New characterizations of the region of complete localization for random Schrödinger operators

DOI10.1007/s10955-005-8068-9zbMath1127.82031arXivmath-ph/0503017OpenAlexW1964939588MaRDI QIDQ2492852

François Germinet, Abel Klein

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/0503017

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) Spectrum, resolvent (47A10) Random linear operators (47B80)

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Cites Work

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• Moment analysis for localization in random Schrödinger operators
• A new proof of localization in the Anderson tight binding model
• Absence of diffusion in the Anderson tight binding model for large disorder or low energy
• Constructive proof of localization in the Anderson tight binding model
• Localization for the Anderson model on a strip with singular potentials
• Dynamical localization for discrete and continuous random Schrödinger operators
• Dynamical localization II with an application to the almost Mathieu operator
• Localization at large disorder and at extreme energies: an elementary derivation
• Localization for some continuous, random Hamiltonians in \(d\)-dimensions
• Microlocalization, percolation, and Anderson localization for the magnetic Schrödinger operator with a random potential
• Localization of classical waves. I: Acoustic waves
• Localization of classical waves. II: Electromagnetic waves
• Explicit finite volume criteria for localization in continuous random media and applications
• Generalized eigenfunctions for waves in inhomogeneous media
• Localization and universality of Poisson statistics for the multidimensional Anderson model at weak disorder.
• Edge and impurity effects on quantization of Hall currents
• Anderson localization for Bernoulli and other singular potentials
• Completely analytical interactions: Constructive description
• Localization for one-dimensional, continuum, Bernoulli-Anderson models.
• Weak disorder localization and Lifshitz tails: Continuous Hamiltonians
• Weak disorder localization and Lifshitz tails
• A general framework for localization of classical waves. II: Random media
• A characterization of the Anderson metal-insulator transport transition
• Localization for some continuous random Schrödinger operators
• Localization phenomenon in gaps of the spectrum of random lattice operators
• Localization of electromagnetic and acoustic waves in random media. Lattice models
• Landau Hamiltonians with random potentials: Localization and the density of states
• Local fluctuation of the spectrum of a multidimensional Anderson tight binding model
• Localization for random and quasiperiodic potentials.
• Dynamical delocalization in random Landau Hamiltonians
• Simplicity of eigenvalues in the Anderson model
• Operators with singular continuous spectrum. IV: Hausdorff dimensions, rank one perturbations, and localization
• Linear response theory for magnetic Schrödinger operators in disordered media
• Equality of the bulk and edge Hall conductances in a mobility gap
• Multiscale Analysis and Localization of Random Operators
• Localization for random perturbations of periodic Schrödinger operators
• Localization bounds for an electron gas
• The noncommutative geometry of the quantum Hall effect
• Operator kernel estimates for functions of generalized Schrödinger operators
• Sub-exponential decay of operator kernels for functions of generalized Schrödinger operators
• LOCALIZATION AT WEAK DISORDER: SOME ELEMENTARY BOUNDS
• CYCLIC VECTORS IN THE ANDERSON MODEL
• On the Quantization of Hall Currents in Presence of Disorder
• Caught by disorder. Bound states in random media
• Multi-scale analysis implies strong dynamical localization
• Bootstrap multiscale analysis and localization in random media
• How to prove dynamical localization
• Finite-volume fractional-moment criteria for Anderson localization