Quantum chaotic resonances from short periodic orbits

TL;DR

This paper introduces an efficient method for approximating quantum resonances in chaotic systems by constructing localized states on short classical periodic orbits, aligning with the fractal Weyl law.

Contribution

The authors develop a novel approach using short periodic orbits to accurately approximate long-lived quantum resonances, improving computational efficiency.

Findings

Approximations match the fractal Weyl law predictions.

Method effectively captures long-lived states with minimal computation.

Validated using the open quantum baker map.

Abstract

We present an approach to calculating the quantum resonances and resonance wave functions of chaotic scattering systems, based on the construction of states localized on classical periodic orbits and adapted to the dynamics. Typically only a few of such states are necessary for constructing a resonance. Using only short orbits (with periods up to the Ehrenfest time), we obtain approximations to the longest living states, avoiding computation of the background of short living states. This makes our approach considerably more efficient than previous ones. The number of long lived states produced within our formulation is in agreement with the fractal Weyl law conjectured recently in this setting. We confirm the accuracy of the approximations using the open quantum baker map as an example.