Random Hamiltonians with arbitrary point interactions in one dimension
| Autor: | Selim Sukhtaiev, David Damanik, Mark Helman, Jake Fillman, Jacob Kesten |
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| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Anderson localization Applied Mathematics 010102 general mathematics Spectrum (functional analysis) Absolute continuity 01 natural sciences 010101 applied mathematics symbols.namesake Operator (computer programming) symbols 0101 mathematics Real line Laplace operator Analysis Realization (probability) Schrödinger's cat Mathematics |
| Zdroj: | Journal of Differential Equations. 282:104-126 |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2021.01.044 |
| Popis: | 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 Schrodinger operators with Bernoulli-type random singular potential and singular density. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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