### Abstract

We prove for a one-dimensional tight-binding Hamiltonian with only off-diagonal randomness that the state at the middle of the band is extended, regardless of the probability distribution of the hopping matrix elements and also derive a sum rule for the density of states. In particular, for the case where the probability distribution of the hopping matrix elements is a generalized Poisson distribution, we derive an expression for the localization length near the middle of the band. We also calculate the localization length for a chain of potential wells with randomly fluctuating depths, separated by regions of zero potential, the length of the latter being also random.

Original language | English (US) |
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Pages (from-to) | 4597-4601 |

Number of pages | 5 |

Journal | Physical Review B |

Volume | 13 |

Issue number | 10 |

DOIs | |

State | Published - Jan 1 1976 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics

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## Cite this

*Physical Review B*,

*13*(10), 4597-4601. https://doi.org/10.1103/PhysRevB.13.4597