On Nonlocal Constitutive Relations, Continued Fraction Expansion for the Wave Vector Dependent Diffusion Coefficient

Abstract

Nonlocal constitutive relations which involve wave vector dependent transport coefficients can be derived from the Boltzmann equation. Diffusion of a Lorentzian gas is treated as an illustrative example. Transport-relaxation equations obtained from the Boltzmann equation with the help of the moment method lead to a continued fraction expansion for the wave vector dependent diffusion coefficient D(k). Rapidly converging upper and lower bounds on D(k)/D(0) are found which are meaningful for all values of lk where l is a mean free path and k is the magnitude of the wave vektor k. Also some remarks on a frequency and wave vector dependent diffusion coefficient are made.