A bound on chaos
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 outoftimeorder 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 λ_{ L } ≤ 2π k _{ B } T/ℏ. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.
 Publication:

Journal of High Energy Physics
 Pub Date:
 August 2016
 DOI:
 10.1007/JHEP08(2016)106
 arXiv:
 arXiv:1503.01409
 Bibcode:
 2016JHEP...08..106M
 Keywords:

 1/N Expansion;
 Black Holes;
 AdSCFT Correspondence;
 High Energy Physics  Theory;
 Condensed Matter  Statistical Mechanics;
 Nonlinear Sciences  Chaotic Dynamics;
 Quantum Physics
 EPrint:
 16+6 pages, 2 figures