Electronic density of states for a one-dimensional liquid

We consider a one-dimensional hard rod liquid with an electronic structure of tight-binding type as a simple model for studying the density of states (DOS) in spatially disordered systems. For a finite number of rods, the DOS is exactly obtained by using a replica trick. Exact expressions in the thermodynamic limit for some particular cases are also given. The resulting DOSs are interpreted in terms of bonding and antibonding orbitals arising from s-type atomic orbitals.