Fluctuations around Hartree states in the mean-field regime

2013/07/02 by Lewin, Mathieu, Nam, Phan Thành, Schlein, Benjamin · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1307.0665

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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• Dispersive estimates and long-time validity for Bogoliubov dynamics of interacting Bose gases

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