title: Rigorous derivation of the Gross-Pitaevskii equation.
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 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.
authors.affiliation: Institute of Mathematics, University of Munich, Theresienstrasse 39, D-80333 Munich, Germany.
authors.forename: László
authors.initials: L
authors.lastname: Erdos
authors.forename: Benjamin
authors.initials: B
authors.lastname: Schlein
authors.forename: Horng-Tzer
authors.initials: HT
authors.lastname: Yau