Anomalous transport properties of the quantum Lorentz gas

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.