Dr. Pierre Degond, MIP, University Toulouse 3 and CNRS
Quantum Hydrodynamic Models Derived From The Entropy Principle
The aim of this talk is to present a new derivation of quantum hydrodynamic
models from the quantum Liouville equation. In classical physics, the passage
from microscopic (kinetic) models to macroscopic fluid-like models involves two
steps:
first, taking moments of the kinetic equations
second, invoking a closure assumption to close the so-obtained moment system
About ten years ago, D. Levermore proposed to use an entropy minimization
procedure to achieve the second step, giving rise to a new hierarchy of fluid
equations.
The goal of this work is to extend this procedure to
quantum systems. The difficulty lies in the fact that entropy on the one hand
and moments on the other hand are naturally defined in different
representations. As a consequence, the resulting closure relations are non-local
in space (i.e. involve operators instead relations involving local values of the
variables).
* This is a joint work with Dr. Ch. Ringhofer
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