Hölder regularity of the integrated density of states for quasi-periodic long-range operators on \(\ell^2(\mathbb{Z}^d)\)
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Publication:2141016
DOI10.1007/s00220-022-04385-yOpenAlexW4224252976MaRDI QIDQ2141016
Lingrui Ge, Xin Zhao, Jiangong You
Publication date: 23 May 2022
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2009.08004
Special classes of linear operators (47Bxx) Equilibrium statistical mechanics (82Bxx) General mathematical topics and methods in quantum theory (81Qxx)
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Cites Work
- Unnamed Item
- Unnamed Item
- The spectrum of a Schrödinger operator with small quasi-periodic potential is homogeneous
- Continuity of the Lyapunov exponents for quasiperiodic cocycles
- Complex one-frequency cocycles
- Hölder continuity of the rotation number for quasi-periodic co-cycles in \({SL(2, \mathbb R)}\)
- \(L^2\)-reducibility and localization for quasiperiodic operators
- Log Hölder continuity of the integrated density of states for stochastic Jacobi matrices
- Positivity and continuity of the Lyapunov exponent for shifts on \(\mathbb T^d\) with arbitrary frequency vector and real analytic potential
- Almost localization and almost reducibility
- 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
- Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation
- Perturbations of lower dimensional tori for Hamiltonian systems
- A note on the variation of the spectrum of an arbitrary matrix
- Duality and singular continuous spectrum in the almost Mathieu equation
- Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential
- Hölder regularity of integrated density of states for the almost Mathieu operator in a perturbative regime
- Homogeneity of the spectrum for quasi-periodic Schrödinger operators
- Sharp phase transitions for the almost Mathieu operator
- All couplings localization for quasiperiodic operators with monotone potentials
- Almost reducibility and non-perturbative reducibility of quasi-periodic linear systems
- Analytic quasi-perodic cocycles with singularities and the Lyapunov exponent of extended Harper's model
- Anderson localization for the discrete one-dimensional quasi-periodic Schrödinger operator with potential defined by a Gevrey-class function
- Analytic quasi-periodic Schrödinger operators and rational frequency approximants
- Generalized Floquet theory for stationary Schrödinger operators in one dimension
- Continuity, positivity and simplicity of the Lyapunov exponents for quasi-periodic cocycles
- Arithmetic version of Anderson localization via reducibility
- Localization for quasiperiodic operators with unbounded monotone potentials
- Uniform positivity and continuity of Lyapunov exponents for a class of \(C^2\) quasiperiodic Schrödinger cocycles
- Regularity and convergence rates for the Lyapunov exponents of linear cocycles
- Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling
- Sharp Hölder continuity of the Lyapunov exponent of finitely differentiable quasi-periodic cocycles
- Hölder continuity of the Lyapunov exponent for analytic quasiperiodic Schrödinger cocycle with weak Liouville frequency
- Continuity of the Lyapunov exponent for analytic quasiperiodic cocycles
- Green's Function Estimates for Lattice Schrodinger Operators and Applications. (AM-158)
- Strong almost reducibility for analytic and Gevrey quasi-periodic cocycles
- A Thouless formula and Aubry duality for long-range Schrödinger skew-products
- Large Deviation Estimates and Hölder Regularity of the Lyapunov Exponents for Quasi-periodic Schrödinger Cocycles
- A nonperturbative Eliasson's reducibility theorem
- 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
- On the integrated density of states for Schrödinger operators on \(\mathbb Z^2\) with quasi periodic potential
