Resonance spectra for quantum maps of kicked scattering systems by complex scaling

TL;DR

This paper investigates the computation of resonance spectra in quantum maps derived from kicked scattering systems, highlighting the limitations of common absorption methods and proposing complex scaling as a more effective approach.

Contribution

It demonstrates that traditional absorptive and projective openings fail to produce accurate resonance spectra, advocating for complex scaling techniques in kicked scattering systems.

Findings

Complex scaling effectively computes resonance spectra.

Standard absorptive openings fail despite not affecting classical trapped sets.

Results are relevant for testing fractal Weyl conjectures and tunneling studies.

Abstract

We consider quantum maps induced by periodically-kicked scattering systems and discuss the computation of their resonance spectra in terms of complex scaling and sufficiently weak absorbing potentials. We also show that strong absorptive and projective openings, as commonly used for open quantum maps, fail to produce the resonance spectra of kicked scattering systems, even if the opening does not affect the classical trapped set. The results are illustrated for a concrete model system whose dynamics resembles key features of ionization and exhibits a trapped set which is organized by a topological horseshoe at large kick strength. Our findings should be useful for future tests of fractal Weyl conjectures and investigations of dynamical tunneling.