非均匀系统中的均匀分布：经典密度泛函理论中产生恒定密度分布的壁势
Uniform distributions in nonuniform systems: Wall potentials generating constant density profiles in classical density functional theory
AI总结：
研究经典密度泛函理论的逆问题，在罗森菲尔德基本测度理论下，求解平面、球形和柱形几何中产生恒定平衡密度分布的壁势，给出平面壁解析表达式，球形壁也有解析处理，柱形情况数值处理，还给出相关公式。
摘要：
我们研究非均匀流体经典密度泛函理论的逆问题：找到能产生恒定平衡密度分布的壁势，即在与基板相邻的可及区域内具有完美平坦的密度分布。在罗森菲尔德的基本测度理论框架内，我们针对平面、球形和柱形几何中的单组分流体解决了这个问题，同时考虑了硬球流体和在平均场水平处理的具有额外截断伦纳德 - 琼斯吸引力的流体。对于平面壁，我们得到了明确的解析表达式，而球形壁也允许以更繁琐的形式进行解析处理。柱形情况则通过数值方法处理。这种构造提供了结构抵消壁场的明确微观实现，这与在润湿和干燥的界面理论中在特殊匹配条件下出现的平坦分布条件相关。该理论还给出了在三种基本几何形状中加权密度和一体直接相关函数的紧凑公式集，为密度泛函实现提供了有用的参考表达式。所得的解析壁势在独立的密度泛函计算中得到验证，这证实了在数值精度范围内恢复了规定的平坦分布。
英文摘要：
We study the inverse problem of classical density functional theory for inhomogeneous fluids: finding the wall potential that produces a constant equilibrium density profile, i.e., a perfectly flat density distribution in the accessible region adjacent to a substrate. Within Rosenfeld's fundamental measure theory, we solve this problem for a one-component fluid in planar, spherical, and cylindrical geometries, considering both a hard-sphere fluid and a fluid with an additional truncated Lennard-Jones attraction treated at the mean-field level. Explicit analytical expressions are obtained for planar walls, while spherical walls also admit an analytical treatment in a more cumbersome form. The cylindrical case is treated numerically. The construction provides an explicit microscopic realization of structure-cancelling wall fields, related to flat-profile conditions that occur under special matching conditions in interfacial theories of wetting and drying. The theory also yields a compact collection of formulae for weighted densities and one-body direct correlation functions in the three fundamental geometries, providing useful reference expressions for density-functional implementations. The resulting analytic wall potentials are validated in independent density functional calculations, which confirm that the prescribed flat profiles are recovered within numerical accuracy.
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