Correlation functions and thermophysical properties of one-dimensional\n liquids

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