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.
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.
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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > General Mathematics |
| Language: | English |
| Date: | December 2015 |
| Deposited On: | 01 Feb 2017 10:58 |
| Last Modified: | 26 Jan 2022 11:39 |
| Publisher: | The Johns Hopkins University Press |
| ISSN: | 1080-6377 |
| OA Status: | Closed |
| Publisher DOI: | https://doi.org/10.1353/ajm.2015.0040 |
Lewin, Mathieu