Multiple scattering model of the quantum random Lorentz gas

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.

Automated summary

A multiple scattering model of a quantum particle interacting with a random Lorentz gas of fixed point scatterers is established, with detailed calculations of scattering amplitude, cross section, and scattering matrix properties, verifying the optical theorem and probability conservation. Numerical computations of differential and total cross sections show a distinct Airy diffraction peak for a large number of scatterers, relevant to the extinction paradox.