最概然分布的少粒子修正是必要的吗?  

Is it necessary to improve themost probable approximation by considering the finite size effect?

作　　者：侯吉旋 HOU Ji-xuan(School of Physics,Southeast University,Nanjing,Jiangsu 211189,China)

机构地区：[1]东南大学物理学院,江苏南京211189

出　　处：《大学物理》2022年第12期1-3,7,共4页College Physics

基　　金：教育部高等学校物理学类专业教学指导委员会项目资助。

摘　　要：统计物理教材中推导最概然分布的过程存在数学缺陷,当粒子数较少时无法自圆其说.于是许多研究者利用更精确的公式对该推导进行少粒子修正.本文通过计算一维谐振子势阱中的理想玻色气体的基态布居数指出,经过少粒子修正后的结果与严格解反而相差更远.因此本文认为计算最概然分布时进行少粒子修正是没有必要的.The derivations of the most probable distribution are not self-consistent in most statistical physics textbooks since the Stirling’s approximation adopted in the derivations is not valid for systems with few particles. Thus, many attempts are devoted by adding higher Stirling terms to improve the prediction. However, by calculating the ground-state fraction of the ideal Bose system in one-dimensional harmonic trap, we show that the predictions considering the finite size effect are much worse than the predicitons given by the original version without modification. Hence, the finite-size modification to the most probable approximation is not necessary at all.

关 键 词：最概然分布 少粒子效应 玻色气体 

分 类 号：O414.21[理学—理论物理]