Condensed Matter Physics Seminar

Speaker: Marcos Rigol, Pennsylvania State University

Title: From unitary dynamics to statistical mechanics in isolated quantum systems

Refreshments available at 3:45 pm.

Date: Mon, 01 Oct 2018, 4:10 pm – 5:10 pm
Type: Seminar
Location: 1400 BPS Bldg.

Abstract:
Recently, experiments with ultra­cold gases have made it poss­ible to study dy­namics of (nearly) iso­lated many-body quan­tum sys­tems. This has revived theo­retical inter­est on this topic [1]. In generic isolated sys­tems, one ex­pects non­equilib­rium dy­namics to re­sult in thermal­ization, namely, equili­bration to states in which observ­ables are station­ary, uni­versal with re­spect to widely differ­ing initial con­ditions, and pre­dictable through the time-tested recipe of statis­tical mechanics. How­ever, it is not obvious what fea­ture of a many-body sys­tem makes quantum thermal­ization poss­ible, in a sense anal­ogous to that in which dynamical chaos makes classical thermal­ization poss­ible. Under­scoring that new rules could apply in the quantum case, experi­mental studies in one-dimen­sional sys­tems have shown that tradi­tional statis­tical mechanics can provide wrong pre­dictions for the out­comes of equili­bration dynamics. We argue that generic iso­lated quantum sys­tems do in fact equili­brate to states in which observ­ables are described by statis­tical mechanics [2]. More­over, we show that time evo­lu­tion itself plays a merely auxil­iary role as thermal­ization hap­pens at the level of indi­vidual eigen­states. We also dis­cuss what hap­pens at integra­bility points, where a dif­ferent set of rules apply [3].

References:
[1] L. D'Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol. From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics. Adv. Phys. 65, 239-362 (2016).
[2] M. Rigol, V. Dunjko, and M. Olshanii. Thermalization and its mechanism for generic isolated quantum systems. Nature 452, 854 (2008).
[3] L. Vidmar and M. Rigol. Generalized Gibbs ensemble in integrable lattice models. J. Stat. Mech. 064007 (2016).