Distribution of resonances in the quantum open baker map

TL;DR

This paper investigates the spectral properties of the quantum open baker map, revealing how the eigenvalue distribution depends on the escape region and confirming the fractal Weyl law across different configurations.

Contribution

It provides a detailed analysis of the eigenvalue distribution in the quantum open baker map, highlighting the influence of the escape region location and validating the fractal Weyl law.

Findings

Eigenvalue distribution varies with escape region position

The fractal Weyl law holds universally in studied cases

Classical and quantum decay rates are correlated

Abstract

We study relevant features of the spectrum of the quantum open baker map. The opening consists of a cut along the momentum $p$ direction of the 2-torus phase space, modelling an open chaotic cavity. We study briefly the classical forward trapped set and analyze the corresponding quantum nonunitary evolution operator. The distribution of eigenvalues depends strongly on the location of the escape region with respect to the central discontinuity of this map. This introduces new ingredients to the association among the classical escape and quantum decay rates. Finally, we could verify that the validity of the fractal Weyl law holds in all cases.