## Abstract

The ac conductivity is considered of systems in which the current is due to the motion of charge carriers between localized states. It is shown first that for any given frequency ω, a number N(ω) can be defined such that carrier paths containing more than N(ω) steps make a negligible contribution to the conductivity σ(ω) at that frequency. For sufficiently high frequencies, N(ω) equals unity, while as ω decreases N(ω) increases. An analysis of the possible paths in terms of transitions that are slow or fast relative to the frequency ω leads, in many cases, to a cluster approximation that is valid for frequencies appreciably greater than a critical percolation frequency. The number of states in each of the clusters that are relevant to the calculation of σ(ω) decreases as ω increases.

Original language | English |
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Pages (from-to) | 323-335 |

Number of pages | 13 |

Journal | Physica B: Physics of Condensed Matter & C: Atomic, Molecular and Plasma Physics, Optics |

Volume | 79 |

Issue number | 4 |

DOIs | |

State | Published - 1975 |

### Bibliographical note

Funding Information:The author thanks the Israel Academy of Sciences and Humanities and the Royal Society for a travel grant to enable him to work at Chelsea College, where much of this research was done, and Professor A. K. Jonscher for his hospitality there. He also thanks Dr. R. M. Hill for many useful discussions.