Anisotropic Bose-Einstein condensates and completely integrable dynamical systems
arXiv:cond-mat/0211353 · doi:10.1103/PhysRevA.65.033603
Abstract
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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Cited by in corpus (8)
- Variational approach for the quantum Zakharov system
- Cosmic Dynamics of Bose-Einstein Condensates
- Recent Applications of the Theory of Lie Systems in Ermakov Systems
- On the Time Dependent Oscillator and the Nonlinear Realizations of the Virasoro Group
- Lie Point Symmetries for Reduced Ermakov Systems
- Ladder operators and squeezed coherent states of a 3-dimensional generalized isotonic nonlinear oscillator
- Relativistic Ermakov-Milne-Pinney Systems and First Integrals
- Parametric Competition in non-autonomous Hamiltonian Systems