Oscillation Theory for the Density of States of High Dimensional Random Operators

DOI10.1093/imrn/rnx246zbMath1459.81039arXiv1706.07498OpenAlexW2964287228MaRDI QIDQ5855170

Julian Großmann, Hermann Schulz-Baldes, Carlos Villegas-Blas

Publication date: 15 March 2021

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.07498

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) General theory of von Neumann algebras (46L10) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Exotic index theories on manifolds (58J22) Covariant wave equations in quantum theory, relativistic quantum mechanics (81R20) Statistical thermodynamics (82B30) Spectral flows (58J30) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Related Items (2)

Space versus energy oscillations of Pr\"ufer phases for matrix Sturm-Liouville and Jacobi operators ⋮ Reduced transfer operators for singular difference equations

Cites Work

• A Glivenko-Cantelli theorem for almost additive functions on lattices
• Topological invariants of edge states for periodic two-dimensional models
• Sturm intersection theory for periodic Jacobi matrices and linear Hamiltonian systems
• The rotation number for almost periodic potentials
• Renormalized oscillation theory for Hamiltonian systems
• Eigenvalue and oscillation theorems for time scale symplectic systems
• Signature and spectral flow of \(J\)-unitary \(\mathbb S^1\)-Fredholm operators
• On the iteration of closed geodesics and the sturm intersection theory
• Oscillation theorems for symplectic difference systems
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