Stability of the non-critical spectral properties i: arithmetic absolute continuity of the integrated density of states

DOI10.1007/S00220-023-04724-7arXiv2204.11000OpenAlexW4366989411MaRDI QIDQ6109369

Svetlana Ya. Jitomirskaya, Unnamed Author, Lingrui Ge

Publication date: 28 July 2023

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

Full work available at URL: https://arxiv.org/abs/2204.11000

Mathematics Subject Classification ID

Special classes of linear operators (47Bxx) General mathematical topics and methods in quantum theory (81Qxx) Ordinary differential operators (34Lxx)

Cites Work

• The spectrum of a Schrödinger operator with small quasi-periodic potential is homogeneous
• On resonances and the formation of gaps in the spectrum of quasi-periodic Schrödinger equations
• A KAM scheme for SL(2, \(\mathbb R\)) cocycles with Liouvillean frequencies
• Hölder continuity of the rotation number for quasi-periodic co-cycles in \({SL(2, \mathbb R)}\)
• Localization for a class of one dimensional quasi-periodic Schrödinger operators
• Une méthode pour minorer les exposants de Lyapounov et quelques exemples montrant le caractère local d'un théorème d'Arnold et de Moser sur le tore de dimension 2
• Log Hölder continuity of the integrated density of states for stochastic Jacobi matrices
• Almost periodic Schrödinger operators: A review
• Almost localization and almost reducibility
• Spectral properties of a class of reflectionless Schrödinger operators
• Global theory of one-frequency Schrödinger operators
• Fine properties of the integrated density of states and a quantitative separation property of the Dirichlet eigenvalues
• Subharmonicity of the Lyapunov index
• Stochastic Schrödinger operators and Jacobi matrices on the strip
• 1\(D\)-quasiperiodic operators. Latent symmetries
• Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation
• The one-dimensional Schrödinger equation with a quasiperiodic potential
• Extended states in the Anderson model on the Bethe lattice
• Duality and singular continuous spectrum in the almost Mathieu equation
• Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential
• Asymptotic behavior of polynomials orthonormal on a homogeneous set
• Cantor spectrum for the almost Mathieu operator
• Absolutely continuous spectrum for 1D quasiperiodic operators.
• Homogeneity of the spectrum for quasi-periodic Schrödinger operators
• Sharp phase transitions for the almost Mathieu operator
• Universal hierarchical structure of quasiperiodic eigenfunctions
• Almost reducibility and non-perturbative reducibility of quasi-periodic linear systems
• On the spectrum of lattice Schrödinger operators with deterministic potential
• Espaces de Hardy et domains de Denjoy. (Hardy spaces and Denjoy domains)
• Anderson localization for one-dimensional difference Schrödinger operator with quasiperiodic potential
• Generalized Floquet theory for stationary Schrödinger operators in one dimension
• Metal-insulator transition for the almost Mathieu operator
• The arithmetic version of the frequency transition conjecture: new proof and generalization
• Arithmetic version of Anderson localization via reducibility
• On the spectrum of multi-frequency quasiperiodic Schrödinger operators with large coupling
• The dynamics of a class of quasi-periodic Schrödinger cocycles
• Uniform positivity and continuity of Lyapunov exponents for a class of \(C^2\) quasiperiodic Schrödinger cocycles
• The Ten Martini problem
• Reducibility or nonuniform hyperbolicity for quasiperiodic Schrödinger cocycles
• Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling
• Schrödinger operators with dynamically defined potentials
• Cantor Spectrum for a Class of $C^2$ Quasiperiodic Schrödinger Operators
• L p Norms of the Borel Transform and the Decomposition of Measures
• A Thouless formula and Aubry duality for long-range Schrödinger skew-products
• A nonperturbative Eliasson's reducibility theorem
• A Maximal Function Characterization of the Class H p
• On nonperturbative localization with quasi-periodic potential.
• Hölder continuity of the integrated density of states for quasi-periodic Schrödinger equations and averages of shifts of subharmonic functions
• Ballistic Transport for One‐Dimensional Quasiperiodic Schrödinger Operators
• Exponential Dynamical Localization: Criterion and Applications

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