NON-ANALYTIC DENSITY BEHAVIOUR OF DIFFUSION COEFFICIENT OF A LORENTZ GAS .2. RENORMALIZATION OF DIVERGENCIES

The logarithmic divergencies, found in the density expansion of the diffusion coefficient of a Lorentz gas are renormalized by summing up the most divergent contributions. Thus logarithmic terms in the density appear, which start in two dimensions as ρ{variant}2 ln ρ{variant} and in three dimensions as ρ{variant}3 ln ρ{variant}, where ρ{variant} is the reduced density. It turns out that the numerical coefficients of the ln ρ{variant} terms are equal to the coefficients of the corresponding logarithmic divergencies in the density expansion. © 1968.