Loschmidt Echo and the Local Density of States

TL;DR

This paper investigates the decay behavior of Loschmidt echo in quantum systems, revealing how local perturbations and coherent oscillations influence the decay rate, especially in chaotic maps.

Contribution

It systematically studies the non-uniform decay regimes of LE in perturbed cat maps, highlighting the effects of local perturbations and oscillations on LDOS and LE decay.

Findings

Coherent oscillations in LDOS width affect LE decay.

Local perturbations amplify the decay effects.

Decay can be governed by LDOS width in local perturbations.

Abstract

Loschmidt echo (LE) is a measure of reversibility and sensitivity to perturbations of quantum evolutions. For weak perturbations its decay rate is given by the width of the local density of states (LDOS). When the perturbation is strong enough, it has been shown in chaotic systems that its decay is dictated by the classical Lyapunov exponent. However, several recent studies have shown an unexpected non-uniform decay rate as a function of the perturbation strength instead of that Lyapunov decay. Here we study the systematic behavior of this regime in perturbed cat maps. We show that some perturbations produce coherent oscillations in the width of LDOS that imprint clear signals of the perturbation in LE decay. We also show that if the perturbation acts in a small region of phase space (local perturbation) the effect is magnified and the decay is given by the width of the LDOS.