Abstract
We consider a discrete Schrödinger operator on l2(ℤ) with a random potential decaying at infinity as ¦n¦−1/2. We prove that its spectrum is purely singular. Together with previous results, this provides simple examples of random Schrödinger operators having a singular continuous component in its spectrum.
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References
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Delyon, F. Appearance of a purely singular continuous spectrum in a class of random schrödinger operators. J Stat Phys 40, 621–630 (1985). https://doi.org/10.1007/BF01009893
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DOI: https://doi.org/10.1007/BF01009893