Long-time tails in a quantum Lorentz gas

The long-time behaviour of the velocity autocorrelation function (VACF) in a quantum Lorentz gas is investigated using both tetradic and double contour methods. The two classes of most divergent diagrams in the double contour analysis, called ladders and stars, are summed explicitly for the case of separable interactions. The ladders lead to the ringsum long-time tail. The stars give rise to a curious t−d2-tail which is of quantum-mechanical nature. Moreover these diagrams yield an additional contribution to the classical t−(d2 + 1)-tail which might explain the discrepancy between the observed and predicted long-time tail coefficient. Extending the star diagrams to the class of ladders of stars, the t−d2-tail is shown to be removed for the two-dimensional case. Quantum corrections to the long time tail coefficient arising from the tetradic ring diagrams are studied in two and three dimensions. A repeated ringsum expression for the VACF has been evaluated numerically for all times to study the cage effect and appearance of the algebraic long-time tail.