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Statistics of Resonances and of Delay Times in Quasiperiodic Schrödinger Equations

Statistics of Resonances and of Delay Times in Quasiperiodic Schrödinger Equations 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 Γ - α and τ - γ on small and large scales, respectively. The exponents α and γ are related to the fractal dimension D 0 E of the spectrum of the closed system as α = 1 + D 0 E and γ = 2 - D 0 E . Our results are verified for the Harper model at the metal-insulator transition and for Fibonacci lattices. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review Letters American Physical Society (APS)

Statistics of Resonances and of Delay Times in Quasiperiodic Schrödinger Equations

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Publisher
American Physical Society (APS)
Copyright
Copyright © 2000 The American Physical Society
ISSN
1079-7114
DOI
10.1103/PhysRevLett.85.4426
Publisher site
See Article on Publisher Site

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 Γ - α and τ - γ on small and large scales, respectively. The exponents α and γ are related to the fractal dimension D 0 E of the spectrum of the closed system as α = 1 + D 0 E and γ = 2 - D 0 E . Our results are verified for the Harper model at the metal-insulator transition and for Fibonacci lattices.

Journal

Physical Review Letters – American Physical Society (APS)

Published: Nov 20, 2000

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