Perturbations and chaos in quantum maps

TL;DR

This paper tests a semiclassical theory predicting the local density of states (LDOS) distribution in quantum maps, finding it accurate for highly chaotic systems and strong perturbations, and providing insights into LDOS width in mixed dynamics.

Contribution

It evaluates the validity of a semiclassical LDOS theory across different degrees of chaos, perturbation regions, and intensities in quantum maps.

Findings

Semiclassical theory accurately predicts LDOS in highly chaotic maps.

LDOS width matches semiclassical expression in mixed classical dynamics.

Theory remains valid for strong perturbations and specific phase space regions.

Abstract

The local density of states (LDOS) is a distribution that characterizes the effect of perturbations on quantum systems. Recently, it was proposed a semiclassical theory for the LDOS of chaotic billiards and maps. This theory predicts that the LDOS is a Breit-Wigner distribution independent of the perturbation strength and also gives a semiclassical expression for the LDOS witdth. Here, we test the validity of such an approximation in quantum maps varying the degree of chaoticity, the region in phase space where the perturbation is applying and the intensity of the perturbation. We show that for highly chaotic maps or strong perturbations the semiclassical theory of the LDOS is accurate to describe the quantum distribution. Moreover, the width of the LDOS is also well represented for its semiclassical expression in the case of mixed classical dynamics.