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 Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1613-1650
Launched on MUSE
2015-11-30
Open Access
No
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