Wegner estimates, Lifshitz tails, and Anderson localization for Gaussian random magnetic fields

DOI10.1063/1.4959219zbMath1348.82041OpenAlexW2477383414MaRDI QIDQ3185684

Naomasa Ueki

Publication date: 4 August 2016

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

Full work available at URL: http://hdl.handle.net/2433/232506

zbMATH Keywords

Anderson localizationLifshitz tailsWegner estimatesGaussian random magnetic fields

Mathematics Subject Classification ID

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) Statistical mechanics of magnetic materials (82D40)

Cites Work

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• Wegner estimate and Anderson localization for random magnetic fields
• Wegner estimate for Gaussian random magnetic fields
• Large deviations and Lifshitz singularity of the integrated density of states of random Hamiltonians
• Absence of diffusion in the Anderson tight binding model for large disorder or low energy
• On spectra of random Schrödinger operators with magnetic fields
• Simple examples of Lifschitz tails in Gaussian random magnetic fields
• Wegner estimate for random magnetic Laplacian on \(\mathbb Z^2\)
• Anderson localization at band edges for random magnetic fields
• Schrödinger operators with singular magnetic vector potentials
• Lifshitz tail for Schrödinger operator with random magnetic field
• Bootstrap multiscale analysis and localization in random media
• The uniqueness of the integrated density of states for the Schrödinger operators with magnetic fields

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