Rate of convergence toward Hartree dynamics with singular interaction potential

We consider a system of N-bosons with a two-body interaction potential V is an element of L-2(R-3) + L-infinity (R-3), possibly more singular than the Coulomb interaction. We show that, with H-1(R-3) initial data, the difference between the many-body Schrodinger evolution in the mean-field regime and the corresponding Hartree dynamics is of order 1/N, for any fixed time. The N-dependence of the bound is optimal. Published by AIP Publishing.