Rigorous derivation of the Gross-Pitaevskii equation.

  title={Rigorous derivation of the Gross-Pitaevskii equation.},
  author={L{\'a}szl{\'o} Erdős and Benjamin Schlein and H. M.-P. Yau},
  journal={Physical review letters},
  volume={98 4},
The time-dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. We present a rigorous proof of this fact starting from a many-body bosonic Schrödinger equation with a short-scale repulsive interaction in the dilute limit. Our proof shows the persistence of an explicit short-scale correlation structure in the condensate. 
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