Abstract
We consider a system of N bosons interacting through a two-body potential with, possibly, Coulomb-type singularities. We show that the difference between the many-body Schrödinger evolution in the mean-field regime and the effective nonlinear Hartree dynamics is at most of the order 1/N, for any fixed time. The N-dependence of the bound is optimal.
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Li Chen is partially supported by National Natural Science Foundation of China (NSFC), grant number 10871112. Benjamin Schlein is partially supported by an ERC Starting Grant.
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Chen, L., Lee, J.O. & Schlein, B. Rate of Convergence Towards Hartree Dynamics. J Stat Phys 144, 872–903 (2011). https://doi.org/10.1007/s10955-011-0283-y
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DOI: https://doi.org/10.1007/s10955-011-0283-y