Mean-Field Dynamics: Singular Potentials and Rate of Convergence |
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Authors: | Antti Knowles Peter Pickl |
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Affiliation: | 1. Theoretische Physik, ETH H?nggerberg, CH-8093, Zürich, Switzerland 2. Mathematisches Institut, Universit?t München, Theresien str. 39, 80333, München, Germany
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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 one-particle state. It is well known that in the mean-field limit N → ∞ 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. |
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