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dc.contributor.authorD'Alessio, Lucaen_US
dc.contributor.authorKafri, Yariven_US
dc.contributor.authorPolkovnikov, Anatolien_US
dc.contributor.authorRigol, Marcosen_US
dc.date.accessioned2019-06-11T15:01:04Z
dc.date.available2019-06-11T15:01:04Z
dc.date.issued2016-01-01
dc.identifierhttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000380760000001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=6e74115fe3da270499c3d65c9b17d654
dc.identifier.citationLuca D'Alessio, Yariv Kafri, Anatoli Polkovnikov, Marcos Rigol. 2016. "From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics." ADVANCES IN PHYSICS, Volume 65, Issue 3, pp. 239 - 362 (124). https://doi.org/10.1080/00018732.2016.1198134
dc.identifier.issn0001-8732
dc.identifier.issn1460-6976
dc.identifier.urihttps://hdl.handle.net/2144/35967
dc.description.abstractThis review gives a pedagogical introduction to the eigenstate thermalization hypothesis (ETH), its basis, and its implications to statistical mechanics and thermodynamics. In the first part, ETH is introduced as a natural extension of ideas from quantum chaos and random matrix theory (RMT). To this end, we present a brief overview of classical and quantum chaos, as well as RMT and some of its most important predictions. The latter include the statistics of energy levels, eigenstate components, and matrix elements of observables. Building on these, we introduce the ETH and show that it allows one to describe thermalization in isolated chaotic systems without invoking the notion of an external bath. We examine numerical evidence of eigenstate thermalization from studies of many-body lattice systems. We also introduce the concept of a quench as a means of taking isolated systems out of equilibrium, and discuss results of numerical experiments on quantum quenches. The second part of the review explores the implications of quantum chaos and ETH to thermodynamics. Basic thermodynamic relations are derived, including the second law of thermodynamics, the fundamental thermodynamic relation, fluctuation theorems, the fluctuation–dissipation relation, and the Einstein and Onsager relations. In particular, it is shown that quantum chaos allows one to prove these relations for individual Hamiltonian eigenstates and thus extend them to arbitrary stationary statistical ensembles. In some cases, it is possible to extend their regimes of applicability beyond the standard thermal equilibrium domain. We then show how one can use these relations to obtain nontrivial universal energy distributions in continuously driven systems. At the end of the review, we briefly discuss the relaxation dynamics and description after relaxation of integrable quantum systems, for which ETH is violated. We present results from numerical experiments and analytical studies of quantum quenches at integrability. We introduce the concept of the generalized Gibbs ensemble and discuss its connection with ideas of prethermalization in weakly interacting systems.en_US
dc.description.sponsorshipThis work was supported by the Army Research Office [grant number W911NF1410540] (L.D., A.P, and M.R.), the U.S.-Israel Binational Science Foundation [grant number 2010318] (Y.K. and A.P.), the Israel Science Foundation [grant number 1156/13] (Y.K.), the National Science Foundation [grant numbers DMR-1506340 (A.P.)and PHY-1318303 (M.R.)], the Air Force Office of Scientific Research [grant number FA9550-13-1-0039] (A.P.), and the Office of Naval Research [grant number N000141410540] (M.R.). The computations were performed in the Institute for CyberScience at Penn State. (W911NF1410540 - Army Research Office; 2010318 - U.S.-Israel Binational Science Foundation; 1156/13 - Israel Science Foundation; DMR-1506340 - National Science Foundation; PHY-1318303 - National Science Foundation; FA9550-13-1-0039 - Air Force Office of Scientific Research; N000141410540 - Office of Naval Research)en_US
dc.format.extentp. 239 - 362en_US
dc.languageEnglish
dc.language.isoen_US
dc.publisherTAYLOR & FRANCIS LTDen_US
dc.relation.ispartofADVANCES IN PHYSICS
dc.subjectScience & technologyen_US
dc.subjectPhysical sciencesen_US
dc.subjectPhysics, condensed matteren_US
dc.subjectQuantum statistical mechanicsen_US
dc.subjectEigenstate thermalizationen_US
dc.subjectQuantum chaosen_US
dc.subjectRandom matrix theoryen_US
dc.subjectQuantum quenchen_US
dc.subjectQuantum thermodynamicsen_US
dc.subjectGeneralized Gibbs ensembleen_US
dc.subjectFree-energy differencesen_US
dc.subjectDependent potential wellen_US
dc.subjectFinite Fermi systemsen_US
dc.subjectRandom-matrix modelen_US
dc.subject2nd lawen_US
dc.subjectCharacteristic vectorsen_US
dc.subjectConservative-systemsen_US
dc.subjectInfinite dimensionsen_US
dc.subjectFluctuation theoremen_US
dc.subjectOscillator systemsen_US
dc.subjectCondensed matter physicsen_US
dc.subjectQuantum physicsen_US
dc.subjectFluids & plasmasen_US
dc.titleFrom quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamicsen_US
dc.typeArticleen_US
dc.description.versionAccepted manuscripten_US
dc.identifier.doi10.1080/00018732.2016.1198134
pubs.elements-sourceweb-of-scienceen_US
pubs.notesEmbargo: Not knownen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Arts & Sciencesen_US
pubs.organisational-groupBoston University, College of Arts & Sciences, Department of Physicsen_US
pubs.publication-statusPublisheden_US
dc.identifier.orcid0000-0002-5549-7400 (Polkovnikov, Anatoli)
dc.identifier.mycv54851


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