 09120 Antti Knowles and Peter Pickl
 MeanField Dynamics: Singular Potentials and Rate of Convergence
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Jul 24, 09

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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 oneparticle state. It is well known that in the meanfield 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 meanfield limit in two directions. First, we allow a large class of singular interaction potentials as well as strong, possibly timedependent external potentials. Second, we derive bounds on the rate of convergence of the quantum $N$body dynamics to the Hartree dynamics.
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