Mathematical Physics Seminar, November 17, 2008
Gross-Pitaevskii Equation for the Dynamics of the Bose-Einstein Condensate
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 and even the emergence of an explicit short scale correlation structure in the condensate.