Estimating the spectral density of unstable scars

TL;DR

This paper investigates how scar states in quantum chaotic systems influence spectral density deviations from RMT predictions, especially when coupled to an environment, supported by theoretical predictions and numerical tests on quantum maps.

Contribution

It provides new predictions for spectral density in open quantum chaotic systems with scar states, extending previous intuitions and analyses.

Findings

Spectral density deviations are linked to scar states in open systems.

Theoretical predictions match numerical results on quantum maps.

Scar states cause significant spectral density deviations from RMT.

Abstract

In quantum chaos, the spectral statistics generally follows the predictions of Random Matrix Theory (RMT). A notable exception is given by scar states, that enhance probability density around unstable periodic orbits of the classical system, therefore causing significant deviations of the spectral density from RMT expectations. In this work, the problem is considered of both RMT-ruled and scarred chaotic systems coupled to an opening. In particular, predictions are derived for the spectral density of a chaotic Hamiltonian scattering into a single- or multiple channels. The results are tested on paradigmatic quantum chaotic maps on a torus. The present report develops the intuitions previously sketched in [D. Lippolis, EPL 126 (2019) 10003].