Resonance distribution in the quantum random Lorentz gas

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 wave number without finding them one by one. The method is applied to two collision models for the individual scatterers, namely a resonant model, and a nonresonant 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.

Automated summary

This article examines the multiple scattering model of a quantum particle in a random Lorentz gas composed of fixed point scatterers. An efficient method is developed to compute the numerical map of the density of scattering resonances in the complex plane of the wave number without the need to find them individually. Two collision models are studied and some of their characteristics are revealed.