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 D₀E of the spectrum of the closed system as α0ex0ex=0ex0ex1+D₀E and γ0ex0ex=0ex0ex2-D₀E. Our results are verified for the Harper model at the metal-insulator transition and for Fibonacci lattices.