Statistics of Spectra for One-dimensional Quasi-Periodic Systems at the Metal-Insulator Transition

Details Statistics of Spectra for One-dimensional Quasi-Periodic Systems at the Metal-Insulator Transition Statistics of Spectra for One-dimensional Quasi-Periodic Systems at the Metal-Insulator Transition

2003-12-26

arxiv.org/abs/cond-mat/0312650v1

Physics

Condensed Matter

RevTex, 5 pages, 5 figures

Scientific paper

We study spectral statistics of one-dimensional quasi-periodic systems at the metal-insulator transition. Several types of spectral statistics are observed at the critical points, lines, and region. On the critical lines, we find the bandwidth distribution $P_B(w)$ around the origin (in the tail) to have the form of $P_B(w) \sim w^{\alpha}$ ($P_B(w) \sim e^{-\beta w^{\gamma}}$) ($\alpha, \beta, \gamma > 0 $), while in the critical region $P_B(w) \sim w^{-\alpha'}$ ($\alpha' > 0$). We also find the level spacing distribution to follow an inverse power law $P_G(s) \sim s^{- \delta}$ ($\delta > 0$)

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