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arXiv · 1007.3180

Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. I. General concept

Stefan Rau·Jörg Main·Günter Wunner
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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.

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Stefan Rau, Jörg Main, Günter Wunner. 2010-08-11. Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. I. General concept. https://doi.org/10.1103/physreva.82.023610

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