Discontinuities of the integrated density of states for random operators on Delone sets

DOI10.1007/s00220-003-0920-7zbMath1098.82016arXivmath-ph/0208027OpenAlexW3103128784MaRDI QIDQ1411060

Steffen Klassert, Peter Stollmann, Daniel H. Lenz

Publication date: 15 October 2003

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

Full work available at URL: https://arxiv.org/abs/math-ph/0208027

zbMATH Keywords

quasicrystalsbounded eigenfunction supporttight binding operators

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Random linear operators (47B80) Tilings in (n) dimensions (aspects of discrete geometry) (52C22)

Related Items (17)

Uniform existence of the integrated density of states on metric Cayley graphs ⋮ On sums of semibounded Cantor sets ⋮ Uniform approximation of the integrated density of states for long-range percolation Hamiltonians ⋮ Uniform existence of the integrated density of states for randomly weighted Hamiltonians on long-range percolation graphs ⋮ Geometric and Spectral Consequences of Curvature Bounds on Tessellations ⋮ A Banach space-valued ergodic theorem and the uniform approximation of the integrated density of states ⋮ Linear Wegner estimate for alloy-type Schrödinger operators on metric graphs ⋮ Uniform existence of the integrated density of states for random Schrödinger operators on metric graphs over \(\mathbb Z^d\) ⋮ An ergodic theorem for Delone dynamical systems and existence of the integrated density of states ⋮ Convergence theorems for graph sequences ⋮ Spectral analysis of percolation Hamiltonians ⋮ An overview of curvature bounds and spectral theory of planar tessellations ⋮ Elliptic operators on planar graphs: Unique continuation for eigenfunctions and nonpositive curvature ⋮ Uniform existence of the integrated density of states for models on \({\mathbb{Z}}^d\) ⋮ Hamiltonians on discrete structures: jumps of the integrated density of states and uniform convergence ⋮ Continuity properties of the integrated density of states on manifolds ⋮ Localisation for Delone operators via Bernoulli randomisation

Cites Work

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• A remark on Schrödinger operators on aperiodic tilings.
• Quasicrystals, aperiodic order, and groupoid von Neumann algebras.
• An ergodic theorem for Delone dynamical systems and existence of the integrated density of states
• Quasiperiodic tilings with tenfold symmetry and equivalence with respect to local derivability
• Dynamics of self-similar tilings
• Uniform ergodic theorems on subshifts over a finite alphabet
• NONCOMMUTATIVE GEOMETRY OF TILINGS AND GAP LABELLING
• The creation of spectral gaps by graph decoration

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