Localization for transversally periodic random potentials on binary trees
| Autor: | Richard Froese, Christian Sadel, Wolfgang Spitzer, Darrick Lee, Günter Stolz |
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| Rok vydání: | 2016 |
| Předmět: |
Coupling constant
Physics Anderson localization Binary tree Bethe lattice Dynamical systems theory 82B44 Hyperbolic space Operator (physics) Mathematical analysis FOS: Physical sciences Statistical and Nonlinear Physics Mathematical Physics (math-ph) Moment (mathematics) Geometry and Topology Mathematical Physics |
| Zdroj: | Journal of Spectral Theory. 6:557-600 |
| ISSN: | 1664-039X |
| Popis: | We consider a random Schr\"odinger operator on the binary tree with a random potential which is the sum of a random radially symmetric potential, $Q_r$, and a random transversally periodic potential, $\kappa Q_t$, with coupling constant $\kappa$. Using a new one-dimensional dynamical systems approach combined with Jensen's inequality in hyperbolic space (our key estimate) we obtain a fractional moment estimate proving localization for small and large $\kappa$. Together with a previous result we therefore obtain a model with two Anderson transitions, from localization to delocalization and back to localization, when increasing $\kappa$. As a by-product we also have a partially new proof of one-dimensional Anderson localization at any disorder. Comment: 25 pages, 1 figure |
| Databáze: | OpenAIRE |
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