Some remarks on discrete aperiodic Schrödinger operators
From MaRDI portal
Publication:2499901
DOI10.1007/BF01048190zbMath1101.39301OpenAlexW2045166124MaRDI QIDQ2499901
Publication date: 23 August 2006
Published in: Journal of Statistical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf01048190
integrated density of statesspectrumminimalityLyapunov exponentFibonacci sequencesunique ergodicityPenrose tilingsaperiodic structuresprimitive substitutionsself-similar tilingsstrict ergodicityDiscrete Schrödinger operators
Classical equilibrium statistical mechanics (general) (82B05) Discrete version of topics in analysis (39A12) Tilings in (2) dimensions (aspects of discrete geometry) (52C20)
Related Items
Singular continuous spectrum for palindromic Schrödinger operators, Spectra of discrete Schrödinger operators with primitive invertible substitution potentials, An application of singular traces to crystals and percolation, Hölder continuity of the integrated density of states for the Fibonacci Hamiltonian, Hierarchical structures in Sturmian dynamical systems, On sums of semibounded Cantor sets, Delone sets with finite local complexity: Linear repetitivity versus positivity of weights, A general Dixmier trace formula for the density of states on open manifolds, Spectral and quantum dynamical properties of the weakly coupled Fibonacci Hamiltonian, UNIFORM ERGODIC THEOREMS ON APERIODIC LINEARLY REPETITIVE TILINGS AND APPLICATIONS, \(L^{2}\)-spectral invariants and convergent sequences of finite graphs, Properties of 1D classical and quantum Ising models: rigorous results, Frequency dependence of Hölder continuity for quasiperiodic Schrödinger operators, Spectral structures and topological methods in mathematical quasicrystals. Abstracts from the workshop held October 1--7, 2017, An ergodic theorem for Delone dynamical systems and existence of the integrated density of states, Singular continuous spectrum for a class of nonprimitive substitution Schrödinger operators, Orthogonal polynomials on the unit circle with Fibonacci Verblunsky coefficients. II. Applications, A condition of Boshernitzan and uniform convergence in the multiplicative ergodic theorem, The Fibonacci Hamiltonian, Groupoids, von Neumann algebras and the integrated density of states, Hamiltonians on discrete structures: jumps of the integrated density of states and uniform convergence, A nonprimitive substitution Schrödinger operator with generic singular continuous spectrum, Substitution Hamiltonians with bounded trace map orbits, A remark on Schrödinger operators on aperiodic tilings., Quasicrystals, aperiodic order, and groupoid von Neumann algebras.
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Updown generation of Penrose patterns
- Almost periodic Schrödinger operators. II: The integrated density of states
- Spectral properties of a tight binding Hamiltonian with period doubling potential
- Absence of localization in a class of Schrödinger operators with quasiperiodic potential
- Symbolic dynamics for the renormalization map of a quasiperiodic Schrödinger equation
- Continuity properties of the electronic spectrum of 1D quasicrystals
- Spectral properties of one dimensional quasi-crystals
- The density of states for almost periodic Schrödinger operators and the frequency module: A counter example
- Lifschitz singularities for periodic operators plus random potentials
- Mean entropy of states in classical statistical mechanics
- Matrix Analysis
- LATTICE GAS MODELS ON SELF-SIMILAR APERIODIC TILINGS
- GAP LABELLING THEOREMS FOR ONE DIMENSIONAL DISCRETE SCHRÖDINGER OPERATORS
- The spectrum of dynamical systems arising from substitutions of constant length