积分几何中的多体关联
Many-body correlations from integral geometry
摘要：
在最近的一封信中，我们提出了一个框架，用于预测大量液体内部的多粒子局部结构的浓度，作为评估接近动力学停滞的液体变化的途径。这一框架的核心是形态学方法，它是积分几何和液态理论的综合，传统上是从基本测量理论中推导出来的。我们提出的形态计量方法在一个新的背景下，作为一个概括的缩放粒子理论，并得出几个形态计量理论的基本和实际利益的硬球。我们的中心结果是一个新的理论，特别适合于处理多体关联函数在硬球液体，我们证明了对模拟的数值试验。
英文摘要：
In a recent letter we presented a framework for predicting the concentrations of many-particle local structures inside the bulk liquid as a route to assessing changes in the liquid approaching dynamical arrest. Central to this framework was the morphometric approach, a synthesis of integral geometry and liquid state theory, which has traditionally been derived from fundamental measure theory. We present the morphometric approach in a new context as a generalisation of scaled particle theory, and derive several morphometric theories for hard spheres of fundamental and practical interest. Our central result is a new theory which is particularly suited to the treatment of many-body correlation functions in the hard sphere liquid, which we demonstrate by numerical tests against simulation.
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