Supersymmetric Cluster Expansions and Applications to Random Schrödinger Operators
| Autor: | Luca Fresta |
|---|---|
| Přispěvatelé: | University of Zurich, Fresta, Luca |
| Rok vydání: | 2021 |
| Předmět: |
Physics
Smoothness (probability theory) Local density of states 010102 general mathematics Spectrum (functional analysis) Function (mathematics) Condensed Matter::Disordered Systems and Neural Networks 01 natural sciences 10123 Institute of Mathematics symbols.namesake 510 Mathematics 0103 physical sciences symbols Cluster (physics) 2608 Geometry and Topology 010307 mathematical physics Geometry and Topology 0101 mathematics Exponential decay 2610 Mathematical Physics Mathematical Physics Schrödinger's cat Cluster expansion Mathematical physics |
| Zdroj: | Mathematical Physics, Analysis and Geometry |
| ISSN: | 1572-9656 1385-0172 |
| DOI: | 10.1007/s11040-021-09375-5 |
| Popis: | We study discrete random Schrödinger operators via the supersymmetric formalism. We develop a cluster expansion that converges at both strong and weak disorder. We prove the exponential decay of the disorder-averaged Green’s function and the smoothness of the local density of states either at weak disorder and at energies in proximity of the unperturbed spectrum or at strong disorder and at any energy. As an application, we establish Lifshitz-tail-type estimates for the local density of states and thus localization at weak disorder. |
| Databáze: | OpenAIRE |
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