Olivier Pinaud
Universite Lyon 1, Institut
Camille Jordan/ISTIL
"On the Moment Problem for Quantum Hydrodynamics"
This work is motivated by a recent series of papers by Degond, Méhats and Ringhofer about the formal derivation of Quantum Hydrodynamics models from the entropy principle. Starting from the Quantum Liouville equation, they obtain a non-closed system for the first moments of the density operator. Then, as in the Levermore moment method for kinetic equations, the system is closed by introducing the solution to the quantum moment problem which consists in minimizing the quantum free energy under some constraints of density, current or energy. The first step towards the rigorous derivation of such Quantum Hydrodynamics models is the mathematical analysis of the quantum moment problem. We will present in the talk a first result of existence for the quantum moment problem under a density constraint and give some elements of the proof. The solution will also be characterized in a simplified setting. This is joint work with Florian Méhats.
Host: Guillaume Bal
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