title: Resolution of the Gross-Pitaevskii equation with the imaginary-time method on a Lagrange mesh.
abstract: The Lagrange-mesh method is an approximate variational calculation which has the simplicity of a mesh calculation. Combined with the imaginary-time method, it is applied to the iterative resolution of the Gross-Pitaevskii equation. Two variants of a fourth-order factorization of the exponential of the Hamiltonian and two types of mesh (Lagrange-Hermite and Lagrange-sinc) are employed and compared. The accuracy is checked with the help of these comparisons and of the virial theorem. The Lagrange-Hermite mesh provides very accurate results with short computing times for values of the dimensionless parameter of the nonlinear term up to 10⁴. For higher values up to 10⁷, the Lagrange-sinc mesh is more efficient. Examples are given for anisotropic and nonseparable trapping potentials.
authors.affiliation: Physique Quantique, C.P. 165/82 and Physique Nucléaire Théorique et Physique Mathématique, C.P. 229, Université Libre de Bruxelles, B 1050 Brussels, Belgium. dbaye@ulb.ac.be
authors.forename: D
authors.initials: D
authors.lastname: Baye
authors.forename: J-M
authors.initials: JM
authors.lastname: Sparenberg