# Fluctuations around Hartree states in the mean-field regime - Zurich Open Repository and Archive

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.

## Statistics

### Citations

5 citations in Web of Science®
2 citations in Scopus®

### Altmetrics

Detailed statistics

Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English December 2015 01 Feb 2017 10:58 07 May 2017 05:07 The Johns Hopkins University Press 1080-6377 https://doi.org/10.1353/ajm.2015.0040