Spectral localization for quantum Hamiltonians with weak random delta interaction |
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| Authors: | Denis I. Borisov Matthias Täufer Ivan Veselić |
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| Affiliation: | 1. Department of Differential Equations, Institute of Mathematics with Computer Center, Ufa Federal Research Center, Russian Academy of Sciences, Chernyshevsky. st. 112, Ufa, 450008, Russia;2. Faculty of Physics and Mathematics, Bashkir State Pedagogical University, October rev. st. 3a, Ufa, 450000, Russia;3. Faculty of Natural Sciences, University of Hradec Králové, Rokitanského 62, 500 03, Hradec Králové, Czech Republic;4. Fakultät für Mathematik, Technische Universität Dortmund, 44227 Dortmund, Germany |
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| Abstract: | We consider a negative Laplacian in multi-dimensional Euclidean space (or a multi-dimensional layer) with a weak disorder random perturbation. The perturbation consists of a sum of lattice translates of a delta interaction supported on a compact manifold of co-dimension one and modulated by coupling constants, which are independent identically distributed random variables times a small disorder parameter. We establish that the spectrum of the considered operator is almost surely a fixed set, characterize its minimum, give an initial length scale estimate and the Wegner estimate, and conclude that there is a small zone of a pure point spectrum containing the almost sure spectral bottom. The length of this zone is proportional to the small disorder parameter. |
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