服从中间统计的理想自由粒子模型的低温比热  

Specific Heat of an Ideal Free-particle Model Obeying Intermediate Statistics at Low Temperatures

作　　者：刘雅晶[1] 云国宏[1] 

机构地区：[1]内蒙古大学理工学院物理系,呼和浩特010021

出　　处：《内蒙古大学学报（自然科学版）》2005年第3期252-258,共7页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金项目(10147203);内蒙古教育厅重大项目(ZJ02004)资助

摘　　要：利用现行标准的统计力学方法推导出中间统计的巨配分函数,得到了服从中间统计的理想自由粒子模型的热力学函数.考虑基态能以及粒子占据数对模型的影响,计算了其低温比热.结果表明:当m(即单粒子态上最多容纳的粒子数)为较小正整数时,其性质与费米系统的性质较为接近,模型比热的变化除在m=2、3处出现反常外,都随着m的增加而逐渐减小;当m为较大整数时,模型的类玻色性增强,热力学性质与玻色系统有较好的相似性.The grand partition function of intermediate statistics with a standard method is derived to calculate the thermodynamic properties of an ideal free-particle model.The specific heat of the model at low temperature is discussed by taking the ground state energy and the occupation number into consideration. The results show that the properties of this model and the ideal fermion model are similar when m (the maximum occupation number in a single-particle state) is a smaller positive integer, and the specific heat decreases with the increase of m except for m being 2 or 3.When m is a bigger positive integer,the properties of the model are similar to that of an ideal boson model.

关 键 词：量子统计 配分函数 比热 

分 类 号：O414.2[理学—理论物理]