Sparse potentials with fractional Hausdorff dimension.

DOI10.1016/S0022-1236(03)00180-0zbMath1038.47026arXivmath-ph/0210054MaRDI QIDQ1428447

Andrej Zlatoš

Publication date: 29 March 2004

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0210054

zbMATH Keywords

Schrödinger operatorfractional dimensionsingular continuous spectrumsparse potentials

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Spectrum, resolvent (47A10) Linear difference operators (47B39)

Related Items (17)

Quantum dynamical applications of Salem's theorem ⋮ Transfer matrices and transport for Schrödinger operators. ⋮ Schrödinger operators with complex sparse potentials ⋮ Dynamical analysis of Schrödinger operators with growing sparse potentials ⋮ Stability of spectral types for Jacobi matrices under decaying random perturbations ⋮ Subordinacy theory on star-like graphs ⋮ Anderson-like transition for a class of random sparse models in \(d\geq 2\) dimensions ⋮ Spectral packing dimensions through power-law subordinacy ⋮ The absolutely continuous spectrum of Jacobi matrices ⋮ On the spacing of zeros of paraorthogonal polynomials for singular measures ⋮ Spectral and dynamical properties of sparse one-dimensional continuous Schrödinger and Dirac operators ⋮ Scaling estimates for solutions and dynamical lower bounds on wavepacket spreading ⋮ Sparse block-Jacobi matrices with arbitrarily accurate Hausdorff dimension ⋮ Power-law bounds on transfer matrices and quantum dynamics in one dimension. II ⋮ ASYMPTOTIC TIME DECAY IN QUANTUM PHYSICS: A SELECTIVE REVIEW AND SOME NEW RESULTS ⋮ Sparse one-dimensional discrete Dirac operators II: Spectral properties ⋮ Progress in the mathematical theory of quantum disordered systems

Cites Work

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• On subordinacy and analysis of the spectrum of one-dimensional Schrödinger operators
• Singular continuous measures in scattering theory
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• Modified Prüfer and EFGP transforms and the spectral analysis of one-dimensional Schrödinger operators
• Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators
• Power-law subordinacy and singular spectra. I: Half-line operators
• On fast Birkhoff averaging
• Schrödinger operators with sparse potentials: asymptotics of the Fourier transform of the spectral measure.

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