Relative asymptotic oscillations of the out-of-time-ordered correlator as a quantum chaos indicator

TL;DR

This paper investigates how the asymptotic behavior of the out-of-time-ordered correlator's fluctuations can serve as a reliable quantum chaos indicator, linking quantum and classical chaos measures through numerical analysis.

Contribution

It introduces a novel chaos indicator based on the asymptotic oscillations of the correlator's standard deviation-to-mean ratio, validated through numerical simulations of the u(3) model.

Findings

Correlator oscillations correlate with classical phase space chaos.

Scaling of oscillations with system size suggests a robust chaos measure.

The method provides a quantitative link between quantum and classical chaos.

Abstract

A detailed numerical study reveals that the asymptotic values of the standard deviation-to-mean ratio of the out-of-time-ordered correlator can be successfully used as a measure of the quantum chaoticity of the system. We employ a finite-size fully connected quantum system with two degrees of freedom, namely the algebraic u(3) model, and demonstrate a clear correspondence between the relative oscillations of the correlators and the ratio of the chaotic part of the volume of phase space in the classical limit of the system. We also show how the relative oscillations scale with the system size and conjecture that the scaling exponent can also serve as a robust chaos indicator.