Analytical solutions for the spin-1 Bose-Einstein condensate in a harmonic trap

The homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions for the Gross-Pitaevskii equations, a set of nonlinear Schrödinger equation used in simulation of spin-1 Bose-Einstein condensates trapped in a harmonic potential. We investigate the one-dimensiona...

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Bibliographic Details
Published in:Frontiers of physics 2013-06, Vol.8 (3), p.319-327
Main Author: 石玉仁 王雪玲 王光辉 刘丛波 周志刚 杨红娟
Format: Article
Language:English
Subjects:
analytical solution
Astronomy
Astrophysics and Cosmology
Atomic
Atomic interactions
Bose-Einstein condensates
Condensed Matter Physics
Exact solutions
Galerkin谱方法
Gross-Pitaevskii equation
homotopy analysis method
Homotopy theory
Molecular
Optical and Plasma Physics
Particle and Nuclear Physics
Physics
Physics and Astronomy
Research Article
Schrodinger equation
Spectral methods
spin-1 Bose-Einstein condensate
势阱
同伦分析
爱因斯坦凝聚
玻色
自旋
谐振
近似解析解
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Summary:The homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions for the Gross-Pitaevskii equations, a set of nonlinear Schrödinger equation used in simulation of spin-1 Bose-Einstein condensates trapped in a harmonic potential. We investigate the one-dimensional case and get the approximate analytical solutions successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are in agreement well with each other when the atomic interaction is weakly. We also find a class of exact solutions for the stationary states of the spin-1 system with harmonic potential for a special case.
ISSN:2095-0462
2095-0470
DOI:10.1007/s11467-013-0332-x