Ubiquity of logarithmic scaling, 1/fpower spectrum, and theπ/2rule

Abstract

For disordered systems governed by activated processes with a broad distribution of barrier heights, the susceptibility should obey logarithmic frequency scaling, and the associated noise power spectrum should be of the 1/f-type (with logarithmic corrections). Further, various ‘‘π/2 rules’’ can be derived from the Kramers-Kronig relationships. The results are valid both near T=0 and near a phase transition when the latter exists. Two new examples of this very general behavior are discussed: the thermal properties of ordinary glasses and the impurity conduction and dielectric response of insulators.