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arXiv 1007.4325math-phmath.MP
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关于经典统计力学中的拟连续逼近

On quasi-continuous approximation in classical statistical mechanics

Sergey Petrenko, Alexei Rebenko, Maksym Tertychnyi

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摘要：

在经典统计力学的框架下，考虑了具有强超稳相互作用的连续无限点粒子系统。近似关联函数族是以这样一种方式确定的，即它们只考虑$\mathbb{R}^d$中粒子的这种配置，对于给定的配置空间$\mathbb{R}^d$的分区，将其划分为具有体积$a^d$的不相交超立方体，每个立方体中包含不超过一个粒子。我们证明了，对于逆温度$β$和逸度$z$的任意正值，如果逼近参数$a\rightarrow 0$满足，则这些函数收敛于初始系统的真关联函数.这一结果在两体相互作用势和多体相互作用势的情况下都得到了证明。

英文摘要：

A continuous infinite system of point particles with strong superstable interaction is considered in the framework of classical statistical mechanics. The family of approximated correlation functions is determined in such a way, that they take into account only such configurations of particles in $\mathbb{R}^d$ which for a given partition of the configuration space $\mathbb{R}^d$ into nonintersecting hyper cubes with a volume $a^d$ contain no more than one particle in every cube. We prove that these functions converge to the proper correlation functions of the initial system if the parameter of approximation $a\rightarrow 0$ for any positive values of an inverse temperature $β$ and a fugacity $z$. This result is proven both for two-body interaction potentials and for many-body case.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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