Rigorous Derivation of the Gross-Pitaevskii Equation
arXiv:math-ph/0612028 · doi:10.1103/PhysRevLett.98.040404
Abstract
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.
4 pages, 1 figure