巨正则系综处理孤立理想量子系统时的误差展示  

Demonstration of discrepancies of grand-canonical ensemble methods for finite isolate quantum systems

作　　者：胡健 周池春 顾昀 陈玉柱 HU Jian;ZHOU Chi-chun;GU Yun;CHEN Yu-zhu(School of Engineering,Dali University,Dali,Yunnan 871003,China;Department of Physics,Tianjin University,Tianjin 300072,China;Department of Physics,Tianjin Polytechnic University,Tianjin 300387,China)

机构地区：[1]大理大学工程学院,云南大理871003 [2]天津大学物理系,天津300072 [3]天津工业大学物理系,天津300387

出　　处：《大学物理》2024年第10期36-38,57,共4页College Physics

基　　金：国家自然科学基金(62106033)资助。

摘　　要：巨正则系综方法是量子统计的重要方法.巨正则系综方法通常用来处理开放系统.巨正则系综方法也常被用作处理孤立系统的近似方法:它使用系综平均粒子数和平均能量近似系统精确粒子数和能量.相较于正则和微正则系综方法,巨正则系综方法能够较为容易的处理全同粒子;作为代价,巨正则系综方法会带来误差.现有结果仅在粒子数趋于无穷时对系统的宏观量的涨落误差有近似的估计.这种误差是用巨正则系综的粒子数分布近似模拟微正则系综的粒子数分布造成的.这个工作中,我们构造了一个可以数值精确求解的孤立系统,并给出微正则系综粒子数分布的精确解和巨正则系综粒子数分布的近似解之间的差别.结果显示:在粒子数很小时,误差较为明显;基态粒子数分布误差要大于激发态;玻色系统的误差要大于费米系统的误差.The grand canonical ensemble method is an important one in quantum statistical mechanics.The grand canonical method is generally used to deal with open systems.The grand canonical method is also used to deal with isolated systems as an approximation method.It is easier for the grand canonical method than the micro canonical ensemble method in dealing with identical particles.In exchange,there are discrepancies in the results of the grand canonical ensemble method when dealing with isolated systems.The discrepancy of macroscopic quantities is provided when the particle number goes to infinity.The discrepancy comes from the different between the particle distribution of the grand canonical ensemble and of the micro canonical ensemble.In this paper,we construct an isolated system which can be exactly solved with the micro canonical ensemble method.By comparing the particle distribution in the grand canonical ensemble method and in the micro canonical ensemble method,we show the discrepancy directly.The result shows that the discrepancy is larger when we have less particle number in the system.The discrepancy of ground states is larger than excited states.The discrepancy of Bose systems is larger than Fermi systems.

关 键 词：系综 粒子数分布 量子统计 

分 类 号：O414-21[理学—理论物理]