Mean-Field- and Classical Limit of Many-Body Schr\"odinger Dynamics for   Bosons
  We present a new proof of the convergence of the N-particle Schroedinger dynamics for bosons towards the dynamics generated by the Hartree equation in the mean-field limit. For a restricted class of two-body interactions, we obtain convergence estimates uniform in the Planck constant , up to an exponentially small remainder. For h=0, the classical dynamics in the mean-field limit is given by the Vlasov equation. 
Juerg Froehlich (1), Sandro Graffi (2), Simon Schwarz(1) ((1)   Theoretische Physik, ETH Zuerich, Switzerland, (2) Dipartime...