The Gibbs Measure of the Renormalized Two Dimensional Stochastic Gross-Pitaevskii

Explore the mathematical foundations of the stochastic Gross-Pitaevskii equation in this 52-minute conference talk that examines a mean-field model for describing Bose-Einstein condensates near critical condensation temperature. Delve into the two-dimensional case where renormalization becomes necessary, as the speaker constructs the Gibbs measure for this complex Ginzburg-Landau equation with harmonic confining potential and additive space-time white noise. Learn how this measure maintains formal invariance for the nonlinear Schrödinger equation with harmonic potential in dimension two, and discover why this measure exhibits singularity with respect to the underlying Gaussian measure. Gain insights from collaborative research conducted with A. Debussche from ENS Rennes and R. Fukuizumi from Waseda University, Japan, presented during the thematic meeting on "New trends of stochastic nonlinear systems: well-posedness, dynamics and numerics" at the Centre International de Rencontres Mathématiques in Marseille, France.