Spectral Properties of Schrödinger Operators Arising in the Study of Quasicrystals
From MaRDI portal
Publication:5350424
DOI10.1007/978-3-0348-0903-0_9zbMath1378.81031arXiv1210.5753OpenAlexW1547504017MaRDI QIDQ5350424
Mark Embree, David Damanik, A. S. Gorodetskii
Publication date: 1 September 2017
Published in: Mathematics of Aperiodic Order (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1210.5753
General topics in linear spectral theory for PDEs (35P05) Applications of operator theory in the physical sciences (47N50) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36) Time-dependent Schrödinger equations and Dirac equations (35Q41)
Related Items
Spectral decimation of a self-similar version of almost Mathieu-type operators ⋮ On the spectrum of the periodic Anderson–Bernoulli model ⋮ Spectral transitions for the square Fibonacci Hamiltonian ⋮ Subshifts with leading sequences, uniformity of cocycles and spectra of Schreier graphs ⋮ Diffusion on Delone sets ⋮ Finite section method for aperiodic Schrödinger operators ⋮ Spectral properties of continuum Fibonacci Schrödinger operators ⋮ Schrödinger operators with dynamically defined potentials ⋮ Spectral approximation of generalized Schrödinger operators via approximation of subwords ⋮ Zero measure Cantor spectra for continuum one-dimensional quasicrystals ⋮ Spectra of Schreier graphs of Grigorchuk's group and Schroedinger operators with aperiodic order ⋮ Empirical risk minimization and complexity of dynamical models ⋮ On the spectrum of 1D quantum Ising quasicrystal ⋮ Ergodic frequency measures for random substitutions ⋮ Multidimensional Schrödinger operators whose spectrum features a half-line and a Cantor set ⋮ Operators, Algebras and Their Invariants for Aperiodic Tilings ⋮ Spectral structures and topological methods in mathematical quasicrystals. Abstracts from the workshop held October 1--7, 2017 ⋮ Continuum Schrödinger operators associated with aperiodic subshifts ⋮ Schrödinger operators generated by locally constant functions on the Fibonacci subshift ⋮ Traces of random operators associated with self-affine Delone sets and Shubin's formula ⋮ Purely singular continuous spectrum for CMV operators generated by subshifts ⋮ Spectral approximation for quasiperiodic Jacobi operators ⋮ The Fibonacci Hamiltonian ⋮ Spectral continuity for aperiodic quantum systems: Applications of a folklore theorem ⋮ Note on Spectra of Non-Selfadjoint Operators Over Dynamical Systems ⋮ Spectra of discrete two-dimensional periodic Schrödinger operators with small potentials ⋮ Tilings and traces ⋮ Computing Spectral Measures of Self-Adjoint Operators ⋮ Almost ballistic transport for the weakly coupled Fibonacci Hamiltonian ⋮ Analyticity of the Lyapunov exponent of meromorphic monotonic cocycles ⋮ Almost sure frequency independence of the dimension of the spectrum of Sturmian Hamiltonians ⋮ On the Hausdorff dimension of the spectrum of the Thue-Morse Hamiltonian ⋮ Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian ⋮ Piecewise continuous almost automorphic functions and Favard's theorems for impulsive differential equations in honor of Russell Johnson ⋮ Transport exponents of Sturmian Hamiltonians