Statistics of resonances and of delay times in quasiperiodic Schrodinger equations

Abstract

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(E)(0) of the spectrum of the closed system as alpha = 1+D(E)(0) and gamma = 2-D(E)(0). Our results are verified for the Harper model at the metal-insulator transition and for Fibonacci lattices.