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From the Hartree Dynamics to the Vlasov Equation

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Abstract

We consider the evolution of quasi-free states describing N fermions in the mean field limit, as governed by the nonlinear Hartree equation. In the limit of large N, we study the convergence towards the classical Vlasov equation. For a class of regular interaction potentials, we establish precise bounds on the 0rate of convergence.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen, Denmark

    Niels Benedikter

  2. Institute of Mathematics, University of Zürich, Winterthurerstrasse 190, 8057, Zurich, Switzerland

    Marcello Porta, Chiara Saffirio & Benjamin Schlein

Authors
  1. Niels Benedikter
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  2. Marcello Porta
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  3. Chiara Saffirio
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  4. Benjamin Schlein
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Corresponding author

Correspondence to Chiara Saffirio.

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Communicated by S. Serfaty

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Benedikter, N., Porta, M., Saffirio, C. et al. From the Hartree Dynamics to the Vlasov Equation. Arch Rational Mech Anal 221, 273–334 (2016). https://doi.org/10.1007/s00205-015-0961-z

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  • DOI: https://doi.org/10.1007/s00205-015-0961-z

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