Must the spectrum of a random Schrödinger operator contain an interval?
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Publication:2159239
DOI10.1007/s00220-022-04395-wOpenAlexW4229373830WikidataQ114230917 ScholiaQ114230917MaRDI QIDQ2159239
A. S. Gorodetskii, David Damanik
Publication date: 28 July 2022
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2112.02445
Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Spectrum, resolvent (47A10) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (47B37) Operators arising in mathematical physics (47B93)
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The almost sure essential spectrum of the doubling map model is connected ⋮ Furstenberg theory of mixed random-quasiperiodic cocycles ⋮ Spectral characteristics of Schrödinger operators generated by product systems ⋮ Random Schrödinger operator on infinite-dimensional hypercube. I: Ergodicity and density of states ⋮ The spectrum of Schrödinger operators with randomly perturbed ergodic potentials
Cites Work
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- Characterizations of uniform hyperbolicity and spectra of CMV matrices
- Unique continuation principle for spectral projections of Schrödinger operators and optimal Wegner estimates for non-ergodic random Schrödinger operators
- Localization of random perturbations of periodic Schrödinger operators with regular Floquet eigenvalues
- Hölder continuity of the rotation number for quasi-periodic co-cycles in \({SL(2, \mathbb R)}\)
- Singular continuous spectrum on a Cantor set of zero Lebesgue measure for the Fibonacci Hamiltonian
- Band edge localization beyond regular Floquet eigenvalues
- An extension of a result by Dinaburg and Sinai on quasi-periodic potentials
- Zero-measure Cantor spectrum for Schrödinger operators with low-complexity potentials
- Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts
- Support theorems for random Schrödinger operators
- Exponential dichotomy, rotation number, and linear differential operators with bounded coefficients
- The spectrum of a quasiperiodic Schrödinger operator
- On subordinacy and analysis of the spectrum of one-dimensional Schrödinger operators
- Sur le spectre des opérateurs aux différences finies aléatoires
- An example of a Schrödinger equation with almost periodic potential and nowhere dense spectrum
- Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation
- Anderson localization for random Schrödinger operators with long range interactions
- Spectral properties of one-dimensional Schrödinger operators with potentials generated by substitutions
- Localization for some continuous, random Hamiltonians in \(d\)-dimensions
- Cantor spectrum for the almost Mathieu operator
- Power-law subordinacy and singular spectra. I: Half-line operators
- Measure zero spectrum of a class of Schrödinger operators
- Difference almost-periodic Schrödinger operators: Corollaries of localization
- Spectral properties of one dimensional quasi-crystals
- Singular spectrum of Lebesgue measure zero for one-dimensional quasicrystals
- A comprehensive proof of localization for continuous Anderson models with singular random potentials
- Uniformly hyperbolic finite-valued \(\mathrm{SL}(2,\mathbb R)\)-cocycles
- Internal Lifshits tails for random perturbations of periodic Schrödinger operators.
- Uniform hyperbolicity and its relation with spectral analysis of 1D discrete Schrödinger operators
- Parametric Furstenberg theorem on random products of \(\mathrm{SL}(2, \mathbb{R})\) matrices
- Random Schrödinger operators with a background potential
- The dynamics of a class of quasi-periodic Schrödinger cocycles
- Dynamics of the quasi-periodic Schrödinger cocycle at the lowest energy in the spectrum
- A condition of Boshernitzan and uniform convergence in the multiplicative ergodic theorem
- Sharp Hölder continuity of the Lyapunov exponent of finitely differentiable quasi-periodic cocycles
- An Invitation to Random Schroedinger operators
- Localization for random perturbations of periodic Schrödinger operators
- Schrödinger operators with dynamically defined potentials
- Random product of quasi-periodic cocycles
- One-Dimensional Ergodic Schrödinger Operators
- Shnol’s theorem and the spectrum of long range operators
- On the spectrum of the periodic Anderson–Bernoulli model
- Invariant manifolds
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