Classical limit for electronic disordered systems: Spectral tails and thermodynamical properties

We consider the classical limit for the density of states of an electron in a disordered one-dimensional chain. The low energy tail of the density of states is analytically studied and we evaluate the thermo-dynamical properties of this system. For the Boltzmann distribution the heat capacity grows when disorder increases. On the other hand in the quantum case, corresponding to the Fermi-Dirac statistic, the heat capacity diminishes when disorder increases.