Representation formula for stochastic Schrödinger evolution equations and applications

Anne De Bouard, Reika Fukuizumi

研究成果: Article査読

9 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)2993-3022
ページ数30
ジャーナルNonlinearity
25
11
DOI
出版ステータスPublished - 2012 11

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学
  • 物理学および天文学(全般)
  • 応用数学

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