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arXiv · 1907.09530

Random Hamiltonians with Arbitrary Point Interactions

David Damanik·Jake Fillman·Mark Helman·Jacob Kesten·Selim Sukhtaiev
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Abstract

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 Schr\"odinger operators with Bernoulli-type random singular potential and singular density.

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David Damanik, Jake Fillman, Mark Helman, Jacob Kesten, Selim Sukhtaiev. 2019-07-22. Random Hamiltonians with Arbitrary Point Interactions. https://arxiv.org/abs/1907.09530

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