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Spectral method for the time-dependent Gross-Pitaevskii equation with a harmonic trap

Claude M. Dion·Eric Cances
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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.

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Claude M. Dion, Eric Cances. 2003-02-24. Spectral method for the time-dependent Gross-Pitaevskii equation with a harmonic trap. https://doi.org/10.1103/physreve.67.046706

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