Rigorous Derivation of the Gross-Pitaevskii Equation
Mathematical Physics
2009-11-11 v1 math.MP
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.
Keywords
Cite
@article{arxiv.math-ph/0612028,
title = {Rigorous Derivation of the Gross-Pitaevskii Equation},
author = {Laszlo Erdos and Benjamin Schlein and Horng-Tzer Yau},
journal= {arXiv preprint arXiv:math-ph/0612028},
year = {2009}
}
Comments
4 pages, 1 figure