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From power pure point to continuous spectrum in disordered systems. (English) Zbl 0579.60056

Summary: We prove that two classes of random Schrödinger operators exhibit a transition from pure point spectrum with power decaying eigenfunctions to purely continuous spectrum when varying the coupling constant. These classes are i) a Schrödinger operator with a random Krönig-Penney potential and an electric field and ii) a Jacobi matrix with a random potential of strength decaying as \(n^{-\alpha}\), \(\alpha =1/2\).

MSC:

60H25 Random operators and equations (aspects of stochastic analysis)
81P20 Stochastic mechanics (including stochastic electrodynamics)
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