Non-monotonic random Schrödinger operators: The Anderson model

DOI10.1006/jmaa.2000.6885zbMath0974.47034OpenAlexW2069052600MaRDI QIDQ1580470

Günter Stolz

Publication date: 29 November 2001

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.2000.6885

zbMATH Keywords

random Schrödinger operatorlocalizationspectral averagingWeyl-Titchmarsh spectral measure

Mathematics Subject Classification ID

Random operators and equations (aspects of stochastic analysis) (60H25) Schrödinger operator, Schrödinger equation (35J10) Random linear operators (47B80)

Related Items (16)

Absence of reflection as a function of the coupling constant ⋮ Quantum Hamiltonians with weak random abstract perturbation. I: Initial length scale estimate ⋮ Quantum Hamiltonians with weak random abstract perturbation. II: Localization in the expanded spectrum ⋮ Low lying spectrum of weak-disorder quantum waveguides ⋮ Annealed asymptotics for Brownian motion of renormalized potential in mobile random medium ⋮ Asymptotics of negative exponential moments for annealed Brownian motion in a renormalized Poisson potential ⋮ Brownian motion and parabolic Anderson model in a renormalized Poisson potential ⋮ Low lying eigenvalues of randomly curved quantum waveguides ⋮ Localisation for non-monotone Schrödinger operators ⋮ Lower transport bounds for one-dimensional continuum Schrödinger operators ⋮ Discrete Schrödinger Operators with Random Alloy-type Potential ⋮ Estimates of initial scales for layers with small random negative-definite perturbations ⋮ Localization for one-dimensional, continuum, Bernoulli-Anderson models. ⋮ Strategies in localization proofs for one-dimensional random Schrödinger operators ⋮ The integrated density of states for some random operators with nonsign definite potentials ⋮ On the Lipschitz continuity of the integrated density of states for sign-indefinite potentials

Cites Work

• Localization in general one-dimensional random systems. II: Continuum Schrödinger operators
• Spectral theory of ordinary differential operators
• Microlocalization, percolation, and Anderson localization for the magnetic Schrödinger operator with a random potential
• Localization for some continuous random Schrödinger operators
• On subordinacy and analysis of the spectrum of Schrödinger operators with two singular endpoints
• On the Nature of the Spectrum of Singular Second Order Linear Differential Equations
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