Quantum Fluctuations and Rate of Convergence Towards Mean Field Dynamics

The nonlinear Hartree equation describes the macroscopic dynamics of initially factorized N-boson states, in the limit of large N. In this paper we provide estimates on the rate of convergence of the microscopic quantum mechanical evolution towards the limiting Hartree dynamics. More precisely, we prove bounds on the difference between the one-particle density associated with the solution of the N-body Schrödinger equation and the orthogonal projection onto the solution of the Hartree equation.