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Article Dans Une Revue Kinetic and Related Models Année : 2011

A problem of moment realizability in quantum statistical physics

Résumé

This work is a generalization of the results previously obtained in [17] in a one-dimensional setting: we revisit the problem of the minimization of the quantum free energy (entropy + energy) under local constraints (moments) and prove the existence of minimizers in various configurations. While [17] addressed the 1D case on bounded domains, we treat in the present paper the multi-dimensional case as well as unbounded domains and non-linear interactions as Hartree/Hartree-Fock. Moreover, whereas [17] dealt with the first moment only, namely the charge density, we extend the results to the second moment, the current density.

Dates et versions

hal-00671989 , version 1 (20-02-2012)

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Citer

Florian Méhats, Olivier Pinaud. A problem of moment realizability in quantum statistical physics. Kinetic and Related Models , 2011, 4 (4), pp.1143-1158. ⟨10.3934/krm.2011.4.1143⟩. ⟨hal-00671989⟩
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