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

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

Organizer(s) Hausenblas, Erika ; Ling, Chengcheng ; Menozzi, Stéphane

Date(s) 20/10/2025 - 24/10/2025

linked URL https://conferences.cirm-math.fr/3374.html

00:00:00 / 00:00:00

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The Gibbs measure of the renormalized two dimensional stochastic Gross-Pitaevskii equation

By Anne de Bouard

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).

Information about the video

Date of recording 23/10/2025
Date of publication 31/10/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20396003
Cite this video de Bouard, Anne (23/10/2025). The Gibbs measure of the renormalized two dimensional stochastic Gross-Pitaevskii equation. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20396003
URL https://dx.doi.org/10.24350/CIRM.V.20396003

Domain(s)

Bibliography

DE BOUARD, Anne, DEBUSSCHE, Arnaud, et FUKUIZUMI, Reika. Long Time Behavior of Gross--Pitaevskii Equation at Positive Temperature. SIAM Journal on Mathematical Analysis, 2018, vol. 50, no 6, p. 5887-5920. - https://doi.org/10.1137/17M1149195
DE BOUARD, Anne, DEBUSSCHE, Arnaud, et FUKUIZUMI, Reika. Stationary martingale solution for the 2D stochastic Gross-Pitaevskii equation (Harmonic Analysis and Nonlinear Partial Differential Equation - http://hdl.handle.net/2433/293087
DE BOUARD, Anne, DEBUSSCHE, Arnaud, et FUKUIZUMI, Reika. Two-Dimensional Gross–Pitaevskii Equation With Space-Time White Noise. International Mathematics Research Notices, 2023, vol. 2023, no 12, p. 10556-10614. - https://doi.org/10.1093/imrn/rnac137
DE BOUARD, Anne, FUKUIZUMI, Reika : Another construction of the Gibbs measure for the 2D stochastic Gross Pitaevskii equation, In preparation
GARDINER, C. W. et DAVIS, M. J. The stochastic gross–pitaevskii equation: Ii. Journal of Physics B: Atomic, Molecular and Optical Physics, 2003, vol. 36, no 23, p. 4731. - https://doi.org/10.1088/0953-4075/36/23/010

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