Quantum chaos without false positives

TL;DR

This paper introduces a new indicator for quantum chaos that overcomes false positives of out-of-time-order correlators, accurately predicting Lyapunov exponents and Ehrenfest time while satisfying chaos bounds.

Contribution

The authors propose an alternative quantum chaos indicator that corrects false positives and retains analytical and theoretical advantages of existing methods.

Findings

Correctly predicts average Lyapunov exponent

Accurately estimates Ehrenfest time in semiclassical limit

Satisfies the bound on quantum chaos

Abstract

Out-of-time-order correlators are widely used as an indicator of quantum chaos, but give false-positive quantum Lyapunov exponents for integrable systems with isolated saddle points. We propose an alternative indicator that fixes this drawback and retains all advantages of out-of-time-order correlators. In particular, the new indicator correctly predicts the average Lyapunov exponent and the Ehrenfest time in the semiclassical limit, can be calculated analytically using the replica trick, and satisfies the bound on chaos.