关于非均匀液体自洽方程的等价性：各种修正的统一描述
On the equivalence of self-consistent equations for nonuniform liquids: a unified description of the various modifications
摘要：
对于外场作用下液体粒子的非均匀状态，包括固体基底上的吸附态和孔隙中的受限态，已经提出了多种自洽（SC）方程。外场不仅代表限制性的几何形状，也代表固定的溶质。我们考虑SC方程的范围从修改后的Poisson-Boltzmann方程的库仑势的流体静力学线性响应方程的平衡密度分布的Lennard-Jones流体。在这里，我们提出了一个统一的方程，解释了以前的形式的明显多样性，并证明了各种SC方程的等价性。这种SC方程的统一描述是由传统的密度泛函理论和统计场论相结合的混合方法得到的。高斯近似的平均场分布周围的密度波动进行的基础上开发的混合框架，使我们能够推导出一种新的形式的大电位密度泛函，提供了统一的SC方程的平衡密度。
英文摘要：
A variety of self-consistent (SC) equations have been proposed for non-uniform states of liquid particles under external fields, including adsorbed states at solid substrates and confined states in pores. External fields represent not only confining geometries but also fixed solutes. We consider SC equations ranging from the modified Poisson-Boltzmann equations for the Coulomb potential to the hydrostatic linear response equation for the equilibrium density distribution of Lennard-Jones fluids. Here, we present a unified equation that explains the apparent diversity of previous forms and proves the equivalence of various SC equations. This unified description of SC equations is obtained from a hybrid method combining the conventional density functional theory and statistical field theory. The Gaussian approximation of density fluctuations around a mean-field distribution is performed based on the developed hybrid framework, allowing us to derive a novel form of the grand-potential density functional that provides the unified SC equation for equilibrium density.
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