Hamburg 2001 – scientific programme

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DY: Dynamik und Statistische Physik

DY 23: Quantenchaos

DY 23.2: Talk

Tuesday, March 27, 2001, 10:45–11:00, S 7

Statistical properties of open quasiperiodic systems at criticality — •A. Ossipov, F. Steinbach, M. Weiss, T. Kottos, and T. Geisel — Max-Planck-Institut für Strömungsforschung und Institut für Nichtlineare Dynamik der Universität Göttingen, Bunsenstraße 10, D-37073 Göttingen

We study the distributions of the resonance widths P (Γ) and of delay times P (τ) in open, one-dimensional quasi-periodic systems at critical conditions. We show that both quantities decay algebraically as Γ^−(1+D₀) and τ^{−(2−D₀)} on small and large scales, respectively, where D₀ is the fractal (box-counting) dimension of the spectrum of the closed system [1]. Moreover, the survival probability P(t), which charactirizes the dynamical properties of open systems, is found to decay algebraically P(t)∼ t^{−(1−D₀)} as well [2]. The latter quantity should be observable in experiments. Our results are obtained numerically for two different types of quasi-periodic tight-binding models and are supported by analytical arguments.

[1] F. Steinbach, A. Ossipov, Tsampikos Kottos, and T. Geisel, Phys. Rev. Lett. 85, 4426 (2000).

[2] A. Ossipov, M. Weiss, Tsampikos Kottos, and T. Geisel (to be published).