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.
Multicomponent fluids of hard hyperspheres in odd dimensions
利用解析逼近方法研究了奇数维空间中硬超球的混合问题。这种技术是基于所谓的有理函数近似，并提供了一个程序，用于评估状态方程，结构因子，径向分布函数，和直接相关函数的添加剂混合物的硬超球与任何数量的组件和任意奇维空间。该方法给出了与Percus-Yevick封闭耦合的Ornstein-Zernike方程的精确解，从而将硬球混合物的解推广到任意奇数维[J. L. Lebowitz，Phys.修订版本\ \textbf{133}，895（1964）]。在五个维度的二元混合物进行显式评价。将计算结果与计算机模拟结果进行了比较，两者吻合较好.
Exact solution of the Percus-Yevick integral equation for fluid mixtures of hard hyperspheres
最近已经在有理函数近似（RFA）的框架中导出了奇数维度的多组分硬球流体的结构和热力学性质[Rohrmann和Santos，Phys. Rev. E \textbf{83}，011201（2011）]。它表明，在这里，RFA技术产生的精确解的Percus-Yevick（PY）封闭的Ornstein-Zernike（OZ）方程的二元混合物在任意奇数维。证明主要依赖于由OZ关系定义的直接关联函数的傅立叶变换$\hat{c}_{ij}(k)$。通过对$\hat{c}_{ij}(k)$极点的分析，我们发现RFA方法计算的直接关联函数在硬核外消失，这与PY理论的要求一致。
Emergent hydrodynamics of chiral active fluids: vortices, bubbles and odd diffusion
School of Sciences and Technology, University of Camerino（卡梅里诺大学科学与技术学院）；Sapienza University of Rome（罗马第一大学）；Paris-Saclay University, CNRS, Laboratoire de Physique des Solides（巴黎萨克雷大学，法国国家科学研究中心，固体物理实验室）
Active fluids, which are driven at the microscale by non-conservative forces, are known to exhibit novel transport phenomena due to the breaking of time reversal symmetry. Recently, Epstein and Mandadapu [arXiv:1907.10041] obtained Green-Kubo relations for the full set of viscous coefficients governing isotropic chiral active fluids, including the so-called odd viscosity, invoking Onsager's regression hypothesis for the decay of fluctuations in active non-equilibrium steady states. In this Communication, we test these Green-Kubo relations using molecular dynamics simulations of a canonical mod…
Diffusion is a fundamental aspect of transport processes in biological systems, and thus, in the development of life itself. And yet, the diffusive dynamics of active fluids with directed rotation, known as chiral fluids, has not been analyzed in detail so far. Here, we describe the diffusive regimes of a two-dimensional chiral fluid, composed in this case of a set of identical disk-shaped rotors. We found strong experimental evidence of odd diffusion. This odd diffusion emerges in the form of a two-dimensional tensor with an antisymmetric part. In particular, we show that chiral diffusion is …
City College of the City University of New York（纽约市立大学城市学院）；The Pennsylvania State University（宾夕法尼亚州立大学）；Western Washington University（西华盛顿大学）；Graduate Center of City University of New York（纽约市立大学研究生中心）
In common fluids, viscosity is associated with dissipation. However, when time-reversal-symmetry is broken a new type of non-dissipative `viscosity' may emerge. Recent theories and experiments on classical 2D systems with active spinning particles have heightened interest in odd viscosity, but a microscopic theory for it in active materials is still absent. Here we present such first-principles microscopic Hamiltonian theory, valid for both 2D and 3D, showing that odd viscosity is present in any system, equilibrium or not, with aligned spinning components. Our work substantially extends the ap…
Reversal of tracer advection and Hall drift in an interacting chiral fluid
University of Potsdam（波茨坦大学）；Leibniz-Institute for Polymer Research（莱布尼茨聚合物研究所）；Technical University of Dresden（德累斯顿工业大学）；Asia Pacific Centre for Theoretical Physics（亚太理论物理中心）；University of Augsburg（奥格斯堡大学）
The flow of momentum and energy in a fluid is typically associated with dissipative transport coefficients: viscosity and thermal conductivity. Fluids that break certain symmetries such as mirror symmetry and time-reversal invariance can display non-dissipative transport coefficients called odd (or Hall) viscosities and thermal conductivities. The goal of this paper is to elucidate the microscopic origin of these dissipationless transport coefficients using kinetic theory. We show that odd viscosity and odd thermal conductivity arise when the linearized collision operator is not Hermitian. Thi…
