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Article Dans Une Revue Journal of Statistical Physics Année : 2010

An inverse problem in quantum statistical physics

Résumé

We address the following inverse problem in quantum statistical physics: does the quantum free energy (von Neumann entropy + kinetic energy) admit a unique minimizer among the density operators having a given local density $n(x)$? We give a positive answer to that question, in dimension one. This enables to define rigourously the notion of local quantum equilibrium, or quantum Maxwellian, which is at the basis of recently derived quantum hydrodynamic models and quantum drift-diffusion models. We also characterize this unique minimizer, which takes the form of a global thermodynamic equilibrium (canonical ensemble) with a quantum chemical potential.
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Dates et versions

hal-00453942 , version 1 (06-02-2010)
hal-00453942 , version 2 (27-05-2010)

Identifiants

Citer

Florian Méhats, Olivier Pinaud. An inverse problem in quantum statistical physics. Journal of Statistical Physics, 2010, 140 (3), pp.565-602. ⟨10.1007/s10955-010-0003-z⟩. ⟨hal-00453942v2⟩
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