Sparse one-dimensional discrete Dirac operators II: Spectral properties

DOI10.1063/1.3600536zbMath1317.81096OpenAlexW2038287521MaRDI QIDQ5266087

Roberto A. Prado, César R. de Oliveira, Silas L. Carvalho

Publication date: 29 July 2015

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

Full work available at URL: http://hdl.handle.net/11449/7123

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Covariant wave equations in quantum theory, relativistic quantum mechanics (81R20) Discrete version of topics in analysis (39A12) Fractals (28A80)

Related Items (7)

Dynamical localization for discrete Anderson Dirac operators ⋮ One-dimensional discrete Dirac operators in a decaying random potential. I: Spectrum and dynamics ⋮ Spectral packing dimensions through power-law subordinacy ⋮ Sparse 1D discrete Dirac operators. I: Quantum transport ⋮ Density of states and Lifshitz tails for discrete 1D random Dirac operators ⋮ Invariants of the trace map and uniform spectral properties for discrete Sturmian Dirac operators ⋮ Location of eigenvalues of non-self-adjoint discrete Dirac operators

Cites Work

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• Sparse 1D discrete Dirac operators. I: Quantum transport
• The analysis of additive set functions in Euclidean space
• Dynamical analysis of Schrödinger operators with growing sparse potentials
• Intermediate spectral theory and quantum dynamics
• Sparse block-Jacobi matrices with arbitrarily accurate Hausdorff dimension
• On subordinacy and analysis of the spectrum of one-dimensional Schrödinger operators
• Singular continuous measures in scattering theory
• 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
• Sparse potentials with fractional Hausdorff dimension.
• Power-law subordinacy and singular spectra. I: Half-line operators
• Quantum dynamics and decompositions of singular continuous spectra
• Operators with singular continuous spectrum. IV: Hausdorff dimensions, rank one perturbations, and localization
• Spectral and localization properties for the one-dimensional Bernoulli discrete Dirac operator
• Asymptotics of the Fourier transform of the spectral measure for Schr$ouml$dinger operators with bounded and unbounded sparse potentials
• Dynamical delocalization for the 1D Bernoulli discrete Dirac operator
• Operators with singular continuous spectrum, V. Sparse potentials
• Spectral transition in a sparse model and a class of nonlinear dynamical systems

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