Statistics of resonances and of delay times in quasiperiodic Schrodinger equations

We study the distributions of the resonance widths P(Gamma) and of delay times P(tau) in one-dimensional quasiperiodic tight-binding systems at critical conditions with one open channel. Both quantities are found to decay algebraically as Gamma (-alpha) and tau (-gamma) on small and large scales, respectively. The exponents alpha and gamma are related to the fractal dimension D-0(E) Of the spectrum of the closed system as alpha = 1 + D-0(E) and gamma = 2 - D-0(E). Our results are verified for the Harper model at the metal-insulator transition and for Fibonacci lattices.