Abstract
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.
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Alastuey, A. Mean-field kinetic theory of a classical electron gas in a periodic potential. I. Formal solution of the Vlasov equation. J Stat Phys 48, 839–871 (1987). https://doi.org/10.1007/BF01019699
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DOI: https://doi.org/10.1007/BF01019699