Localization in chaotic systems with a single-channel opening

TL;DR

This paper studies how introducing a single-channel opening in chaotic quantum and classical systems causes localization effects and deviations from random matrix theory predictions, revealing resonance trapping phenomena.

Contribution

It demonstrates the emergence of localization due to a single-channel opening and connects quantum wavefunction behavior with classical propagator statistics.

Findings

Localization occurs as a deviation from RMT predictions.

Resonance trapping involves fast-decaying states localized on the opening.

A linear relation between wavefunction intensities and decay rates is derived.

Abstract

We introduce a single-channel opening in a random Hamiltonian and a quantized chaotic map: localization on the opening occurs as a sensible deviation of the wavefunction statistics from the predictions of random matrix theory, even in the semiclassical limit. Increasing the coupling to the open channel in the quantum model, we observe a similar picture to resonance trapping, made of few fast-decaying states, whose left (right) eigenfunctions are entirely localized on the (preimage of the) opening, and plentiful long-lived states, whose probability density is instead suppressed at the opening. For the latter we derive and test a linear relation between the wavefunction intensities and the decay rates, similar to Breit-Wigner law. We then analyze the statistics of the eigenfunctions of the corresponding (discretized) classical propagator, finding a similar behavior to the quantum system only in the weak-coupling regime.