Rigorous Derivation of the Cubic NLS in Dimension One

@article{Adami2007RigorousDO,
  title={Rigorous Derivation of the Cubic NLS in Dimension One},
  author={Riccardo Adami and François Golse and Alessandro Teta},
  journal={Journal of Statistical Physics},
  year={2007},
  volume={127},
  pages={1193-1220}
}
We derive rigorously the one-dimensional cubic nonlinear Schrödinger equation from a many-body quantum dynamics. The interaction potential is rescaled through a weak-coupling limit together with a short-range one. We start from a factorized initial state, and prove propagation of chaos with the usual two-step procedure: in the former step, convergence of the solution of the BBGKY hierarchy associated to the many-body quantum system to a solution of the BBGKY hierarchy obtained from the cubic… 
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