Generalized nonpolynomial Schrodinger equations for matter waves under anisotropic transverse confinement
Abstract
Starting from the three-dimensional Gross-Pitaevskii equation we derive a 1D generalized nonpolynomial Schrodinger equation, which describes the dynamics of Bose-Einstein condensates under the action of a generic potential in the longitudinal axial direction and of an anisotropic harmonic potential in the transverse radial direction. This equation reduces to the familiar 1D nonpolynomial Schrodinger equation [Phys. Rev. A 65, 043614 (2002)] in the case of isotropic transverse harmonic confinement. In addition, we show that if the longitudinal potential models a periodic optical lattice the 3D GPE can be mapped into a 1D generalized discrete nonpolynomial Schrodinger equation.
Keywords
Cite
@article{arxiv.0907.1248,
title = {Generalized nonpolynomial Schrodinger equations for matter waves under anisotropic transverse confinement},
author = {Luca Salasnich},
journal= {arXiv preprint arXiv:0907.1248},
year = {2015}
}
Comments
9 pages, 2 figures, to be published in Journal of Physics A: Math. Theor