Statistics of resonances and of delay times in quasiperiodic Schrodinger equations

F Steinbach; A Ossipov; T Kottos; T Geisel

doi:10.1103/PhysRevLett.85.4426

Statistics of resonances and of delay times in quasiperiodic Schrodinger equations

Phys Rev Lett. 2000 Nov 20;85(21):4426-9. doi: 10.1103/PhysRevLett.85.4426.

Authors

F Steinbach¹, A Ossipov, T Kottos, T Geisel

Affiliation

¹ Max-Planck-Institut fur Stromungsforschung und Fakultat Physik der Universitat Gottingen, Bunsenstrasse 10, D-37073 Gottingen, Germany.

PMID: 11082562
DOI: 10.1103/PhysRevLett.85.4426

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.