The energy criterion in the interpretation of the universal dielectric response

The universal dielectric response follows a frequency dependence of the complex susceptibility given by a fractional power law in which the ratio of energy lost per radian to energy stored at the peak is independent of frequency. It is shown that this energy criterion can be satisfied in any solid state system in which the energy lost in every microscopic reversal of polarization is independent of the rate of reversals. Specific models are discussed, such as dipolar and charge carrier polarizations in solids, and it is shown that the exponent n is related to the density of the polarizing species and also to the dipole length, which in the case of hopping charge carriers means the hopping distance. The limiting forms of dielectric response corresponding to the flat low-loss behavior characteristic of good insulators, with n → 1, are obtained with low density systems. In high-density systems the highly lossy Debye-like dipolar or low-frequency dispersion charge carrier response is found to be in good agreement with experimental observations