作为抽象聚合物气体的正则包体中的连续粒子
Continuos particles in the Canonical Ensemble as an abstract polymer gas
摘要：
我们重温最近提出的扩展Pulvirenti和Tsagkarogiannis的$N$连续粒子系统的规范合奏。在粒子通过回火和稳定的对势相互作用并受到通常的自由边界条件的唯一假设下，我们显示了低密度下亥姆霍兹自由能的解析性，并使用彭罗斯树图恒等式，我们建立了一个收敛半径的下界，这个下界恰好与巨正则系综中维里级数收敛半径的下界相同由莱博维茨和彭罗斯于1964年创立。我们还表明，（Helmholtz）自由能可以写为一系列的密度的$k$阶系数重合，模项$o(N)/N$，与$k$阶维里系数除以$k+1$，根据其表达的$m$阶（与$m\le k+1$）简单连接的集群积分第一次由迈耶在1942年。最后，我们给出了一个上限的$k$阶维里系数略有改善，在高温下，由Lebowitz和彭罗斯得到的界。
英文摘要：
We revisit the expansion recently proposed by Pulvirenti and Tsagkarogiannis for a system of $N$ continuous particles in the canonical ensemble. Under the sole assumption that the particles interact via a tempered and stable pair potential and are subjected to the usual free boundary conditions, we show the analyticity of the Helmholtz free energy at low densities and, using the Penrose tree graph identity, we establish a lower bound for the convergence radius which happens to be identical to the lower bound of the convergence radius of the virial series in the grand canonical ensemble established by Lebowitz and Penrose in 1964. We also show that the (Helmholtz) free energy can be written as a series in power of the density whose $k$ order coefficient coincides, modulo terms $o(N)/N$, with the $k$-order virial coefficient divided by $k+1$, according to its expression in terms of the $m$-order (with $m\le k+1$) simply connected cluster integrals first given by Mayer in 1942. We finally give an upper bound for the $k$-order virial coefficient which slightly improves, at high temperatures, the bound obtained by Lebowitz and Penrose.
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