Chaos signatures in the short and long time behavior of the out-of-time ordered correlator

TL;DR

This paper investigates how out-of-time order correlators (OTOCs) reveal chaos signatures in quantum maps, showing exponential approach to stationarity governed by classical chaos features like Ruelle-Pollicot resonances.

Contribution

It demonstrates that the long-time behavior of OTOCs in quantum maps is governed by classical chaos indicators, extending understanding beyond short-time Lyapunov exponent analysis.

Findings

OTOCs approach stationary value exponentially

Rate determined by Ruelle-Pollicot resonances

Classical chaos influences quantum correlator dynamics

Abstract

Two properties are needed for a classical system to be chaotic: exponential stretching and mixing. Recently, out-of-time order correlators were proposed as a measure of chaos in a wide range of physical systems. While most of the attention has previously been devoted to the short time stretching aspect of chaos, characterized by the Lyapunov exponent, we show for quantum maps that the out-of-time correlator approaches its stationary value exponentially with a rate determined by the Ruelle-Pollicot resonances. This property constitutes clear evidence of the dual role of the underlying classical chaos dictating the behavior of the correlator at different timescales.