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A bound on chaos

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Aug 2016Embargo end date: 01 Jan 2015Publisher:Springer Science and Business Media LLCJournal:Journal of High Energy Physics, volume 2,016 (eissn: 1029-8479,

Authors: Maldacena, Juan; Shenker, Stephen; Stanford, Douglas;

doi: 10.1007/jhep08(2016)106 , 10.48550/arxiv.1503.01409

arXiv: http://arxiv.org/abs/1503.01409

A bound on chaos

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Abstract

We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent $��_L \le 2 ��k_B T/\hbar$. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.

16+6 pages, 2 figures

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Keywords

High Energy Physics - Theory, Nuclear and High Energy Physics, Quantum Physics, High Energy Physics - Theory (hep-th), Statistical Mechanics (cond-mat.stat-mech), FOS: Physical sciences, Chaotic Dynamics (nlin.CD), Nonlinear Sciences - Chaotic Dynamics, Quantum Physics (quant-ph), Condensed Matter - Statistical Mechanics

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