paper

Nonlinear dynamics of Bose-condensed gases by means of a low- to high-density variational approach

arXiv:0801.3428 · doi:10.1016/j.physa.2008.06.055

Abstract

We propose a versatile variational method to investigate the spatio-temporal dynamics of one-dimensional magnetically-trapped Bose-condensed gases. To this end we employ a \emph{q}-Gaussian trial wave-function that interpolates between the low- and the high-density limit of the ground state of a Bose-condensed gas. Our main result consists of reducing the Gross-Pitaevskii equation, a nonlinear partial differential equation describing the T=0 dynamics of the condensate, to a set of only three equations: \emph{two coupled nonlinear ordinary differential equations} describing the phase and the curvature of the wave-function and \emph{a separate algebraic equation} yielding the generalized width. Our equations recover those of the usual Gaussian variational approach (in the low-density regime), and the hydrodynamic equations that describe the high-density regime. Finally, we show a detailed comparison between the numerical results of our equations and those of the original Gross-Pitaevskii equation.

11 pages, 12 figures, submitted to Phys. Rev. A, January 2008

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