Fractal nature and scaling exponents of non-Drude currents in non-Fermi liquids

In many oxides of the perovskite and pseudoperovskite families there are phase transitions between insulating and normal metallic (Fermi-liquid) phases that are separated by an intermediate phase that is often called a non-Fermi liquid. The dc resistivity of the intermediate or non-Fermi-liquid phase often exhibits a T temperature dependence. in contrast with the T-2 dependence expected from a bad normal metal. The same alloys exhibit a non-Drude omega (2 alpha) frequency dependence, with alpha approximate to 0.5, in contrast with the Drude dependence omega (2) characteristic of samples with the T-2 behaviour. Various attempts have been made to modify the algebra of continuum Fermi-liquid theory to derive the non-Drude exponent ct, but these have been based on artifices designed to explain only this one parameter. The discrete filamentary model has been used to calculate many properties of high-temperature superconductors, and to explain the asymmetric nature of the intermediate phase. Here it is used to derive alpha by the same rules previously used for several other discrete relaxation calculations that are in excellent agreement with other quite different experiments. The results are, for (cubic) perovskites. alpha = 0.45 and, for planar conductivity of bilayered pseudoperovskites, alpha = 0.70. The corresponding experimental values are (0.4, 0.5) and 0.7.