Quantitative Anderson localization of Schrödinger eigenstates under disorder potentials
- This paper analyzes spectral properties of linear Schrödinger operators under oscillatory high-amplitude potentials on bounded domains. Depending on the degree of disorder, we prove the existence of spectral gaps among the lowermost eigenvalues and the emergence of exponentially localized states. We quantify the rate of decay in terms of geometric parameters that characterize the potential. The proofs are based on the convergence theory of iterative solvers for eigenvalue problems and their optimal local operator preconditioning by domain decomposition.
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| Author: | Robert AltmannORCiDGND, Patrick Henning, Daniel PeterseimORCiDGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-644617 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/64461 |
| Parent Title (English): | Mathematical Models & Methods in Applied Sciences |
| Publisher: | World Scientific |
| Place of publication: | Singapore |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2020 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2019/11/07 |
| Volume: | 30 |
| Issue: | 5 |
| First Page: | 917 |
| Last Page: | 955 |
| DOI: | https://doi.org/10.1142/S0218202520500190 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  Deutsches Urheberrecht |
