### Abstract

The transfer-matrix method is applied to quasi-one-dimensional disordered media described by a one-dimensional tight-binding Hamiltonian with long-range random interactions. We investigate the scaling properties of the whole Lyapunov spectrum in the limit of the interaction range b tending to infinity. Two different energy dependencies are found around the maximum and the minimum Lyapunov exponents. Moreover, a singular behavior in the lower part of the Lyapunov spectrum is found at the band edge. Finally, scaling properties of the fluctuations are also analyzed.

Original language | English |
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Pages (from-to) | R5553-R5556 |

Number of pages | 4 |

Journal | Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 53 |

Issue number | 6 |

Publication status | Published - Jun 1996 |

### Keywords

- INVERSE PARTICIPATION RATIO
- DISORDERED-SYSTEMS
- LOCALIZATION
- LIMIT
- CHAOS

## Cite this

Kottos, T., Politi, A., Izrailev, F. M., & Ruffo, S. (1996). Scaling properties of Lyapunov spectra for the band random matrix model.

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,*53*(6), R5553-R5556.