Spectral theory for two-component porous media

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Abstract
Recently, several attempts have been made to explain the static and the frequency-dependent behavior of the dielectric properties of porous media. We present a theory for the dielectric response of a rock-and-brine system. The theory is based on the spectral representation and the associated sum rules for two-component systems. This theory explains the principal experimental characteristics of rock-and-brine systems. Some scaling laws, proposed in the context of random resistor networks, are shown to follow from this theory. We find that critical exponents governing the static and dynamic behavior are not universal.