09-120 Antti Knowles and Peter Pickl
Mean-Field Dynamics: Singular Potentials and Rate of Convergence (594K, Postscript) Jul 24, 09
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. We consider the time evolution of a system of $N$ identical bosons whose interaction potential is rescaled by $N^{-1}$. We choose the initial wave function to describe a condensate in which all particles are in the same one-particle state. It is well known that in the mean-field limit $N \to \infty$ the quantum $N$-body dynamics is governed by the nonlinear Hartree equation. Using a nonperturbative method, we extend previous results on the mean-field limit in two directions. First, we allow a large class of singular interaction potentials as well as strong, possibly time-dependent external potentials. Second, we derive bounds on the rate of convergence of the quantum $N$-body dynamics to the Hartree dynamics.

Files: 09-120.src( 09-120.keywords , knowles_pickl.ps )