Subleading Bounds on Chaos
Abstract
Chaos, in quantum systems, can be diagnosed by certain outoftimeorder correlators (OTOCs) that obey the chaos bound of Maldacena, Shenker, and Stanford (MSS). We begin by deriving a dispersion relation for this class of OTOCs, implying that they must satisfy many more constraints beyond the MSS bound. Motivated by this observation, we perform a systematic analysis obtaining an infinite set of constraints on the OTOC. This infinite set includes the MSS bound as the leading constraint. In addition, it also contains subleading bounds that are highly constraining, especially when the MSS bound is saturated. These new bounds, among other things, imply that the MSS bound cannot be exactly saturated over any duration of time, however short. Furthermore, we derive a sharp bound on the Lyapunov exponent $\lambda_2 \le \frac{6\pi}{\beta}$ of the subleading correction to maximal chaos.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.03826
 Bibcode:
 2021arXiv210903826K
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Statistical Mechanics;
 General Relativity and Quantum Cosmology;
 Nonlinear Sciences  Chaotic Dynamics;
 Quantum Physics
 EPrint:
 34 pages, 5 figures