Quantum Chaos and the Correspondence Principle

TL;DR

This paper investigates the validity of the correspondence principle in quantum chaos, demonstrating that proper treatment of singular points restores the principle and confirms the OTOC's role in diagnosing chaotic dynamics.

Contribution

It shows that the correspondence principle holds in quantum chaos when singular points are properly handled, reaffirming the OTOC's diagnostic effectiveness.

Findings

Proper treatment of singular points restores the correspondence principle.

OTOC remains a reliable diagnostic of chaos.

The early-time exponential growth of OTOC can be explained within this framework.

Abstract

The correspondence principle is a cornerstone in the entire construction of quantum mechanics. This principle has been recently challenged by the observation of an early-time exponential increase of the out-of-time-ordered correlator (OTOC) in classically non-chaotic systems [E.B. Rozenbaum et al., Phys. Rev. Lett. 125, 014101 (2020)], Here we show that the correspondence principle is restored after a proper treatment of the singular points. Furthermore our results show that the OTOC maintains its role as a diagnostic of chaotic dynamics.