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Section: New Results

A problem of moment realizability in quantum statistical physics

Participant : Florian Méhats.

This work [34] is a generalization of the results previously obtained by F. Méhats and O. Pinaud , in J. Stat. Phys. (2010), 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 the above quoted article 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 this article dealt with the first moment only, namely the charge density, we extend the results to the second moment, the current density.