Browsing by Author "Helman, Mark"

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    Random Hamiltonians with arbitrary point interactions in one dimension
    (Elsevier, 2021) Damanik, David; Fillman, Jake; Helman, Mark; Kesten, Jacob; Sukhtaiev, Selim
    We consider disordered Hamiltonians given by the Laplace operator subject to arbitrary random self-adjoint singular perturbations supported on random discrete subsets of the real line. Under minimal assumptions on the type of disorder, we prove the following dichotomy: Either every realization of the random operator has purely absolutely continuous spectrum or spectral and exponential dynamical localization hold. In particular, we establish Anderson localization for Schrödinger operators with Bernoulli-type random singular potential and singular density.