Wegner estimate and localization for alloy-type models with sign-changing exponentially decaying single-site potentials

DOI10.1142/S0129055X15500075zbMath1331.82027arXiv1309.0109WikidataQ59311972 ScholiaQ59311972MaRDI QIDQ5261022

Martin Tautenhahn, Karsten Leonhardt, Ivan Veselić, Norbert Peyerimhoff

Publication date: 1 July 2015

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

Full work available at URL: https://arxiv.org/abs/1309.0109

zbMATH Keywords

random Schrödinger operatorsintegrated density of statesWegner estimatesingle-site potentialdiscrete alloy-type modelalloy-type model

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) 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)

Related Items (8)

Quantum Hamiltonians with weak random abstract perturbation. I: Initial length scale estimate ⋮ Wegner estimate for discrete Schrödinger operators with Gaussian random potentials ⋮ Universal regularity of higher-dimensional disorder and density of states under non-local interactions. I: Infinite smoothness and localization ⋮ Some abstract Wegner estimates with applications ⋮ Minami's estimate: beyond rank one perturbation and monotonicity ⋮ Discrete Schrödinger Operators with Random Alloy-type Potential ⋮ Band edge localization beyond regular Floquet eigenvalues ⋮ Estimates of initial scales for layers with small random negative-definite perturbations

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