Generalized Kotani's trick for unitary operators

DOI10.1016/S0034-4877(17)30032-0zbMath1384.81050OpenAlexW2612170441MaRDI QIDQ1744669

Wagner Monteiro, César R. de Oliveira

Publication date: 19 April 2018

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0034-4877(17)30032-0

zbMATH Keywords

unitary operatorsHausdorff continuityrank one perturbationsKotani's trick

Mathematics Subject Classification ID

Perturbation theories for operators and differential equations in quantum theory (81Q15) Operator algebra methods applied to problems in quantum theory (81R15)

Cites Work

• Analogs of the \(m\)-function in the theory of orthogonal polynomials on the unit circle
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• Spectral properties of a periodically kicked quantum Hamiltonian
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• Localization for random unitary operators
• A Floquet operator with purely point spectrum and energy instability
• Operators with singular continuous spectrum. IV: Hausdorff dimensions, rank one perturbations, and localization
• Fractional moment estimates for random unitary operators
• Cyclicity in rank-1 perturbation problems
• Pure point spectrum for the time evolution of a periodically rank-N kicked Hamiltonian
• Continuity of spectral averaging
• Spectral averaging techniques for Jacobi matrices
• Singular continuous spectrum under rank one perturbations and localization for random hamiltonians
• $\mathbf {\operatorname {SL} _2({\mathbb {R}})}$, exponential Herglotz representations, and spectral averaging
• On kicked systems modulated along the Thue-Morse sequence
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