Journal of Statistical Physics, Vol. 48, Nos, 3/4, 1987. p. 839-871.
We study the static and dynamic behavior of a classical electron gas in the periodic potential created by an ionic lattice. Using the well-known Vlasov approximation, we derive a mean-field kinetic equation for the density-response function of the electrons. This equation is formally solved in terms of the trajectories of one electron in the mean-field equilibrium potential which determines the local electronic density. The mean-field expressions of the static and dynamic structure factors are then obtained through the fluctuation-dissipation
theorem. These expressions are used to show that within the mean-field approximation the system is a conductor at all temperatures and for all dimensions.