Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. I. General concept
arXiv:1007.3180 · doi:10.1103/PhysRevA.82.023610
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.
10 pages, submitted to Phys. Rev. A, minor corrections
References in corpus (15)
- Bose-Einstein condensation of chromium
- Bose-Einstein condensation in trapped dipolar gases
- Trapped atomic condensates with anisotropic interactions
- Anisotropic solitons in dipolar Bose-Einstein Condensates
- All-Optical Production of Chromium Bose-Einstein Condensates
- Bose Condensates with 1/r Interatomic Attraction: Electromagnetically Induced ``Gravity''
- Bogoliubov modes of a dipolar condensate in a cylindrical trap
- Numerical computation of real or complex elliptic integrals
- Bose-Einstein condensates with attractive 1/r interaction: The case of self-trapping
- Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. II. Applications
- Pitchfork bifurcations in blood-cell shaped dipolar Bose-Einstein condensates
- Bifurcations, order, and chaos in the Bose-Einstein condensation of dipolar gases
- Dynamics and stability of Bose-Einstein condensates with attractive 1/r interaction
- Fictitious time wave packet dynamics: I. Nondispersive wave packets in the quantum Coulomb problem
- Fictitious time wave packet dynamics: II. Hydrogen atom in external fields
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