Loschmidt echo in quantum maps: the elusive nature of the Lyapunov regime

TL;DR

This paper investigates the behavior of the Loschmidt echo in quantum maps, revealing that instead of the expected Lyapunov decay, an anomalous decay pattern occurs, explained through a new semiclassical analytical expression.

Contribution

The authors derive an analytical semiclassical formula for the averaged fidelity amplitude, clarifying the origin of the non-Lyapunov decay regimes in quantum chaotic systems.

Findings

Identified non-uniform decay of Loschmidt echo in quantum maps

Derived a semiclassical expression linking fidelity decay to anomalous behavior

Explained the elusive nature of the Lyapunov regime in quantum chaos

Abstract

The Loschmidt echo is a measure of the stability and reversibility of quantum evolution under perturbations of the Hamiltonian. One of the expected and most relevant characteristics of this quantity for chaotic systems is an exponential decay with a perturbation independent decay rate given by the classical Lyapunov exponent. However, a non-uniform decay -- instead of the Lyapunov regime -- has been reported in several systems. In this work we find an analytical semiclassical expression for the averaged fidelity amplitude that can be related directly to the anomalous -- unexpected-- behaviour of the LE.