A time-splitting spectral method for coupled Gross-Pitaevskii equations with applications to rotating Bose-Einstein condensates

Authors:
Hanquan Wang
Affiliations:
Department of Computational Science, National University of Singapore, Singapore 117543, Singapore
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 5
Cited 7

On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime

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Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation

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An Explicit Unconditionally Stable Numerical Method for Solving Damped Nonlinear Schrödinger Equations with a Focusing Nonlinearity

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A Fourth-Order Time-Splitting Laguerre--Hermite Pseudospectral Method for Bose--Einstein Condensates

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An efficient and spectrally accurate numerical method for computing dynamics of rotating Bose-Einstein condensates

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A time-splitting spectral method for computing dynamics of spinor F=1 Bose-Einstein condensates

International Journal of Computer Mathematics - Splitting Methods for Differential Equations
A minimisation approach for computing the ground state of Gross-Pitaevskii systems

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Numerical Simulations on Stationary States for Rotating Two-Component Bose-Einstein Condensates

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High accuracy representation of the free propagator

Applied Numerical Mathematics
Maximum norm error bound of a linearized difference scheme for a coupled nonlinear Schrödinger equations

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An efficient numerical method for computing dynamics of spin F=2 Bose-Einstein condensates

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An efficient spectral method for computing dynamics of rotating two-component Bose-Einstein condensates via coordinate transformation

Journal of Computational Physics

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Abstract

We propose a time-splitting spectral method for the coupled Gross-Pitaevskii equations, which describe the dynamics of rotating two-component Bose-Einstein condensates at a very low temperature. The new numerical method is explicit, unconditionally stable, time reversible, time transverse invariant, and of spectral accuracy in space and second-order accuracy in time. Moreover, it conserves the position densities in the discretized level. Numerical applications on studying the generation of topological modes and the vortex lattice dynamics for the rotating two-component Bose-Einstein condensates are presented in detail.