Treffer: Representation formula for stochastic Schrodinger evolution equations and applications
Title:
Representation formula for stochastic Schrodinger evolution equations and applications
Authors:
Source:
Nonlinearity (Bristol. Print). 25(11):2993-3022
Publisher Information:
Bristol: Institute of Physics, 2012.
Publication Year:
2012
Physical Description:
print, 29 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Theoretical physics, Physique théorique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Equations aux dérivées partielles, Partial differential equations, Topologie. Variétés et complexes cellulaires. Analyse globale et analyse sur variétés, Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds, Analyse globale, analyse sur des variétés, Global analysis, analysis on manifolds, Probabilités et statistiques, Probability and statistics, Théorie des probabilités et processus stochastiques, Probability theory and stochastic processes, Analyse stochastique, Stochastic analysis, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Divers, Other topics in mathematical methods in physics, Analyse non linéaire, Nonlinear analysis, análisis no lineal, Approximation non linéaire, Non linear approximation, Aproximación no lineal, Approximation stochastique, Stochastic approximation, Aproximación estocástica, Bruit blanc, White noise, Ruido blanco, Condensation, Condensación, Equation Einstein, Einstein equation, Ecuación Einstein, Equation Schrödinger, Schrödinger equation, Ecuación Schrödinger, Equation non linéaire, Non linear equation, Ecuación no lineal, Equation stochastique, Stochastic equation, Ecuación estocástica, Equation énergie, Energy equation, Ecuación energía, Equation évolution, Evolution equation, Ecuación evolución, Fibre, Fiber, Fibra, Non linéarité, Nonlinearity, No linealidad, Optique, Optics, Optica, Physique mathématique, Mathematical physics, Física matemática, Potentiel, Potential, Potencial, Problème Cauchy, Cauchy problem, Problema Cauchy, Représentation, Representation, Representación, 35Q55, 58D25, 60H35, 60K40, 62L20, 65J08, Approximation diffusion, Espace L2, Espace énergie, Energy space, Solution équation
Document Type:
Fachzeitschrift
Article
File Description:
text
Language:
English
Author Affiliations:
Centre de Mathématiques Appliquées, CNRS et Ecole Polytechnique, 91 128 Palaiseau, France
Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan
Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan
ISSN:
0951-7715
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Theoretical physics
Theoretical physics
Accession Number:
edscal.26569526
Database:
PASCAL Archive
Weitere Informationen
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 L2 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.