Multiple scattering model of the quantum random Lorentz gas

TL;DR

This paper develops a comprehensive quantum multiple scattering model for a particle interacting with a random Lorentz gas, deriving key scattering properties and demonstrating diffraction effects related to the extinction paradox.

Contribution

It introduces a detailed quantum scattering model for the Lorentz gas, including derivations of scattering amplitude, cross sections, and verification of probability conservation in arbitrary dimensions.

Findings

Derived scattering amplitude in terms of scattering length

Confirmed optical theorem and probability conservation

Observed Airy diffraction peak related to the extinction paradox

Abstract

A multiple scattering model of a quantum particle interacting with a random Lorentz gas of fixed point scatterers is established in an Euclidean space of arbitrary dimension. At the core of the model, the scattering amplitude for the point scatterers is derived in detail, and expressed in terms of the scattering length. The fundamental properties of the model, such as the cross section and the scattering matrix, are calculated. In addition, the model is shown to verify the optical theorem and thus probability conservation. Finally, the differential and total cross sections are numerically computed in two situations whether the Lorentz gas is smaller or larger than the mean free path. A distinct Airy diffraction peak is obtained for a large enough number of scatterers. This observation is related to the extinction paradox.