## Abstract

For the calculation of the contribution to the ac conductivity σ(ω), or to the dielectric loss ε{lunate}″(ω), from transitions of charge carriers between states in a small cluster, the rate equations provide the most convenient formalism. These equations are derived for carriers obeying either classical or Fermi-Dirac statistics, and their formal solution is presented in terms of a distribution of relaxation times. The application of our results to amorphous semiconductors reveals, inter alia, an error in previous applications of the pair approximation in the case of uncorrelated charge carriers obeying Fermi-Dirac statistics. Our method also has considerable advantages over previous methods for the numerical calculation of σ(ω) for any given real or model system. For dielectrics, our analysis permits some general predictions as to the number of relaxation times that will be observed, and their dependence on temperature in some cases.

Original language | English |
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Pages (from-to) | 336-349 |

Number of pages | 14 |

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 spend the academic year 1973/4 at Chelsea College, where part of this work was performed, and Professor A. K. Jonscher for his hospitality there.