Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Jisuan wuli

Dynamic Study for Numerical Solutions ofthe Gross-Pitaevskii Equation

H. Wei

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

The ground state wavefunctions of dilute Bose-condensed atoms in a harmonic trap at T=0 are evaluated by a symplectic shooting method.Stability of the wavefunctions is tested,and a stable wavefunction is used as the initial input of the time-dependent Gross-Pitaevskii equation. The dynamic property of stable wavefunctions is numerically examined in two phase spaces when the harmonic potential is altered suddenly.The figures in the two phase spaces are regular even after a long time of interations.For negative nonlinear coefficients,two eigenvalues related to the same negative nonlinear coefficient are calculated,and the stability of the corresponding two wavefunctions is tested.

Related papers

Stationary Solutions of the Gross-Pitaevskii Equation for Neutral Atoms in Harmonic Trap

Wei Hua, Xue‐Shen Liu, Peizhu Ding

We solve the time-independent Gross-Pitaevskii equation that describes the dilute Bose-condensed atoms in harmonic trap at T =0 by symplectic shooting method (SSM). Both the repulsive nonlinearity and the attractive nonlinearity cases are studied, and the bounded state eigenvalues as well as the corresponding wave functions are presented.

CRC Press eBooks•Apr 29, 2019•1 citation

Bose-Einstein Condensation Dynamics from the Numerical Solution of the Gross-Pitaevskii Equation by the Pseudospectral Method

Paulsamy Muruganandam, Sadhan K. Adhikari

We study certain stationary and time-evolution problems of trapped Bose-Einstein condensates of weakly interacting alkali atoms described by a nonlinear Gross-Pitaevskii (GP) equation. We suggest a pseudospectral method involving Laguerre polynomials to solve the time dependent GP for a spherically symmetric trap potential. The radial wavefunction and energy values have been calculated for different nonlinearities. Further, we study the effect of suddenly changing the interatomic scattering length or harmonic oscillator trap potential in the condensate. We also investigate the frequency of oscillation due to the variation in the strength of nonlinearity.

arXiv:cond-mat/0310403•Oct 17, 2003•0 citations

Bose-Einstein condensation dynamics from the numerical solution of the Gross-Pitaevskii equation

Sadhan K. Adhikari, Paulsamy Muruganandam

We study certain stationary and time-evolution problems of trapped Bose-Einstein condensates using the numerical solution of the Gross-Pitaevskii (GP) equation with both spherical and axial symmetries. We consider time-evolution problems initiated by suddenly changing the interatomic scattering length or harmonic trapping potential in a stationary condensate. These changes introduce oscillations in the condensate which are studied in detail. We use a time iterative split-step method for the solution of the time-dependent GP equation, where all nonlinear and linear non-derivative terms are treated separately from the time propagation with the kinetic energy terms. Even for an arbitrarily strong nonlinear term this leads to extremely accurate and stable results after millions of time iterations of the original equation.

arXiv:cond-mat/0205172•Journal of Physics B Atomic Molecular and Optical Physics•Jun 10, 2002•137 citations

Improved Shooting Method for Gross-Pitaevskii Equation:Interference of Three Bose-Einstein Condensates

Xue‐Shen Liu

An improved shooting method is applied to 1D Gross-Pitaevskii equation,which describes Bose-Einstein condensate of neutral atoms in harmonic trapping potential at zero temperature.Eigenvalues of ground state of condensates with different nonlinear coefficient are given.Interference of three condensates after removing the trapping potential is studied with symplectic method.A periodic evolution is shown.Influence of relative phase on interference of condensates is discussed.

Jisuan wuli•Jan 1, 2011•0 citations

Analytical Solutions for the Two-Dimensional Gross—Pitaevskii Equation with a Harmonic Trap

Yu-Ren Shi, Xue-Ling Wang, Guanghui Wang +2 more

Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation, a nonlinear Schrödinger equation used in describing the system of Bose-Einstein condensates trapped in a harmonic potential. The approximate analytical solutions are obtained successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are agreement very well with each other when the atomic interaction is not too strong.

Communications in Theoretical Physics•Mar 1, 2013•4 citations

Ground State Properties for Bose-Condensed Gas in Anisotropic Traps

Xu Zhi-Jun, Haibin Li, Xin Xiao-Tian +2 more

Based on the energy functional and variational method, we present a new method to investigate the ground state properties for a weakly interacting Bose-condensed gas in an anisotropic harmonic trap at zero temperature. With this method we are able to find the analytic expression of the ground-state wavefunction and to explore the relevant quantities, such as energy, chemical potential, and the aspect ratio of the velocity distribution. These results agree well with previous ground state numerical solutions of the Gross–Pitaevskii equation given by Dalfovo et al. [Phys. Rev. A 53 (1996) 2477] This new method is simple compared to other methods used to solve numerically the Gross–Pitaevskii equation, and one can obtain analytic and reliable results.

Chinese Physics Letters•May 30, 2006•2 citations
The ground state wavefunctions of dilute Bose-condensed atoms in a harmonic trap at T=0 are evaluated by a symplectic shooting method.Stability of the wavefunctions is tested,and a stable wavefunction is used as the initial input of the time-dependent Gross-Pitaevskii equation. The dynamic property of stable wavefunctions is numerically examined in two phase spaces when the harmonic potential is altered suddenly.The figures in the two phase spaces are regular even after a long time of interations.For negative nonlinear coefficients,two eigenvalues related to the same negative nonlinear coefficient are calculated,and the stability of the corresponding two wavefunctions is tested.
We study certain stationary and time-evolution problems of trapped Bose-Einstein condensates of weakly interacting alkali atoms described by a nonlinear Gross-Pitaevskii (GP) equation. We suggest a pseudospectral method involving Laguerre polynomials to solve the time dependent GP for a spherically symmetric trap potential. The radial wavefunction and energy values have been calculated for different nonlinearities. Further, we study the effect of suddenly changing the interatomic scattering length or harmonic oscillator trap potential in the condensate. We also investigate the frequency of oscillation due to the variation in the strength of nonlinearity.
We study certain stationary and time-evolution problems of trapped Bose-Einstein condensates using the numerical solution of the Gross-Pitaevskii (GP) equation with both spherical and axial symmetries. We consider time-evolution problems initiated by suddenly changing the interatomic scattering length or harmonic trapping potential in a stationary condensate. These changes introduce oscillations in the condensate which are studied in detail. We use a time iterative split-step method for the solution of the time-dependent GP equation, where all nonlinear and linear non-derivative terms are treated separately from the time propagation with the kinetic energy terms. Even for an arbitrarily strong nonlinear term this leads to extremely accurate and stable results after millions of time iterations of the original equation.
Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation, a nonlinear Schrödinger equation used in describing the system of Bose-Einstein condensates trapped in a harmonic potential. The approximate analytical solutions are obtained successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are agreement very well with each other when the atomic interaction is not too strong.
Based on the energy functional and variational method, we present a new method to investigate the ground state properties for a weakly interacting Bose-condensed gas in an anisotropic harmonic trap at zero temperature. With this method we are able to find the analytic expression of the ground-state wavefunction and to explore the relevant quantities, such as energy, chemical potential, and the aspect ratio of the velocity distribution. These results agree well with previous ground state numerical solutions of the Gross–Pitaevskii equation given by Dalfovo et al. [Phys. Rev. A 53 (1996) 2477] This new method is simple compared to other methods used to solve numerically the Gross–Pitaevskii equation, and one can obtain analytic and reliable results.