# 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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