Stationary martingale solution for the 2D stochastic Gross-Pitaevskii equation
Anne de Bouard, Arnaud Debussche, Reika Fukuizumi
TL;DR
This paper proves the existence of a stationary solution for the 2D stochastic Gross-Pitaevskii equation driven by space-time white noise, advancing understanding of stochastic quantum fluid models.
Contribution
It provides the first rigorous proof of stationary solutions for the 2D stochastic Gross-Pitaevskii equation with white noise forcing.
Findings
Existence of stationary solutions established
Method applicable to stochastic quantum fluid models
Framework for future analysis of stochastic PDEs in quantum physics
Abstract
In this short report we give a proof of the existence of a stationary solution to the Gross-Pitaevskii equation in driven by a space-time white noise.
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Taxonomy
TopicsCold Atom Physics and Bose-Einstein Condensates · Advanced Mathematical Physics Problems · Opinion Dynamics and Social Influence