Transfer matrices, hyperbolic geometry and absolutely continuous spectrum for some discrete Schrödinger operators on graphs

DOI10.1016/j.jfa.2005.04.004zbMath1094.35104OpenAlexW2050854593MaRDI QIDQ813940

David Hasler, Richard Froese, Wolfgang L. Spitzer

Publication date: 2 February 2006

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2005.04.004

zbMATH Keywords

Green's functionabsolutely continuous spectrumdiscrete Schrödinger operator

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Linear difference operators (47B39)

Related Items (30)

Quantum ergodicity on regular graphs ⋮ On the preservation of absolutely continuous spectrum for Schrödinger operators ⋮ Anderson transition at two-dimensional growth rate on antitrees and spectral theory for operators with one propagating channel ⋮ Continuity of the integrated density of states on random length metric graphs ⋮ Absolutely continuous spectrum for random operators on trees of finite cone type ⋮ The essential spectrum of the Laplacian on rapidly branching tessellations ⋮ Absolutely continuous spectrum for the Anderson model on a tree: a geometric proof of Klein's theorem ⋮ Periodic Jacobi matrices on trees ⋮ Localized phase for the Erdős-Rényi graph ⋮ Absolutely continuous spectrum for Schrödinger operators with random decaying matrix potentials on the strip ⋮ Absolutely continuous spectrum for the Anderson model on some tree-like graphs ⋮ On the AC spectrum of one-dimensional random Schrödinger operators with matrix-valued potentials ⋮ Spectral theory of one-channel operators and application to absolutely continuous spectrum for Anderson type models ⋮ The absolutely continuous spectrum of Jacobi matrices ⋮ On the spectral theory of trees with finite cone type ⋮ Curvature, geometry and spectral properties of planar graphs ⋮ Action of complex symplectic matrices on the Siegel upper half space ⋮ Quantum diffusion of the random Schrödinger evolution in the scaling limit ⋮ Delocalization transition for critical Erdős-Rényi graphs ⋮ Quantum diffusion and eigenfunction delocalization in a random band matrix model ⋮ Absolutely continuous spectrum for multi-type Galton-Watson trees ⋮ Stability of the absolutely continuous spectrum of random Schrödinger operators on tree graphs ⋮ Green matrix estimates of block Jacobi matrices. I: Unbounded gap in the essential spectrum ⋮ On the spectrum of Schrödinger operators with a finitely supported potential on the \(d\)-regular tree ⋮ The Altshuler-Shklovskii formulas for random band matrices. I: The unimodular case ⋮ Transfer matrices for discrete Hermitian operators and absolutely continuous spectrum ⋮ Absolutely continuous spectrum of a Schrödinger operator on a tree ⋮ Localization for Anderson models on metric and discrete tree graphs ⋮ ABSOLUTELY CONTINUOUS SPECTRUM FOR A RANDOM POTENTIAL ON A TREE WITH STRONG TRANSVERSE CORRELATIONS AND LARGE WEIGHTED LOOPS ⋮ Jacobi matrices on trees generated by Angelesco systems: asymptotics of coefficients and essential spectrum

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