Loschmidt Echo for edge of chaos and chaotic sea in Standard Map: Cases Study

TL;DR

This paper investigates the decay behavior of the quantum Loschmidt Echo in the Standard Map, revealing universal decay laws and stages in mixed phase space regimes, enhancing understanding of quantum-classical correspondence.

Contribution

It introduces a universal decay law for quantum Loschmidt Echo in mixed phase spaces and verifies it through numerical simulations, advancing the analysis of quantum dynamical stability.

Findings

Identification of three typical decay stages.

Derivation of time-scale relations for LE decay.

Critical perturbation thresholds for decay comparison.

Abstract

Using the Standard Map model, this study explores the quantum Loschmidt Echo (LE) decay laws for mixed-type phase spaces, including edge of chaos and chaotic sea regimes. A universal decay law is proposed and numerically verified, characterizing the intricate dynamics of LE decay processes with a semi-classical statistical approach. Key findings include three typical decay stages and time-scale relations as well as the critical perturbations for comparing the decay extent, with critical insights into classical-quantum correspondences through the construction of classical ensemble from the uncertainty of quantum state. This work provides analytical and numerical advancements in understanding dynamical stability in quantum systems.