title: Spectral method for the time-dependent Gross-Pitaevskii equation with a harmonic trap.
abstract: We study the numerical resolution of the time-dependent Gross-Pitaevskii equation, a nonlinear Schrödinger 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 scissor modes.
authors.affiliation: CERMICS, Ecole Nationale des Ponts et Chaussées, 6 & 8 avenue Blaise Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne-la-Vallée, France.
authors.forename: Claude M
authors.initials: CM
authors.lastname: Dion
authors.forename: Eric
authors.initials: E
authors.lastname: Cancès