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 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.
Erdos
László
L
Institute of Mathematics, University of Munich, Theresienstrasse 39, D-80333 Munich, Germany.
Schlein
Benjamin
B
Yau
Horng-Tzer
HT