Proof of dynamical localization for perturbations of discrete 1D Schrödinger operators with uniform electric fields

DOI10.1007/s00209-018-2103-4zbMath1486.47065OpenAlexW2886489362MaRDI QIDQ2633118

Mariane Pigossi, César R. de Oliveira

Publication date: 8 May 2019

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-018-2103-4

zbMATH Keywords

electric fieldsdiscrete Schrödinger operatorspure point spectrumdynamical localizationKAM technique

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Perturbation theories for operators and differential equations in quantum theory (81Q15) Linear difference operators (47B39)

Related Items (3)

Point spectrum and SULE for time-periodic perturbations of discrete 1D Schrödinger operators with electric fields ⋮ Localization of polynomial long-range hopping lattice operator with uniform electric fields ⋮ Some generic fractal properties of bounded self-adjoint operators

Cites Work

• Intermediate spectral theory and quantum dynamics
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• Quantum dynamics and decompositions of singular continuous spectra
• Operators with singular continuous spectrum. IV: Hausdorff dimensions, rank one perturbations, and localization
• ON THE STABILITY OF PERIODICALLY TIME-DEPENDENT QUANTUM SYSTEMS
• How to prove dynamical localization
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