AC conductivity of a disordered chain: real-space renormalisation group approach

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Abstract
The authors investigate the hopping conduction of a binary disordered chain with nearest-neighbour transitions, both analytically and numerically. The Miller-Abrahams equations (1960) are solved by the renormalisation group decimation technique; the solution is used to calculate the AC conductivity, for which asymptotic formulae, in the low- and high-frequency limit, are also deduced. The numerical calculation is performed for two classes of systems: a chain with a non-singular distribution of transition rates and the broken-bond model. A comparison with alternative approaches is made.