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Conference on "Mathematical properties of large quantum systems"
Organizers: Maria J. Esteban (CNRS), Mathieu Lewin (CNRS), Robert Seiringer (McGill, Montréal) & Jan Philip Solovej (Copenhagen)


Phan Thanh Nam (Cergy-Pontoise, France): "Fluctuation around the condensation of bosons in mean-field regime"
Friday 21 June 2013, 11:50 - 12:35
Amphi Hermite


We consider the large-N limit of a system of N bosons interacting with a potential of intensity 1/N. The system has the ability to undergo Bose-Einstein condensation, which means that (1) in the ground or excited states, most of particles live in a common quantum state; and (2) the condensation is stable in time under the Schrodinger flow. Mathematically, this condensation corresponds to the convergence of the many-body wave functions toward the Hartree states in terms of the reduced density matrices. In this talk, I will discuss the Bogoliubov fluctuation around the Hartree states, which gives the convergence of the many-body wave functions in norm. The talk is bases on recent joint works with M. Lewin, S. Serfaty, J.P. Solovej and B. Schlein.