Fluctuations around Hartree states in the mean-field regime
Mathematical Physics
2015-07-10 v3 Analysis of PDEs
math.MP
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.
Keywords
Cite
@article{arxiv.1307.0665,
title = {Fluctuations around Hartree states in the mean-field regime},
author = {Mathieu Lewin and Phan Thành Nam and Benjamin Schlein},
journal= {arXiv preprint arXiv:1307.0665},
year = {2015}
}
Comments
Typos corrected. To appear in Amer. J. Math