The dynamic conductivity of one-dimensional hopping systems with aperiodically distributed transition rates is studied. The low-frequency behavior is shown to be regular or singular depending on the specific substitution which generates the aperiodicity. Explicit formulas are given for three cases with different spectral measures of the transition-rate sequences. We give general high-frequency expansions that are valid whenever the correlation functions exist. A numerical calculation of the conductivity in the range of intermediate frequencies by a decimation procedure is also included.

• Received 2 April 1987

DOI:https://doi.org/10.1103/PhysRevLett.60.1672