Subleading Bounds on Chaos
arXiv:2109.03826 · doi:10.1007/JHEP04(2022)010
Abstract
Chaos, in quantum systems, can be diagnosed by certain out-of-time-order 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 by the leading term. 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 of the subleading correction to maximal chaos.
arXiv comment35 pages, 5 figures; In v2 it has been clarified that the MSS bound and its generalizations can be derived from a weaker factorization assumption
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