Interacting hard-sphere fluids in an external field

We present a method for studying equilibrium properties of interacting fluids in an arbitrary external field. The fluid is composed of monodisperse spherical particles with hard-core repulsion and additional interactions of arbitrary shape and limited range. Our method of analysis is exact in one dimension and provides demonstrably good approximations in higher dimensions. It can cope with homogeneous and inhomogeneous environments. We derive an equation for the pair distribution function. The solution, to be evaluated numerically, in general, or analytically for special cases, enters expressions for the entropy and free energy functionals. For some one-dimensional systems, our approach yields analytic solutions, reproducing available exact results from different approaches.

Automated summary

The paper introduces a method for studying equilibrium properties of interacting fluids in arbitrary external fields, exact in one dimension and approximations in higher dimensions, applicable to systems with hard-core repulsion and additional interactions of limited range. The method can handle both homogeneous and inhomogeneous environments, deriving equations for pair distribution functions with solutions to be numerically evaluated, and providing analytic solutions for special cases for the entropy and free energy functionals. In one-dimensional systems, the approach can yield analytic solutions and reproduce exact results obtained from different methods.