Unique continuation principle for spectral projections of Schrödinger operators and optimal Wegner estimates for non-ergodic random Schrödinger operators

DOI10.1007/s00220-013-1795-xzbMath1281.47026arXiv1209.4863OpenAlexW2049373765MaRDI QIDQ380044

Abel Klein

Publication date: 11 November 2013

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.4863

Mathematics Subject Classification ID

Random operators and equations (aspects of stochastic analysis) (60H25) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Schrödinger operator, Schrödinger equation (35J10) PDEs with randomness, stochastic partial differential equations (35R60) Random linear operators (47B80) Continuation and prolongation of solutions to PDEs (35B60)

Related Items

Scale-free and quantitative unique continuation for infinite dimensional spectral subspaces of Schrödinger operators ⋮ Wegner estimate for Landau-breather Hamiltonians ⋮ Sampling inequality for \(L^2\)-norms of eigenfunctions, spectral projectors, and Weyl sequences of Schrödinger operators ⋮ Harmonic Analysis and Random Schrödinger Operators ⋮ Local Wegner and Lifshitz tails estimates for the density of states for continuous random Schrödinger operators ⋮ Must the spectrum of a random Schrödinger operator contain an interval? ⋮ An abstract Logvinenko-Sereda type theorem for spectral subspaces ⋮ Unique continuation and lifting of spectral band edges of Schrödinger operators on unbounded domains ⋮ Scale-free uncertainty principles and Wegner estimates for random breather potentials ⋮ Local eigenvalue statistics for higher-rank Anderson models after Dietlein–Elgart ⋮ Unique continuation for the gradient of eigenfunctions and Wegner estimates for random divergence-type operators ⋮ A “lifting” method for exponential large deviation estimates and an application to certain non-stationary 1D lattice Anderson models ⋮ Scale-free unique continuation principle for spectral projectors, eigenvalue-lifting and Wegner estimates for random Schrödinger operators ⋮ Scale-free quantitative unique continuation and equidistribution estimates for solutions of elliptic differential equations ⋮ Quantitative unique continuation for spectral subspaces of Schrödinger operators with singular potentials ⋮ Conditional Wegner estimate for the standard random breather potential ⋮ Some abstract Wegner estimates with applications ⋮ Semiclassical resolvent estimates for bounded potentials ⋮ Wegner estimate and disorder dependence for Alloy-type Hamiltonians with bounded magnetic potential ⋮ Random Schrödinger operators and Anderson localization in aperiodic media ⋮ Quantitative unique continuation principle for Schrödinger operators with singular potentials ⋮ Level spacing and Poisson statistics for continuum random Schrödinger operators ⋮ Lower bounds for Dirichlet Laplacians and uncertainty principles ⋮ Sampling and equidistribution theorems for elliptic second order operators, lifting of eigenvalues, and applications ⋮ Band edge localization beyond regular Floquet eigenvalues ⋮ Eigensystem multiscale analysis for the Anderson model via the Wegner estimate ⋮ A lower Wegner estimate and bounds on the spectral shift function for continuum random Schrödinger operators ⋮ Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function

Cites Work

• Unnamed Item
• Bounds on the density of states for Schrödinger operators
• An uncertainty principle, Wegner estimates and localization near fluctuation boundaries
• Localization for some continuous, random Hamiltonians in \(d\)-dimensions
• Explicit finite volume criteria for localization in continuous random media and applications
• A comprehensive proof of localization for continuous Anderson models with singular random potentials
• Characterization of the Anderson metal-insulator transition for non ergodic operators and application
• Scale-free unique continuation estimates and applications to random Schrödinger operators
• An optimal Wegner estimate and its application to the global continuity of the integrated density of states for random Schrödinger operators
• On localization in the continuous Anderson-Bernoulli model in higher dimension
• New characterizations of the region of complete localization for random Schrödinger operators
• Bootstrap multiscale analysis and localization in random media