Fluctuations around hartree states in the mean-field regime

Mathieu Lewin; Phan Thành Nam; Benjamin Schlein

doi:10.1353/ajm.2015.0040

Fluctuations around hartree states in the mean-field regime

Mathieu Lewin
, Phan Thành Nam
, Benjamin Schlein

CY Cergy Paris Université
Institute for Applied Mathematics
University Bonn

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

69 Citations (Scopus)

Résumé

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.

langue originale	Anglais
Pages (de - à)	1613-1650
Nombre de pages	38
journal	American Journal of Mathematics
Volume	137
Numéro de publication	6
Les DOIs	https://doi.org/10.1353/ajm.2015.0040
état	Publié - 1 déc. 2015
Modification externe	Oui

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10.1353/ajm.2015.0040

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title = "Fluctuations around hartree states in the mean-field regime",

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{\textquoteright}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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AB - 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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Fluctuations around hartree states in the mean-field regime

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