Representation formula for stochastic Schrödinger evolution equations and applications

Anne De Bouard, Reika Fukuizumi

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We prove a representation formula for solutions of Schrödinger equations with potentials multiplied by a temporal real-valued white noise in the Stratonovich sense. Using this formula, we obtain a dispersive estimate which allows us to study the Cauchy problem in L 2 or in the energy space of model equations arising in Bose-Einstein condensation, Abdullaev et al (2001 Nonlinearity and Disorder: Theory and Applications (NATO Science Series vol 45) ed F Abdullaev et al (Dodrecht: Kluwer)), or in fiber optics, Abdullaev et al (2000 Physica D 135 369-86). Our results also give a justification of diffusion-approximation for stochastic nonlinear Schrödinger equations.

Original languageEnglish
Pages (from-to)2993-3022
Number of pages30
JournalNonlinearity
Volume25
Issue number11
DOIs
Publication statusPublished - 2012 Nov

ASJC Scopus subject areas

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

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