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

• Published in: Frontiers of physics Vol. 8; no. 3; pp. 319 - 327
• Main Author: 石玉仁 王雪玲 王光辉 刘丛波 周志刚 杨红娟
• Format: Journal Article
• Language: English
• Published: Heidelberg Higher Education Press 01.06.2013; SP Higher Education Press; Springer Nature B.V
• 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; analytical solution; homotopy analysis method; Gross-Pitaevskii equation; spin-1 Bose-Einstein condensate
• ISSN: 2095-0462; 2095-0470
• DOI: 10.1007/s11467-013-0332-x

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.