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

Research output: Contribution to journal › Article › peer-review

69 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1613-1650
Number of pages	38
Journal	American Journal of Mathematics
Volume	137
Issue number	6
DOIs	https://doi.org/10.1353/ajm.2015.0040
Publication status	Published - 1 Dec 2015
Externally published	Yes

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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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AU - Nam, Phan Thành

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N2 - 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.

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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DO - 10.1353/ajm.2015.0040

M3 - Article

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JO - American Journal of Mathematics

JF - American Journal of Mathematics

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Fluctuations around hartree states in the mean-field regime

Abstract

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