Universal Response of Quantum Systems with Chaotic Dynamics

TL;DR

This paper demonstrates that quantum systems with classically chaotic dynamics universally exhibit a Breit-Wigner distribution in their local density of states under various perturbations, with a semiclassical expression accurately predicting its width.

Contribution

It establishes the universal Breit-Wigner form of the LDOS in chaotic quantum systems and derives an accurate semiclassical expression for its width.

Findings

LDOS follows a Breit-Wigner distribution under general perturbations

Semiclassical expression for LDOS width is highly accurate

Universal response characteristic of quantum chaos systems

Abstract

The prediction of the response of a closed system to external perturbations is one of the central problems in quantum mechanics, and in this respect, the local density of states (LDOS) provides an in- depth description of such a response. The LDOS is the distribution of the overlaps squared connecting the set of eigenfunctions with the perturbed one. Here, we show that in the case of closed systems with classically chaotic dynamics, the LDOS is a Breit-Wigner distribution under very general perturbations of arbitrary high intensity. Consequently, we derive a semiclassical expression for the width of the LDOS which is shown to be very accurate for paradigmatic systems of quantum chaos. This Letter demonstrates the universal response of quantum systems with classically chaotic dynamics.