Long time behaviour of the nested ring diagrams in a quantum Lorentz gas

Abstract The contribution of the class of nested ring diagrams to the velocity autocorrelation function of a quantum Lorentz gas is considered. It is argued that this class gives rise to a t −( d /2+1) long time nail. This indicates that the t −( d /2) tail found recently by resummation of the leading order parts of these diagrams is removed by classes of less divergent contributions.