Statistics of resonances and of delay times in quasiperiodic Schr"odinger equations

Details Statistics of resonances and of delay times in quasiperiodic Schr"odinger equations Statistics of resonances and of delay times in quasiperiodic Schr"odinger equations

2000-07-06

arxiv.org/abs/cond-mat/0007105v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 3 figures, submitted to Phys. Rev. Lett

Scientific paper

We study the statistical distributions of the resonance widths ${\cal P} (\Gamma)$, and of delay times ${\cal P} (\tau)$ in one dimensional quasi-periodic tight-binding systems 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.

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