Non-monotonous short-time decay of the Loschmidt echo in quasi-one-dimensional systems

TL;DR

This paper investigates the short-time behavior of the Loschmidt echo in quasi-one-dimensional quantum systems, revealing non-monotonous decay patterns linked to classical particle trajectories and providing analytical decay estimates.

Contribution

It provides the first analytical and numerical analysis of non-monotonous short-time LE decay in quasi-one-dimensional systems, highlighting unique dimensional effects.

Findings

LE exhibits non-monotonous decay with pronounced minima and maxima.

Envelope decay of LE is approximately Gaussian with derived decay times.

Non-monotonous decay is specific to one-dimensional and quasi-one-dimensional systems.

Abstract

We study the short-time stability of quantum dynamics in quasi-one-dimensional systems with respect to small localized perturbations of the potential. To this end, we address, analytically and numerically, the decay of the Loschmidt echo (LE) during times short compared to the Ehrenfest time. We find that the LE is generally a non-monotonous function of time and exhibits strongly pronounced minima and maxima at the instants of time when the corresponding classical particle traverses the perturbation region. We also show that, under general conditions, the envelope decay of the LE is well approximated by a Gaussian, and we derive explicit analytical formulas for the corresponding decay time. Finally, we demonstrate that the observed non-monotonicity of the LE decay is only pertinent to one-dimensional (and, more generally, quasi-one-dimensional systems), and that the short-time decay of the LE can be monotonous in higher number of dimensions.