Correlation functions and thermophysical properties of one-dimensional liquids

TL;DR

This paper analytically investigates the thermophysical properties and correlation functions of various one-dimensional liquids with different interaction potentials, comparing approximation methods and analyzing asymptotic behaviors.

Contribution

It provides analytical solutions for thermodynamic quantities and correlation functions of several 1D liquid models, including comparisons of approximation methods and asymptotic analysis.

Findings

Analytical expressions for equation of state and thermodynamic quantities.

Comparison of Percus–Yevick and hypernetted-chain approximations.

Identification of Fisher–Widom line for the triangle-well potential.

Abstract

The properties of one-dimensional liquids are studied for several interaction potentials for which, under certain assumptions, the properties of the system admit an analytical solution. The studied potentials are the triangle-well and the ramp potential, and then we use the knowledge of these ones to study the hard-rod and the sticky-hard-rod potentials. For each one of these potentials, we study its equation of state and other thermodynamic quantities such as the compressibility factor and the internal energy. Then, we study its correlation functions, such as the radial distribution function, the structure factor and the direct correlation function. For the latter one, the approximations known as Percus--Yevick and hypernetted-chain have been compared to the analytical result. Finally, the asymptotic behaviour of the radial distribution function is studied and the Fisher--Widom line computed for the triangle-well potential.