A simple Dufort-Frankel-type scheme for the Gross-Pitaevskii equation of Bose-Einstein condensates on different geometries

Ming-Chih Lai; Chung Yin Huang; Te-Sheng Lin

doi:10.1002/num.20008

A simple Dufort-Frankel-type scheme for the Gross-Pitaevskii equation of Bose-Einstein condensates on different geometries

Ming-Chih Lai^*, Chung Yin Huang, Te-Sheng Lin

^*Corresponding author for this work

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We develop a simple Dufort-Frankel-type scheme for solving the time-dependent Gross-Pitaevskii equation (GPE). The GPE is a nonlinear Schrodinger equation describing the Bose-Einstein condensation (BEC) at very low temperature. Three different geometries including 1D spherically symmetric, 2D cylindrically symmetric, and 3D anisotropic Cartesian domains are considered. The present finite difference method is explicit, linearly unconditional stable and is able to handle the coordinate singularities in a natural way. Furthermore, the scheme is time reversible and satisfies a discrete analogue of density conservation law.

Original language	English
Pages (from-to)	624-638
Number of pages	15
Journal	Numerical Methods for Partial Differential Equations
Volume	20
Issue number	4
DOIs	https://doi.org/10.1002/num.20008
State	Published - 1 Jul 2004

Keywords

Bose-Einstein condensates
Dufort-Frankel scheme
Gross-Pitaevskii equation
Nonlinear Schrödinger equation

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title = "A simple Dufort-Frankel-type scheme for the Gross-Pitaevskii equation of Bose-Einstein condensates on different geometries",

abstract = "We develop a simple Dufort-Frankel-type scheme for solving the time-dependent Gross-Pitaevskii equation (GPE). The GPE is a nonlinear Schrodinger equation describing the Bose-Einstein condensation (BEC) at very low temperature. Three different geometries including 1D spherically symmetric, 2D cylindrically symmetric, and 3D anisotropic Cartesian domains are considered. The present finite difference method is explicit, linearly unconditional stable and is able to handle the coordinate singularities in a natural way. Furthermore, the scheme is time reversible and satisfies a discrete analogue of density conservation law.",

keywords = "Bose-Einstein condensates, Dufort-Frankel scheme, Gross-Pitaevskii equation, Nonlinear Schr{\"o}dinger equation",

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AU - Lai, Ming-Chih

AU - Huang, Chung Yin

AU - Lin, Te-Sheng

PY - 2004/7/1

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N2 - We develop a simple Dufort-Frankel-type scheme for solving the time-dependent Gross-Pitaevskii equation (GPE). The GPE is a nonlinear Schrodinger equation describing the Bose-Einstein condensation (BEC) at very low temperature. Three different geometries including 1D spherically symmetric, 2D cylindrically symmetric, and 3D anisotropic Cartesian domains are considered. The present finite difference method is explicit, linearly unconditional stable and is able to handle the coordinate singularities in a natural way. Furthermore, the scheme is time reversible and satisfies a discrete analogue of density conservation law.

AB - We develop a simple Dufort-Frankel-type scheme for solving the time-dependent Gross-Pitaevskii equation (GPE). The GPE is a nonlinear Schrodinger equation describing the Bose-Einstein condensation (BEC) at very low temperature. Three different geometries including 1D spherically symmetric, 2D cylindrically symmetric, and 3D anisotropic Cartesian domains are considered. The present finite difference method is explicit, linearly unconditional stable and is able to handle the coordinate singularities in a natural way. Furthermore, the scheme is time reversible and satisfies a discrete analogue of density conservation law.

KW - Bose-Einstein condensates

KW - Dufort-Frankel scheme

KW - Gross-Pitaevskii equation

KW - Nonlinear Schrödinger equation

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