arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2203.01795cond-mat.softcond-mat.stat-mech
收藏

力密度泛函理论的平衡态和非平衡态

Force density functional theory in- and out-of-equilibrium

S. M. Tschopp, F. Sammüller, S. Hermann, M. Schmidt, J. M. Brader

摘要:

当流体受到外部场的作用时,如在界面附近或在空间限制下的情况,则密度变得空间不均匀。虽然单体密度提供了许多有用的信息,但两体相关提供了更高水平的分辨率。这些给出了流体内部微观结构的统计描述,并能够计算平均粒子间力,这在确定相互作用流体的平衡和动态特性方面起着至关重要的作用。我们提出了一个理论框架的非均匀(经典)多体系统的描述,明确的基础上的两体关联函数。通过考虑局部Noether不变性对系统的空间畸变,我们证明了Yvon-Born-Green(YBG)方程的基本地位,作为一个局部的力平衡内的流体。使用非齐次Ornstein-Zernike方程,我们表明,两体相关性是密度泛函,因此,进入YBG方程的平均粒子间力也是一个功能的单体密度。我们发展的力为基础的理论提供了一种替代标准的密度泛函理论的非均匀系统的研究在和出平衡。我们比较力为基础的密度分布的结果,标准的潜在的(动态)密度泛函理论。在平衡状态下,我们确认分析和数值计算的标准方法产生的配置文件是一致的压缩性压力,而力密度泛函的配置文件与维里压力一致。该理论的结构提供了深入的见解,在密集和非均匀系统的相关性的性质。

英文摘要:

When a fluid is subject to an external field, as is the case near an interface or under spatial confinement, then the density becomes spatially inhomogeneous. Although the one-body density provides much useful information, a higher level of resolution is provided by the two-body correlations. These give a statistical description of the internal microstructure of the fluid and enable calculation of the average interparticle force, which plays an essential role in determining both the equilibrium and dynamic properties of interacting fluids. We present a theoretical framework for the description of inhomogeneous (classical) many-body systems, based explicitly on the two-body correlation functions. By consideration of local Noether-invariance against spatial distortion of the system we demonstrate the fundamental status of the Yvon-Born-Green (YBG) equation as a local force-balance within the fluid. Using the inhomogeneous Ornstein-Zernike equation we show that the two-body correlations are density functionals and, thus, that the average interparticle force entering the YBG equation is also a functional of the one-body density. The force-based theory we develop provides an alternative to standard density functional theory for the study of inhomogeneous systems both in- and out-of-equilibrium. We compare force-based density profiles to the results of the standard potential-based (dynamical) density functional theory. In equilibrium, we confirm both analytically and numerically that the standard approach yields profiles that are consistent with the compressibility pressure, whereas the force-density functional gives profiles consistent with the virial pressure. The structure of the theory offers deep insights into the nature of correlation in dense and inhomogeneous systems.

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。

↑