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Fluctuations around Hartree states in the mean-field regime
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 137, Number 6, December 2015
- pp. 1613-1650
- 10.1353/ajm.2015.0040
- Article
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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.