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Annales Henri Poincaré

, Volume 18, Issue 1, pp 113–191 | Cite as

Quantum Many-Body Fluctuations Around Nonlinear Schrödinger Dynamics

  • Chiara Boccato
  • Serena Cenatiempo
  • Benjamin Schlein
Article

Abstract

We consider the many-body quantum dynamics of systems of bosons interacting through a two-body potential \({N^{3\beta-1} V (N^\beta x)}\), scaling with the number of particles N. For \({0 < \beta < 1}\), we obtain a norm-approximation of the evolution of an appropriate class of data on the Fock space. To this end, we need to correct the evolution of the condensate described by the one-particle nonlinear Schrödinger equation by means of a fluctuation dynamics, governed by a quadratic generator.

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Chiara Boccato
    • 1
  • Serena Cenatiempo
    • 1
  • Benjamin Schlein
    • 1
  1. 1.Institute of MathematicsUniversity of ZurichZurichSwitzerland

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