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

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

2002-09-27

arxiv.org/abs/cond-mat/0209646v3

Phys. Rev. E 67, 046706 (2003)

Physics

Condensed Matter

Soft Condensed Matter

23 pages, 5 figures

Scientific paper

10.1103/PhysRevE.67.046706

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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