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
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/64461
Parent Title (English):Mathematical Models & Methods in Applied Sciences
Publisher:World Scientific
Place of publication:Singapore
Year of first Publication:2020
Publishing Institution:Universität Augsburg
Release Date:2019/11/07
First Page:917
Last Page:955
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