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Fluctuations around Hartree states in the mean-field regime


Lewin, Mathieu; Nam, Phan Thành; Schlein, Benjamin (2015). Fluctuations around Hartree states in the mean-field regime. American Journal of Mathematics, 137(6):1613-1650.

Abstract

We consider the dynamics of a large system of $N$ interacting bosons in the mean-field regime where the interaction is of order $1/N$. We prove that the fluctuations around the nonlinear Hartree state are generated by an effective quadratic Hamiltonian in Fock space, which is derived from Bogoliubov's approximation. We use a direct method in the $N$-particle space, which is different from the one based on coherent states in Fock space.

Abstract

We consider the dynamics of a large system of $N$ interacting bosons in the mean-field regime where the interaction is of order $1/N$. We prove that the fluctuations around the nonlinear Hartree state are generated by an effective quadratic Hamiltonian in Fock space, which is derived from Bogoliubov's approximation. We use a direct method in the $N$-particle space, which is different from the one based on coherent states in Fock space.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:December 2015
Deposited On:01 Feb 2017 10:58
Last Modified:14 Feb 2018 11:31
Publisher:The Johns Hopkins University Press
ISSN:1080-6377
OA Status:Closed
Publisher DOI:https://doi.org/10.1353/ajm.2015.0040

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