A remark on Schrödinger operators on aperiodic tilings.

DOI10.1007/BF02179262zbMath1081.82521MaRDI QIDQ1593320

A. L. Hof

Publication date: 16 January 2001

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

zbMATH Keywords

minimalitydiscrete Schrödinger operatorsintegrated density of states, spectrum, Penrose tilings, projection method, unique ergodicity

Mathematics Subject Classification ID

Statistical mechanics of crystals (82D25) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Tilings in (n) dimensions (aspects of discrete geometry) (52C22)

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An application of singular traces to crystals and percolation ⋮ On sums of semibounded Cantor sets ⋮ Delone sets with finite local complexity: Linear repetitivity versus positivity of weights ⋮ Discontinuities of the integrated density of states for random operators on Delone sets ⋮ Spectral structures and topological methods in mathematical quasicrystals. Abstracts from the workshop held October 1--7, 2017 ⋮ Translation numbers for a class of maps on the dynamical systems arising from quasicrystals in the real line ⋮ An ergodic theorem for Delone dynamical systems and existence of the integrated density of states ⋮ Groupoids, von Neumann algebras and the integrated density of states ⋮ Hamiltonians on discrete structures: jumps of the integrated density of states and uniform convergence ⋮ Random Schrödinger operators arising from lattice gauge fields. I. Existence and examples ⋮ Quasicrystals, aperiodic order, and groupoid von Neumann algebras.

Cites Work

• Unnamed Item
• Space tilings and local isomorphism
• On diffraction by aperiodic structures
• Some remarks on discrete aperiodic Schrödinger operators
• Dynamics of self-similar tilings
• Quasiperiodic patterns and icosahedral symmetry

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