Stochastic fluctuations in the Gross-Pitaevskii equation

Anne De Bouard, Reika Fukuizumi

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)2823-2844
Number of pages22
JournalNonlinearity
Volume20
Issue number12
DOIs
Publication statusPublished - 2007 Dec 1
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Stochastic fluctuations in the Gross-Pitaevskii equation'. Together they form a unique fingerprint.

  • Cite this