## Abstract

We present a long-range hopping tight-binding model in which the ensemble averaged density of states, rho (E), undergoes a gradual transition from a homogeneous form with almost no variation to strongly peaked behaviour as an external electric field grows. The model consists of N*N band random matrices of bandwidth b. The corresponding matrix elements, h_{ij}, have all vanishing average except on the diagonal where, (h_{ii})= alpha i. Here, the parameter alpha plays the role of the electric field. We approximate the behaviour of the width, sigma _{E}, of the local density of states, rho _{L}(E), and use it to predict the value of alpha around which the transition is centred.

Original language | English |
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Article number | 012 |

Pages (from-to) | 7367-7376 |

Number of pages | 10 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 26 |

Issue number | 24 |

DOIs | |

State | Published - 1 Dec 1993 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- General Physics and Astronomy