Out-of-time-order correlators in bipartite nonintegrable systems

TL;DR

This paper investigates out-of-time-order correlators (OTOCs) in bipartite quantum systems, revealing how different subsystem dynamics influence chaos indicators and relaxation behaviors, with implications for understanding quantum chaos and scrambling.

Contribution

It provides a comparative analysis of OTOC growth in bipartite systems with various combinations of chaotic and regular subsystems, including new results on weakly coupled systems with different Lyapunov exponents.

Findings

OTOC growth varies significantly with subsystem dynamics.

Weakly coupled subsystems show distinct Lyapunov exponent effects.

Strongly chaotic subsystems exhibit exponential relaxation modeled by random matrices.

Abstract

Out-of-time-order correlators (OTOC) being explored as a measure of quantum chaos, is studied here in a coupled bipartite system. Each of the subsystems can be chaotic or regular and lead to very different OTOC growths both before and after the scrambling or Ehrenfest time. We present preliminary results on weakly coupled subsystems which have very different Lyapunov exponents. We also review the case when both the subsystems are strongly chaotic when a random matrix model can be pressed into service to derive an exponential relaxation to saturation.