Egorov property in perturbed cat map

TL;DR

This paper investigates the quantum-classical correspondence in perturbed cat maps, revealing that quantum-classical fidelity decays faster than exponential under small perturbations, challenging typical expectations.

Contribution

It provides a detailed analysis of quantum-classical fidelity decay in perturbed cat maps, explaining the observed faster-than-exponential decay and apparent violation of QCC.

Findings

QCF decays faster than exponential in the studied regime

The behavior explains an apparent violation of QCC

Provides insights into quantum-classical correspondence in perturbed systems

Abstract

We study the time evolution of the quantum-classical correspondence (QCC) for the well known model of quantised perturbed cat maps on the torus in the very specific regime of semi-classically small perturbations. The quality of the QCC is measured by the overlap of classical phase-space density and corresponding Wigner function of the quantum system called quantum-classical fidelity (QCF). In the analysed regime the QCF strongly deviates from the known general behaviour in particular it decays faster then exponential. Here we study and explain the observed behavior of the QCF and the apparent violation of the QCC principle.