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We propose a general formalism to study the static properties of a systemcomposed of particles with nearest neighbor interactions that are located onthe sites of a one-dimensional lattice confined by walls (``confined Takahashilattice gas''). Linear recursion relations for generalized partition functionsare derived, from which thermodynamic quantities, as well as densitydistributions and correlation functions of arbitrary order can be determined inthe presence of an external potential. Explicit results for density profilesand pair correlations near a wall are presented for various situations. As aspecial case of the Takahashi model we consider in particular the hard rodlattice gas, for which a system of nonlinear coupled difference equations forthe occupation probabilities has been presented previously by Robledo andVarea. A solution of these equations is given in terms of the solution of asystem of independent linear equations. Moreover, for zero external potentialin the hard rod system we specify various central regions between the confiningwalls, where the occupation probabilities are constant and the correlationfunctions are translationally invariant in the canonical ensemble. In the grandcanonical ensemble such regions do not exist.Comment: 34 pages, 4 figure

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