Spectral method for the time-dependent Gross-Pitaevskii equation with a harmonic trap
arXiv:cond-mat/0209646 · doi:10.1103/PhysRevE.67.046706
Abstract
We study the numerical resolution of the time-dependent Gross-Pitaevskii equation, a non-linear Schroedinger equation used to simulate the dynamics of Bose-Einstein condensates. Considering condensates trapped in harmonic potentials, we present an efficient algorithm by making use of a spectral Galerkin method, using a basis set of harmonic oscillator functions, and the Gauss-Hermite quadrature. We apply this algorithm to the simulation of condensate breathing and scissors modes.
23 pages, 5 figures
References in corpus (15)
- Theory of Bose-Einstein condensation in trapped gases
- Superchemistry: dynamics of coupled atomic and molecular Bose-Einstein condensates
- Bose-Einstein Condensation of Metastable Helium
- Watching a superfluid untwist itself: Recurrence of Rabi oscillations in a Bose-Einstein condensate
- Dark soliton states of Bose-Einstein condensates in anisotropic traps
- Observation of the scissors mode and superfluidity of a trapped Bose-Einstein condensed gas
- Structure of binary Bose-Einstein condensates
- Scissors mode and superfluidity of a trapped Bose-Einstein condensed gas
- Coherent Evolution of Bouncing Bose-Einstein Condensates
- A numerical approach to the ground and excited states of a Bose-Einstein condensed gas confined in a completely anisotropic trap
- Numerical study of the spherically-symmetric Gross-Pitaevskii equation in two space dimensions
- Asymptotic solutions to the Gross-Pitaevskii gain equation: growth of a Bose-Einstein condensate
- Dynamics of two colliding Bose-Einstein condensates in an elongated magneto-static trap
- Generation and evolution of vortex-antivortex pairs in Bose-Einstein condensates
- Output coupling and flow of a dilute Bose-Einstein condensate
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