Scaling properties of Lyapunov spectra for the band random matrix model

Year: 1996

Authors: Kottos T., Politi A., Izrailev FM., Ruffo S.

Autors Affiliation: Department of Physics, University of Crete, P.O. Box 2208, 71003 Heraklion-Crete, Greece;
Research Center of Crete, P.O. Box 2208, 71003 Heraklion-Crete, Greece
Istituto Nazionale di Ottica, Largo E. Fermi 6, 50125 Firenze, Italy;
Istituto Nazionale di Fisica della Materia – Forum, Firenze, Italy;
Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, Firenze, Italy;
Budker Institute of Nuclear Physics, Novosibirsk, Russia;
Dipartimento di Energetica, Università di Firenze, Firenze, Italy

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.

Journal/Review: PHYSICAL REVIEW E

Volume: 53 (6)      Pages from: R5553  to: R5556

KeyWords: Inverse Participation Ratio; Disordered-systems; Localization; Limit; Chaos
DOI: 10.1103/PhysRevE.53.R5553

Citations: 14
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