Anisotropic Bose-Einstein condensates and completely integrable dynamical systems

Details Anisotropic Bose-Einstein condensates and completely integrable dynamical systems Anisotropic Bose-Einstein condensates and completely integrable dynamical systems

2002-11-17

arxiv.org/abs/cond-mat/0211353v1

Phys. Rev. A v. 65 (2002) 033603-033609

Physics

Condensed Matter

Scientific paper

10.1103/PhysRevA.65.033603

A Gaussian ansatz for the wave function of two-dimensional harmonically trapped anisotropic Bose-Einstein condensates is shown to lead, via a variational procedure, to a coupled system of two second-order, nonlinear ordinary differential equations. This dynamical system is shown to be in the general class of Ermakov systems. Complete integrability of the resulting Ermakov system is proven. Using the exact solution, collapse of the condensate is analyzed in detail. Time-dependence of the trapping potential is allowed.

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