Related Experiment Video
Updated: Jun 5, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Resolution of the Gross-Pitaevskii equation with the imaginary-time method on a Lagrange mesh
1Physique 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
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.
Related Concept Videos
Poisson's And Laplace's Equation
Differential Form of Maxwell's Equations
Mesh Analysis
A fundamental concept in mesh analysis is the definition of meshes and mesh currents. A mesh is a closed...
Eulerian and Lagrangian Flow Descriptions
The Eulerian method focuses on fixed points in space where fluid properties, such as velocity, pressure, and temperature, are observed as the fluid moves between these...
Impulse-Momentum Theorem
By writing Newton's second law of motion in terms of the momentum of an object and the external force acting on it, and simultaneously using the definition of the impulse vector, it can be shown that the total impulse on an object is equal to its net...
Magnetostatic Boundary Conditions
