Random Schrödinger operators arising from lattice gauge fields. I. Existence and examples

DOI10.1063/1.533041zbMath0961.47021OpenAlexW2054265218MaRDI QIDQ4498489

Oliver Knill

Publication date: 16 August 2000

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

Full work available at URL: https://doi.org/10.1063/1.533041

zbMATH Keywords

graphSchrödinger operatormagnetic fieldtilingergodic theorymoment expansionfree Laplaciannon-Abelian lattice gauge fields

Mathematics Subject Classification ID

Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Applications of operator theory to differential and integral equations (47N20) Random linear operators (47B80) Linear difference operators (47B39)

Cites Work

• Almost periodic Schrödinger operators. II: The integrated density of states
• On the origin of integrability in matrix models
• Analyticity of the density of states and replica method for random Schrödinger operators on a lattice
• 1\(D\)-quasiperiodic operators. Latent symmetries
• Discrete magnetic Laplacian
• Zero measure spectrum for the almost Mathieu operator
• Analyticity of the density of states in the Anderson model on the Bethe lattice
• A remark on Schrödinger operators on aperiodic tilings.
• Anderson localization for the almost Mathieu equation. II: Point spectrum for \(\lambda > 2\)
• Analysis of the spectrum of a particle on a triangular lattice with two magnetic fluxes by algebraic and numerical methods
• Products of coboundaries for commuting nonsingular automorphisms