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- W4310006589 abstract "We study the level statistics of one-dimensional Schrodinger operator with random potential decaying like $x^{-alpha}$ at infinity. We consider the point process $xi_L$ consisting of the rescaled eigenvalues and show that : (i)(ac spectrum case) for $alpha > frac 12$, $xi_L$ converges to a clock process, and the fluctuation of the eigenvalue spacing converges to Gaussian. (ii)(critical case) for $alpha = frac 12$, $xi_L$ converges to the limit of the circular $beta$-ensemble." @default.
- W4310006589 created "2022-11-30" @default.
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- W4310006589 date "2012-10-15" @default.
- W4310006589 modified "2023-09-23" @default.
- W4310006589 title "Level statistics of one-dimensional Schrodinger operators with random decaying potential" @default.
- W4310006589 doi "https://doi.org/10.48550/arxiv.1210.4224" @default.
- W4310006589 hasPublicationYear "2012" @default.
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