Resonance distribution in the quantum random Lorentz gas

TL;DR

This paper introduces an efficient numerical method to analyze the distribution of scattering resonances in a quantum Lorentz gas, revealing new structures and effects of Anderson localization across different models and dimensions.

Contribution

Develops a novel numerical approach to map resonance densities in quantum Lorentz gases, identifying new resonance structures and effects of localization.

Findings

Resonance maps reveal spiral arms as proximity resonances.

Hard-sphere model uncovers previously unknown resonance structures.

Anderson localization influences resonance width distribution, especially in 1D.

Abstract

The multiple scattering model of a quantum particle in a random Lorentz gas consisting of fixed point scatterers is considered in arbitrary dimension. An efficient method is developed to numerically compute the map of the density of scattering resonances in the complex plane of the wavenumber without finding them one by one. The method is applied to two collision models for the individual scatterers, namely a resonant model, and a non-resonant hard-sphere model. The results obtained with the former are compared to the literature. In particular, the spiral arms surrounding the single-scatterer resonance are identified as proximity resonances. Moreover, the hard-sphere model is used to reveal previously unknown structures in the resonance density. Finally, it is shown how Anderson localization affects the distribution of resonance widths, especially in the one-dimensional case.