High Temperature Behavior of the Chern-Simons Diffusion Rate in the 1+1 D Abelian Higgs Model

We give arguments that in the 1+1 dimensional abelian Higgs model the classical approximation can be good for the leading high temperature behavior of real time processes. The Chern-Simons diffusion rate (`sphaleron rate') is studied numerically in this approximation. New results at high temperature show a $T^{2/3}$ behavior of the rate at sufficiently small lattice spacing.