Rate of convergence toward Hartree dynamics with singular interaction potential

Abstract

We consider a system of N-bosons with a two-body interaction potential V∈L2(R3)+L∞(R3), possibly more singular than the Coulomb interaction. We show that, with H1(R3) initial data, the difference between the many-body Schrödinger 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.