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Boltzmann distributed quantum steady states and their classical limit. (English) Zbl 0788.35110

Author’s summary: “We prove the existence and uniqueness of Boltzmann distributed quantum steady states of an electron ensemble which moves under the actions of the self consistent Coulomb potential and of an external potential. The case of the particles confined to a three- dimensional bounded domain and the whole space case in \(\mathbb{R}^ 3\) is analyzed. Also we prove the existence of the classical limit. As the Planck constant tends to zero we obtain a Maxwellian equilibrium solution of the Vlasov-Poisson problem”.

MSC:

35Q40 PDEs in connection with quantum mechanics
35P20 Asymptotic distributions of eigenvalues in context of PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
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