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Rate of Convergence Towards Hartree Dynamics

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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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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People’s Republic of China

    Li Chen

  2. Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon, 305701, Republic of Korea

    Ji Oon Lee

  3. Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, 53115, Bonn, Germany

    Benjamin Schlein

Authors
  1. Li Chen
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  2. Ji Oon Lee
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  3. Benjamin Schlein
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Corresponding author

Correspondence to Benjamin Schlein.

Additional information

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

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