Out-of-time-order fluctuation-dissipation theorem

TL;DR

This paper proves a generalized fluctuation-dissipation theorem for out-of-time-ordered correlators in quantum systems, linking quantum chaos and nonlinear response through a modified statistical average involving bipartite OTOCs.

Contribution

It introduces a new fluctuation-dissipation relation for bipartite OTOCs, connecting quantum chaos with nonlinear response functions in thermal equilibrium.

Findings

Derived a universal relation between chaos and nonlinear response.

Quantified the difference between bipartite and physical OTOCs using Wigner-Yanase skew information.

Extended the theorem to higher-order n-partite OTOCs.

Abstract

We prove a generalized fluctuation-dissipation theorem for a certain class of out-of-time-ordered correlators (OTOCs) with a modified statistical average, which we call bipartite OTOCs, for general quantum systems in thermal equilibrium. The difference between the bipartite and physical OTOCs defined by the usual statistical average is quantified by a measure of quantum fluctuations known as the Wigner-Yanase skew information. Within this difference, the theorem describes a universal relation between chaotic behavior in quantum systems and a nonlinear-response function that involves a time-reversed process. We show that the theorem can be generalized to higher-order $n$-partite OTOCs as well as in the form of generalized covariance.