Rate of convergence in nonlinear Hartree dynamics with factorized initial data

The mean field dynamics of an N-particle weekly interacting Boson system can be described by the nonlinear Hartree equation. In this paper, we present estimates on the 1/N rate of convergence of many-body Schrödinger dynamics to the one-body nonlinear Hartree dynamics with factorized initial data wi...

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Bibliographic Details
Published in:Journal of mathematical physics 2011-05, Vol.52 (5), p.052108-052108-25
Main Authors: Chen, Li, Lee, Ji Oon
Format: Article
Language:English
Subjects:
Atoms & subatomic particles
BOSONS
CONVERGENCE
DIFFERENTIAL EQUATIONS
EQUATIONS
Exact sciences and technology
INTERACTING BOSON MODEL
MANY-BODY PROBLEM
MATHEMATICAL LOGIC
MATHEMATICAL METHODS AND COMPUTING
Mathematical methods in physics
MATHEMATICAL MODELS
MATHEMATICAL SOLUTIONS
Mathematics
MEAN-FIELD THEORY
Nonlinear equations
NONLINEAR PROBLEMS
NUCLEAR MODELS
PARTIAL DIFFERENTIAL EQUATIONS
Physics
Quantum physics
SCHROEDINGER EQUATION
Sciences and techniques of general use
SHELL MODELS
TWO-BODY PROBLEM
WAVE EQUATIONS
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Summary:The mean field dynamics of an N-particle weekly interacting Boson system can be described by the nonlinear Hartree equation. In this paper, we present estimates on the 1/N rate of convergence of many-body Schrödinger dynamics to the one-body nonlinear Hartree dynamics with factorized initial data with two-body interaction potential V in \documentclass[12pt]{minimal}\begin{document}$L^3 (\mathbb {R}^3)+ L^{\infty } (\mathbb {R}^3)$\end{document} L 3 ( R 3 ) + L ∞ ( R 3 ) .
ISSN:0022-2488
1089-7658
DOI:10.1063/1.3589962