Rigorous Derivation of the Gross-Pitaevskii Equation
  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 Schroedinger 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. 
Laszlo Erdos, Benjamin Schlein, Horng-Tzer Yau