June 18,  19,  20   2003
 
 
 

04:00 PM - Wednesday, June 18, 2003 - Amphitheater Darboux

Pierre Degond

Mathématiques pour l'Industrie et la Physique
Unité Mixte 5640, CNRS Université Paul Sabatier
118, route de Narbonne, 31062 Toulouse cedex, France

degond@mip.ups-tlse.fr

Quantum Hydrodynamic Models Derived from the Entropy Principle (joint work with Ch. Ringhofer)

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).