Localization of Chaotic Resonance States due to a Partial Transport Barrier

TL;DR

This paper investigates how chaotic resonance states localize in quantum systems with partial transport barriers, revealing that openness can induce localization even when classical flux is resolved, supported by quantum-classical correspondence analysis.

Contribution

It introduces a new class of fractal measures to explain localization in open quantum systems and demonstrates quantum-to-classical correspondence in localization transitions.

Findings

Localization occurs even when flux is resolved in open systems.

A new class of fractal measures explains localization.

Quantum-to-classical correspondence is observed in localization transitions.

Abstract

Chaotic eigenstates of quantum systems are known to localize on either side of a classical partial transport barrier if the flux connecting the two sides is quantum mechanically not resolved due to Heisenberg's uncertainty. Surprisingly, in open systems with escape chaotic resonance states can localize even if the flux is quantum mechanically resolved. We explain this using the concept of conditionally invariant measures from classical dynamical systems by introducing a new quantum mechanically relevant class of such fractal measures. We numerically find quantum-to-classical correspondence for localization transitions depending on the openness of the system and on the decay rate of resonance states.