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We prove a formula for the current in an electron gas in a semiclassical limit
corresponding to strong, constant, magnetic fields. Little regularity is assumed for the
scalar potential . In particular, the result can be applied to the mean field from
magnetic Thomas-Fermi theory . The proof is based on an estimate on the
density of states in the second Landau band.
In this paper we prove the existence of infinitely many solutions of the Dirac-Fock equations with electrons turning around a nucleus of atomic charge , satisfying and , where is the fundamental constant of the electromagnetic interaction (approximately 1/137). This work is an improvement of an article of Esteban-Séré, where the same result was proved under more restrictive assumptions on .
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