论文标题
经典统计力学和晶体问题的相关功能的身份
Identities for correlation functions in classical statistical mechanics and the problem of crystal states
论文作者
论文摘要
令$ z $为$ {\ bf r}^ν$中经典平衡统计力学描述的点粒子的活动。相关函数$ρ^z（x_1，\ dots，x_k）$表示在$ x_1，\ dots，x_k $中查找$ k $粒子的概率。让$ ϕ^z（x_1，\ dots，x_k）$为群集函数，对应于$ρ^z（x_1，\ dots，x_k）/z^k $我们在类型$$ ϕ^{z_0+z'}（x_1，x_1，x___k）$ dots，x__k）的标识 =\sum_{n=0}^\infty{z'^n\over n!}\int dx_{k+1}\dots\int dx_{k+n}\,ϕ^{z_0}(x_1,\dots,x_{k+n}) $$ It is then non-rigorously argued that, assuming a suitable cluster property (decay of相关性）对于晶体状态，压力和翻译不变相关函数\ - $ρ^z（x_1，\ dots，x_k）$是$ z $的真实分析函数。
Let $z$ be the activity of point particles described by classical equilibrium statistical mechanics in ${\bf R}^ν$. The correlation functions $ρ^z(x_1,\dots,x_k)$ denote the probability densities of finding $k$ particles at $x_1,\dots,x_k$. Letting $ϕ^z(x_1,\dots,x_k)$ be the cluster functions corresponding to the $ρ^z(x_1,\dots,x_k)/z^k$ we prove identities of the type $$ ϕ^{z_0+z'}(x_1,\dots,x_k) $$ $$ =\sum_{n=0}^\infty{z'^n\over n!}\int dx_{k+1}\dots\int dx_{k+n}\,ϕ^{z_0}(x_1,\dots,x_{k+n}) $$ It is then non-rigorously argued that, assuming a suitable cluster property (decay of correlations) for a crystal state, the pressure and the translation invariant correlation functions \- $ρ^z(x_1,\dots,x_k)$ are real analytic functions of $z$.
