### 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

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

*53*(6), R5553-R5556.

**Scaling properties of Lyapunov spectra for the band random matrix model.** / Kottos, T ; Politi, A ; Izrailev, F M ; Ruffo, S .

Research output: Contribution to journal › Article

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 53, no. 6, pp. R5553-R5556.

}

TY - JOUR

T1 - Scaling properties of Lyapunov spectra for the band random matrix model

AU - Kottos, T

AU - Politi, A

AU - Izrailev, F M

AU - Ruffo, S

PY - 1996/6

Y1 - 1996/6

N2 - 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.

AB - 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.

KW - INVERSE PARTICIPATION RATIO

KW - DISORDERED-SYSTEMS

KW - LOCALIZATION

KW - LIMIT

KW - CHAOS

M3 - Article

VL - 53

SP - R5553-R5556

JO - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 6

ER -