Spectral properties of a non-degenerate polaron gas

We apply the dynamic mean field theory to calculate the low-density limit of the small polaron optical conductivity in the Holstein model. Classical schemes of approximation are recovered in weak coupling and in the adiabatic and anti-adiabatic strong coupling limits. Such schemes are not suitable for the intermediate coupling regime, where our theory gives an anomalous increase of the spectral weight at low energy as the temperature decreases. This result could be relevant to interpret some features observed in MIR and FIR optical conductivity of the oxide compounds.