F Santos
Mar 20, 2021·Physical Review. E·Nicolás Mirkin, Diego Wisniacki

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