Bounds on the tight-binding approximation for the Gross-Pitaevskii equation with a periodic potential
Mathematical Physics
2007-11-20 v1 Dynamical Systems
math.MP
Abstract
We justify the validity of the discrete nonlinear Schrodinger equation for the tight-binding approximation in the context of the Gross-Pitaevskii equation with a periodic potential. Our construction of the periodic potential and the associated Wannier functions is based on the previous work, while our analysis involving energy estimates and Gronwall's inequality addresses time-dependent localized solutions on large but finite time intervals.
Keywords
Cite
@article{arxiv.0711.2694,
title = {Bounds on the tight-binding approximation for the Gross-Pitaevskii equation with a periodic potential},
author = {Dmitry Pelinovsky and Guido Schneider},
journal= {arXiv preprint arXiv:0711.2694},
year = {2007}
}
Comments
9 pages, 2 figures