Simplicity of eigenvalues in the Anderson model

DOI10.1007/s10955-005-8009-7zbMath1152.82010arXivmath-ph/0503061OpenAlexW2048489017MaRDI QIDQ2492849

Abel Klein, Stanislav Alekseevich Molchanov

Publication date: 14 June 2006

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0503061

Mathematics Subject Classification ID

Related Items (32)

Finite volume approximation of the Anderson model ⋮ Level spacing for non-monotone Anderson models ⋮ Enhanced Wegner and Minami estimates and eigenvalue statistics of random Anderson models at spectral edges ⋮ An eigensystem approach to Anderson localization ⋮ Generalized eigenvalue-counting estimates for the Anderson model ⋮ On the spatial extent of localized eigenfunctions for random Schrödinger operators ⋮ Local eigenvalue statistics for higher-rank Anderson models after Dietlein–Elgart ⋮ DISTRIBUTION OF LOCALIZATION CENTERS IN SOME DISCRETE RANDOM SYSTEMS ⋮ Eigensystem multiscale analysis for Anderson localization in energy intervals ⋮ Derivation of Kubo's formula for disordered systems at zero temperature ⋮ Simplicity of eigenvalues in Anderson-type models ⋮ The repulsion between localization centers in the Anderson model ⋮ Quantitative Anderson localization of Schrödinger eigenstates under disorder potentials ⋮ Minami's estimate: beyond rank one perturbation and monotonicity ⋮ Uniform Anderson localization, unimodal eigenstates and simple spectra in a class of ``haarsh deterministic potentials ⋮ Global multiplicity bounds and spectral statistics for random operators ⋮ Eigenvalue statistics for random Schrödinger operators with non rank one perturbations ⋮ Correlation estimates in the Anderson model ⋮ Multiplicity bound of singular spectrum for higher rank Anderson models ⋮ Generalized eigenvalue-counting estimates for some random acoustic operators ⋮ Eigenvalue statistics for lattice Hamiltonian with off-diagonal disorder ⋮ New characterizations of the region of complete localization for random Schrödinger operators ⋮ Level spacing and Poisson statistics for continuum random Schrödinger operators ⋮ Multi-scale Jacobi method for Anderson localization ⋮ On multiplicity of spectrum for Anderson type operators with higher rank perturbations ⋮ Decorrelation estimates for random Schrödinger operators with non rank one perturbations ⋮ The optimal spectral gap for regular and disordered harmonic networks of oscillators ⋮ Eigensystem multiscale analysis for the Anderson model via the Wegner estimate ⋮ A theorem on the multiplicity of the singular spectrum of a general Anderson-type Hamiltonian ⋮ Eigenvector localization for random band matrices with power law band width ⋮ Localization and eigenvalue statistics for the lattice Anderson model with discrete disorder ⋮ SPECTRAL PROPERTIES OF DYNAMICAL LOCALIZATION FOR SCHRÖDINGER OPERATORS

Cites Work

• A new proof of localization in the Anderson tight binding model
• Constructive proof of localization in the Anderson tight binding model
• Localization at large disorder and at extreme energies: an elementary derivation
• Localization for some continuous, random Hamiltonians in \(d\)-dimensions
• Local fluctuation of the spectrum of a multidimensional Anderson tight binding model
• New characterizations of the region of complete localization for random Schrödinger operators
• Simplicity of singular spectrum in Anderson-type Hamiltonians
• CYCLIC VECTORS IN THE ANDERSON MODEL

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