Mean field propagation of infinite dimensional Wigner measures with a singular two-body interaction potential

• Zied Ammari ^[2] ; Francis Nier ^[1]
  1. [1] Paris 13 University

     Paris 13 University

     Arrondissement de Saint-Denis, Francia

     
  2. [2] Université de Rennes I, France
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 14, Nº 1, 2015, págs. 155-220
• Idioma: inglés
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• Resumen

  • We consider the quantum dynamics of many bosons systems in the mean field limit with a singular pair-interaction potential, including the attractive or repulsive Coulombic case in three dimensions. By using a measure transportation technique developed in [3], we show that Wigner measures propagate along the nonlinear Hartree flow. Such property was previously proved only for bounded potentials in our works [5, 6] with a slightly different strategy