  It has been argued by Grigoriev and Rubakov that one can simulate real time
processes involving baryon number non-conservation at high temperature using
real time evolution of classical equations, and summing over initial conditions
with a classical thermal weight. It is known that such a naive algorithm is
plagued by ultraviolet divergences. In quantum theory the divergences are
regularized, but the corresponding graphs involve the contributions from the
hard momentum region and also the new scale $\sim gT$ comes into play. We
propose a modified algorithm which involves solving the classical equations of
motion for the effective hard thermal loop Hamiltonian with an ultraviolet
cutoff $\mu \gg gT$ and integrating over initial conditions with a proper
thermal weight. Such an algorithm should provide a determination of the
infrared behavior of real time correlation function $<Q(t) Q(0)>_T$ determining
the baryon violation rate. Hopefully, the results obtained in this modified
algorithm would be cutoff-independent.
