An inverse problem in quantum statistical physics
The authors address the problem to establish existence and uniqueness of a statistical operator minimizing the quantum free energy given by the sum of von Neumann entropy and kinetic energy, with the constraint of a given local density \(n(x)\). They provide a rigorous positive answer to the question in dimension one, in a finite box with periodic boundary conditions. The thus obtained statistical operator indeed has a Gibbs form with a suitable chemical potential. The motivation for this work is to obtain a rigorous definition of the notion of local quantum equilibrium state, which is at the basis of recently derived quantum hydrodynamic models.
scientific article; zbMATH DE number 5786221
scientific article