高维δ函数在系综理论里的应用

对Gibbs系综的概念进行抽象和推广,把系综表示为三元组{Γ,Ω,ρ（q）}.运用高维δ函数将态矢量q的分量以及函数的几率分布写为统一的积分形式.导出一个约束条件下等概率系综的分布函数,它可以写成δ函数的形式.将所得结论用于讨论理想气体,运用Laplace变换法解决δ函数积分的问题,导出经典理想气体的麦克斯韦-玻尔兹曼分布律.

The Application of Dirac Function in Ensemble Theory

Based on the generalizing and abstracting of Gibbs ensemble, the triad {Γ,Ω,ρ（q）} was used to de- scribe an ensemble. By the use of dirac-δfunction,the probability distribution of the components and functions of the state vector q can be written in a general form of integration. Under one constrain, the probability density function of equal probability ensemble was derived which can be written in the form of δfunction. These results were used to discuss the classical ideal gas, and Maxwell-Bohzmann distribution was derived by the use of La- place transform method.