Novel feature of the universal power law dispersion of the ac conductivity in disordered matter

The ac conductivity σac of different types of materials as a function of angular frequency ω is approximated by a ‘universal’ power law σac = Aωn, A and n are fitting parameters .The exponent and the pre-exponential factor depend on temperature, in general. In the present Letter, we suggest an empirical law that states that the temperature evolution of log A is proportional to the temperature evolution of n. Data reported on different materials ascertain that the ratio −log A/n is constant, regardless the nature of the material and the type of conductivity.