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Stochastic fluctuations in the Gross–Pitaevskii equation

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Published 15 November 2007 • 2007 IOP Publishing Ltd and London Mathematical Society
, , Citation Anne de Bouard and Reika Fukuizumi 2007 Nonlinearity 20 2823 DOI 10.1088/0951-7715/20/12/005

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Author affiliations

1 CNRS, Laboratoire de Mathématiques d'Orsay, Orsay Cedex, F-91405, France

2 Univ Paris-Sud, Orsay Cedex, F-91405, France

3 Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan

4 Current address: Laboratoire de Mathématiques d'Orsay, Univ Paris-Sud, Orsay Cedex, F-91405, France.

Dates

  1. Received 2 April 2007
  2. Published

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0951-7715/20/12/2823

Abstract

We study from a mathematical point of view a model equation for a Bose–Einstein condensation, in the case where the trapping potential varies randomly in time. The model is the so-called Gross–Pitaevskii equation, with a quadratic potential with white noise fluctuations in time. We prove the existence of solutions in 1D and 2D in the energy space. The blow-up phenomenon is also discussed under critical and super critical nonlinear interactions in the attractive case.

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10.1088/0951-7715/20/12/005