Localization for quasiperiodic Schrödinger operators with multivariable Gevrey potential functions

DOI10.4171/JST/76zbMath1454.81084arXiv1204.3086OpenAlexW1991479959MaRDI QIDQ2256850

Silvius Klein

Publication date: 23 February 2015

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.3086

zbMATH Keywords

Łojasiewicz inequalityLyapunov exponentAnderson localizationtransversality conditionGevrey regularityquasiperiodic Schrödinger operatorskew shift

Mathematics Subject Classification ID

Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Linear difference operators (47B39)

Related Items

Logarithmic Quantum Dynamical Bounds for Arithmetically Defined Ergodic Schrödinger Operators with Smooth Potentials ⋮ Sharp Hölder continuity of the Lyapunov exponent of finitely differentiable quasi-periodic cocycles ⋮ An asymptotic formula for the Lyapunov exponent of Gevrey skew-shift Schrödinger operator ⋮ Spectral theory of the multi-frequency quasi-periodic operator with a Gevrey type perturbation ⋮ Upper bounds on quantum dynamics in arbitrary dimension ⋮ Anosov-Katok constructions for quasi-periodic \(\operatorname{SL}(2, \mathbb{R})\) cocycles ⋮ Dynamics and spectral theory of quasi-periodic Schrödinger-type operators ⋮ Quantitative inductive estimates for Green's functions of non-self-adjoint matrices ⋮ A formula related to CMV matrices and Szegő cocycles ⋮ Continuity, positivity and simplicity of the Lyapunov exponents for quasi-periodic cocycles ⋮ Hölder continuity of absolutely continuous spectral measure for multi-frequency Schrödinger operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On resonances and the formation of gaps in the spectrum of quasi-periodic Schrödinger equations
• The spectrum of skew-shift Schrödinger operators contains intervals
• Fine properties of the integrated density of states and a quantitative separation property of the Dirichlet eigenvalues
• Discrete one-dimensional quasi-periodic Schrödinger operators with pure point spectrum
• On the spectrum of lattice Schrödinger operators with deterministic potential. II.
• Anderson localization for the discrete one-dimensional quasi-periodic Schrödinger operator with potential defined by a Gevrey-class function
• Multiscale analysis for ergodic Schrödinger operators and positivity of Lyapunov exponents
• Method of variations of potential of quasi-periodic Schrödinger equations
• Positive lyapounov exponents for most energies
• On the growth and stability of real-analytic functions
• Green's Function Estimates for Lattice Schrodinger Operators and Applications. (AM-158)
• Explicit bounds for the Łojasiewicz exponent in the gradient inequality for polynomials
• Positive Lyapunov exponent and minimality for a class of one-dimensional quasi-periodic Schrödinger equations
• On nonperturbative localization with quasi-periodic potential.
• An effective Łojasiewicz inequality for real polynomials
• Hölder continuity of the integrated density of states for quasi-periodic Schrödinger equations and averages of shifts of subharmonic functions
• Anderson localization for Schrödinger operators on \(\mathbb Z\) with potentials given by the skew-shift