Localization of resonance eigenfunctions on quantum repellers

TL;DR

This paper introduces a new phase space representation for open quantum systems and demonstrates its effectiveness by analyzing resonance eigenfunctions of the baker map, revealing their scarred structures and localization properties.

Contribution

It presents a novel phase space method for studying eigenstates of open quantum systems and applies it to the baker map to uncover detailed resonance structures.

Findings

Long-lived resonances are strongly scarred along classical periodic orbits.

Short-lived eigenstates have distinct shape characteristics.

Antiunitary symmetry measure quantifies resonance localization on the repeller.

Abstract

We introduce a new phase space representation for open quantum systems. This is a very powerful tool to help advance in the study of the morphology of their eigenstates. We apply it to two different versions of a paradigmatic model, the baker map. This allows to show that the long-lived resonances are strongly scarred along the shortest periodic orbits that belong to the classical repeller. Moreover, the shape of the short-lived eigenstates is also analyzed. Finally, we apply an antiunitary symmetry measure to the resonances that permits to quantify their localization on the repeller.