Anomalous transport: a mathematical framework

Details Anomalous transport: a mathematical framework Anomalous transport: a mathematical framework

1997-06-24

arxiv.org/abs/cond-mat/9706239v1

Physics

Condensed Matter

43 pages, Latex

Scientific paper

We develop a mathematical framework allowing to study anomalous transport in homogeneous solids. The main tools characterizing the anomalous transport properties are spectral and diffusion exponents associated to the covariant Hamiltonians describing these media. The diffusion exponents characterize the spectral measures entering in Kubo's formula for the conductivity and hence lead to anomalies in Drude's formula. We give several formulas allowing to calculate these exponents and treat, as an example, Wegner's $n$-orbital model as well as the Anderson model in coherent potential approximation.

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