Bridge diagram and Fundamental Measure Theory: a test in One Dimension
Résumé
A formal and general expression for the bridge function is obtained from the Fundamental Measure Theory. This expression involves solely the knowledge of an analytical form of the free-energy, the weight functions and the pair correlation function, and comes out in terms of combinations of convolution products of the two latter quantities, thus lifting the irreducibility of the concerned diagrams. It is applicable to mixtures and inhomogeneous fluids. The validity of this expression is then tested in the case of a one-dimensional hard rods fluid, for which exact expression of the correlations are known, and the Fundamental Measure Theory is also exact. The formalism allows to sum the infinite series and produce a compact analytical expression for the exact bridge function. However, the numerical term by term evaluation of the series shows that severe convergence problems arise in the high density regime, questioning the pertinence of usual such attempts. The present approach opens interesting perspectives for the Theory of Liquids.
Origine : Fichiers produits par l'(les) auteur(s)