Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. I. General concept
Abstract
The variational method of coupled Gaussian functions is applied to Bose-Einstein condensates with long-range interactions. The time-dependence of the condensate is described by dynamical equations for the variational parameters. We present the method and analytically derive the dynamical equations from the time-dependent Gross-Pitaevskii equation. The stability of the solutions is investigated using methods of nonlinear dynamics. The concept presented in this paper will be applied to Bose-Einstein condensates with monopolar 1/r and dipolar 1/r^3 interaction in the subsequent paper [S. Rau et al., Phys. Rev. A, submitted], where we will present a wealth of new phenomena obtained by using the ansatz with coupled Gaussian functions.
Cite
@article{arxiv.1007.3180,
title = {Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. I. General concept},
author = {Stefan Rau and Jörg Main and Günter Wunner},
journal= {arXiv preprint arXiv:1007.3180},
year = {2010}
}
Comments
10 pages, submitted to Phys. Rev. A, minor corrections