Statistics of Resonances and of Delay Times in Quasiperiodic Schrödinger Equations

F. Steinbach, A. Ossipov, Tsampikos Kottos, and T. Geisel
Phys. Rev. Lett. 85, 4426 – Published 20 November 2000
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Abstract

We study the distributions of the resonance widths P(Γ) and of delay times P(τ) in one-dimensional quasiperiodic tight-binding systems at critical conditions with one open channel. Both quantities are found to decay algebraically as Γα and τγ on small and large scales, respectively. The exponents α and γ are related to the fractal dimension D0E of the spectrum of the closed system as α=1+D0E and γ=2D0E. Our results are verified for the Harper model at the metal-insulator transition and for Fibonacci lattices.

  • Received 6 July 2000

DOI:https://doi.org/10.1103/PhysRevLett.85.4426

©2000 American Physical Society

Authors & Affiliations

F. Steinbach, A. Ossipov, Tsampikos Kottos, and T. Geisel

  • Max-Planck-Institut für Strömungsforschung und Fakultät Physik der Universität Göttingen, Bunsenstraße 10, D-37073 Göttingen, Germany

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Vol. 85, Iss. 21 — 20 November 2000

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