Anomalous transport properties of the quantum Lorentz gas

Abstract

The two-scatter contribution to the Laplace transformed velocity autocorrelation function is investigated with the use of a double contour method which contains the microscopic information in terms of off-shell T-matrix elements. By analysing the full off-shell two-scatterer expression both analytically and numerically for a particular model we demonstrate explicitly that this contribution diverges logarithmically for a two-dimensional Lorentz gas, while it is finite for a three-dimensional system. The connection with the classical method of analysis is discussed. It is shown that the boundstate contributions in three dimensions give rise to an until recently unknown slowly decaying long time tail in the velocity autocorrelation function. Consequently the frequency-dependent electrical conductivity can have a logarithmic singularity at a certain finite frequency