三维简谐势阱中玻色-爱因斯坦凝聚的边界效应

摘要

By defining the characteristic length, the boundary effects of Bose-Einstein condensation in a three-dimensional harmonic trap are investigated using the Euler-MacLaurin formula. Results show that the condensed fraction of particles reduces due to the finite-size effects and the effects of finite particle number;the corrections of the condensation fraction and the condensation temperature have, respectively, a maximum value due to the boundary effect, hence it is very effective to optimize the parameters of the harmonic traps for improving the condensation fraction and the condensation temperature. In the jump of heat capacity exist the boundary effects and the effects of finite particle number, and the jump of heat capacity has a minimum because the parameters of harmonic traps are selected to be reasonable. The equation of state is derived for a finite ideal Bose gas system in a three-dimensional harmonic trap; the anisotropy (or isotropy) of the pressure is determined by the anisotropy (or isotropy) of the frequency of the harmonic potential.%在定义特征长度的基础上，应用Euler-MacLaurin公式，研究了理想玻色气体在三维简谐势阱中玻色-爱因斯坦凝聚的边界效应。结果表明：粒子的凝聚分数由于有限尺度和有限粒子数效应而减小，修正的凝聚分数和凝聚温度由于边界效应存在一个极大值，选择优化的最佳势阱参数，可以有效提高凝聚分数和凝聚温度；热容量的跃变存在边界效应和粒子数效应，选择合理的势阱参数时，热容量的跃变存在一个极小值。导出了简谐势阱中有限理想玻色气体的状态方程，揭示了压强的各向异性(或各向同性)取决于简谐势频率的各向异性(或各向同性)。