Detecting localized eigenstates of linear operators

DOI10.1007/s40687-018-0152-2zbMath1425.35128arXiv1709.03364OpenAlexW2963420776MaRDI QIDQ2319765

Stefan Steinerberger, Jian-feng Lu

Publication date: 20 August 2019

Published in: Research in the Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.03364

zbMATH Keywords

stochastic differential equationseigenvectorslocalizationAnderson localizationpower iterationrandomized numerical linear algebra

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Random operators and equations (aspects of stochastic analysis) (60H25) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Eigenvalue problems for linear operators (47A75) Schrödinger operator, Schrödinger equation (35J10)

Related Items

Magnetic Schrödinger operators and landscape functions ⋮ Localization of Neumann eigenfunctions near irregular boundaries ⋮ Quantitative Anderson localization of Schrödinger eigenstates under disorder potentials ⋮ Regularized potentials of Schrödinger operators and a local landscape function ⋮ The exponential decay of eigenfunctions for tight-binding Hamiltonians via landscape and dual landscape functions ⋮ Fast localization of eigenfunctions via smoothed potentials ⋮ Localization of eigenfunctions via an effective potential ⋮ The effective potential of an M-matrix ⋮ Triangles and triple products of Laplace eigenfunctions ⋮ Localized Computation of Eigenstates of Random Schrödinger Operators ⋮ An algorithm for identifying eigenvectors exhibiting strong spatial localization

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