  We form a highly simplified model of an atomic wire on a surface by the
coupling of two one-dimensional chains, one with electron-electron interactions
to represent the wire and and one with no electron-electron interactions to
represent the surface. We use exact diagonalization techniques to calculate the
eigenstates and response functions of our model, in order to determine both the
nature of the coupling and to what extent the coupling affects the Luttinger
liquid properties we would expect in a purely one-dimensional system. We find
that while there are indeed Luttinger liquid indicators present, some residual
Fermi liquid characteristics remain.
