摘要翻译：
本文用解析近似方法研究了奇数空间维数D$中硬超球单组分流体的结构性质，该方法推广了以前在硬球流体研究中引入的有理函数近似[S.B.Yuste和A.Santos,Phys.Rev.A{\BF 43},5418（1991）]。该理论利用径向分布函数的精确形式到密度的一阶，并通过对定义在拉普拉斯空间中的函数假定有理形式，将其推广到有限密度，系数由简单的物理要求确定。反向贝塞尔多项式的傅里叶变换构成了该近似的数学框架，由此得到了静态结构因子的解析表达式。该方法以其最基本的形式将Percus-Yevick闭包的解恢复到奇维超球面的Ornstein-Zernike方程。目前的形式允许人们超越它，得到在维里和可压缩性路线之间具有热力学一致性的解，以达到任何所需的状态方程。在$d=5$和$d=7$时，与现有的计算机模拟数据吻合得很好。作为本研究的一个副产品，给出了任意奇维上两个相同超球面交体积的精确而显式的多项式表达式。
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英文标题：
《Structure of hard-hypersphere fluids in odd dimensions》
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作者：
Rene D. Rohrmann and Andres Santos
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics        物理学
二级分类：Soft Condensed Matter        软凝聚态物质
分类描述：Membranes, polymers, liquid crystals, glasses, colloids, granular matter
膜，聚合物，液晶，玻璃，胶体，颗粒物质
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一级分类：Physics        物理学
二级分类：Chemical Physics        化学物理学
分类描述：Experimental, computational, and theoretical physics of atoms, molecules, and clusters - Classical and quantum description of states, processes, and dynamics; spectroscopy, electronic structure, conformations, reactions, interactions, and phases. Chemical thermodynamics. Disperse systems. High pressure chemistry. Solid state chemistry. Surface and interface chemistry.
原子、分子和团簇的实验、计算和理论物理-状态、过程和动力学的经典和量子描述；光谱学，电子结构，构象，反应，相互作用和相。化学热力学。分散系统。高压化学。固态化学。表面和界面化学。
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英文摘要：
  The structural properties of single component fluids of hard hyperspheres in odd space dimensionalities $d$ are studied with an analytical approximation method that generalizes the Rational Function Approximation earlier introduced in the study of hard-sphere fluids [S. B. Yuste and A. Santos, Phys. Rev. A {\bf 43}, 5418 (1991)]. The theory makes use of the exact form of the radial distribution function to first order in density and extends it to finite density by assuming a rational form for a function defined in Laplace space, the coefficients being determined by simple physical requirements. Fourier transform in terms of reverse Bessel polynomials constitute the mathematical framework of this approximation, from which an analytical expression for the static structure factor is obtained. In its most elementary form, the method recovers the solution of the Percus-Yevick closure to the Ornstein-Zernike equation for hyperspheres at odd dimension. The present formalism allows one to go beyond by yielding solutions with thermodynamic consistency between the virial and compressibility routes to any desired equation of state. Excellent agreement with available computer simulation data at $d=5$ and $d=7$ is obtained. As a byproduct of this study, an exact and explicit polynomial expression for the intersection volume of two identical hyperspheres in arbitrary odd dimensions is given.
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PDF链接：
https://arxiv.org/pdf/708.2677