Rigorous Derivation of the Gross-Pitaevskii Equation
- Author(s): Erdos, Laszlo
- Schlein, Benjamin
- Yau, Horng-Tzer
- et al.
Published Web Locationhttps://arxiv.org/pdf/math-ph/0612028.pdf
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.