Average localization of resonances on the quantum repeller

TL;DR

This paper investigates the localization properties of quantum resonances in a partially open quantum system, revealing localization on short periodic orbits and novel enhancements in scaled states using the LR representation.

Contribution

It introduces a new analysis of quantum resonance localization in the tribaker map using the LR representation, highlighting localization on short orbits and unassociated enhancements.

Findings

Localization on shortest periodic orbits

Enhanced scaled states not linked to periodic orbits

LR representation reveals new localization features

Abstract

There has been a very recent surge in the interest on the localization properties of resonances associated to partially open (scattering) systems, which are of great relevance when studying resonant cavities such as those used in microlasers. Very recently, it has been found that no localization is present in a scaled form of these states. Moreover, a new kind of scarring on structures different from periodic orbits is described for non scaled resonances. In this paper, we analyze the localization of a distribution function corresponding to the quantum LR representation -- based on the non unitary evolution operator decomposition into left and right resonances -- for the partially open quantum tribaker map, a paradigmatic system. We find localization on the shortest periodic orbits. Also, scaled states present enhancements that could not be associated to periodic orbits and that become more evident when looking at the LR representation. These findings open the door for new perspectives on recent theoretical developments.