An inverse problem in quantum statistical physics

Details An inverse problem in quantum statistical physics An inverse problem in quantum statistical physics

2010-02-07

arxiv.org/abs/1002.1453v2

Journal of Statistical Physics 140, 3 (2010) 565-602

Mathematics

Analysis of PDEs

Scientific paper

10.1007/s10955-010-0003-z

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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