Apparaît dans la collection : New trends of stochastic nonlinear systems: well-posedeness, dynamics and numerics / Nouvelles tendances en analyse non linéaire stochastique: caractère bien posé, dynamique et aspects numériques
The stochastic Gross-Pitaevskii equation is a mean-field model designed to describe a Bose-Einstein condensate close to the critical condensation temperature. It is a complex Ginzburg-Landau equation, with a harmonic confining potential and additive space-timewhite noise. In this talk, we will discuss the space dimension-two case, for which renormalization is required. We will construct the Gibbs measure for this equation, which is also formally invariant for the nonlinear Schr¨odinger equation with harmonic potential indimension two. It will also be shown that this measure is singular with respect to the underlying Gaussian measure.This talk is based on joint works with A. Debussche (ENS Rennes) and R. Fukuizumi (Waseda University, Japan).
De Arnaud Debussche
De Elena Issoglio
