An inverse problem in quantum statistical physics
Analysis of PDEs
2010-07-29 v2 Mathematical Physics
math.MP
Abstract
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 ? 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.
Keywords
Cite
@article{arxiv.1002.1453,
title = {An inverse problem in quantum statistical physics},
author = {Florian Méhats and Olivier Pinaud},
journal= {arXiv preprint arXiv:1002.1453},
year = {2010}
}