The role of short periodic orbits in quantum maps with continuous openings

TL;DR

This paper demonstrates that short periodic orbits in a continuously open quantum map are crucial for understanding long-lived resonances, with robustness observed even under perturbations and specific reflectivity functions.

Contribution

It extends semiclassical theory of short periodic orbits to continuously open quantum maps, highlighting their role in resonance support and spectral properties.

Findings

Short periodic orbits support long-lived resonances.

Robustness of orbits in perturbative regimes.

Reduced orbit requirements for step-like reflectivity functions.

Abstract

We apply a recently developed semiclassical theory of short periodic orbits to the continuously open quantum tribaker map. In this paradigmatic system the trajectories are partially bounced back according to continuous reflectivity functions. This is relevant in many situations that include optical microresonators and more complicated boundary conditions. In a perturbative regime, the shortest periodic orbits belonging to the classical repeller of the open map - a cantor set given by a region of exactly zero reflectivity - prove to be extremely robust in supporting a set of long-lived resonances of the continuously open quantum maps. Moreover, for step like functions a significant reduction in the number needed is obtained, similarly to the completely open situation. This happens despite a strong change in the spectral properties when compared to the discontinuous reflectivity case.