Wall-induced density profiles and density correlations in confined Takahashi lattice gases

We propose a general formalism to study the static properties of a system c omposed of particles with nearest neighbor interactions that are located on the sites of a one-dimensional lattice confined by walls ("confined Takaha shi lattice gas"). Linear recursion relations for generalized partition fun ctions are derived, from which thermodynamic quantities, as well as density distributions and correlation functions of arbitrary order can be determin ed in the presence of an external potential. Explicit results for density p rofiles and pair correlations near a wall are presented for various situati ons. As a special case of the Takahashi model we consider in particular the hard rod lattice gas, for which a system of nonlinear coupled difference e quations for the occupation probabilities has been presented by Robledo and Varea. A solution of these equations is given in terms of the solution of a system of independent linear equations. Moreover, for zero external poten tial in the hard-rod system we specify various central regions between the confining walls, where the occupation probabilities are constant and the co rrelation functions are translationally invariant in the canonical ensemble . In the grand canonical ensemble such regions do not exist.