Lyapunov decay in quantum irreversibility

TL;DR

This paper investigates the universality of Lyapunov decay in quantum irreversibility, demonstrating that averaging over initial states reveals the classical Lyapunov regime in quantum systems like the stadium billiard.

Contribution

The authors introduce an analogous fidelity measure for infinite-dimensional quantum systems and show its universality in revealing Lyapunov decay.

Findings

Lyapunov decay observed in quantum stadium billiard

Averaging over Haar measure recovers Lyapunov regime

Universality of Lyapunov decay in quantum chaos

Abstract

The Loschmidt echo -- also known as fidelity -- is a very useful tool to study irreversibility in quantum mechanics due to perturbations or imperfections. Many different regimes, as a function of time and strength of the perturbation, have been identified. For chaotic systems, there is a range of perturbation strengths where the decay of the Loschmidt echo is perturbation independent, and given by the classical Lyapunov exponent. But observation of the Lyapunov decay depends strongly on the type of initial state upon which an average is done. This dependence can be removed by averaging the fidelity over the Haar measure, and the Lyapunov regime is recovered, as it was shown for quantum maps. In this work we introduce an analogous quantity for systems with infinite dimensional Hilbert space, in particular the quantum stadium billiard, and we show clearly the universality of the Lyapunov regime.