We present the semi-conductor Boltzmann equation,
which is time-reversible, and indicate that it can be formally derived
by considering the large time and small perturbing potential limit
in the Von-Neumann equation (time-reversible). We then rigorously compute
the corresponding asymptotics in the case of the Von-Neumann equation on
the Torus. We show that the limiting equation we obtain does not coincide
with the physically realistic model. The former is indeed
an equation of Boltzmann type, yet with memory in time, so that it appears
to be time-reversible. We comment on this point, and further describe
the properties of the limiting equation.