Error estimates in mean field dynamics

In bosonic many body systems described by mean-field Hamiltonians, the time evolution of factorized N body wave functions can be described in the limit of large N by the solution of a nonlinear Hartree equation. More precisely, one can prove that the one-particle density associated with the solution of the N body Schroedinger equation converges, as N tends to infinity, to the orthogonal projection onto the solution to the Hartree equation. Although the difference between the one-particle density and the orthogonal projection can be shown to be of order 1/N for short times, so far it has not been possible to extend this estimate on the error to long times. In this talk I am going to present some preliminary result in this direction obtained in collaboration with I. Rodnianski.