Abstract
We use the KAM technique to present a proof of pure point spectrum for the quasi-energy operator and a version of the SULE condition for suitable small time-periodic perturbations of discrete one-dimensional Schrödinger operators with uniform electric fields.
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Acknowledgements
The authors thank one of the referees for pointing a divergent series in the first version of this manuscript that has implied in substantial modifications. MP was supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (Brazilian agency). CRdO thanks partial support by Conselho Nacional de Desenvolvimento Científico e Tecnológico (Brazilian agency, Universal Project 41004/2014-8).
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de Oliveira, C.R., Pigossi, M. Point Spectrum and SULE for Time-Periodic Perturbations of Discrete 1D Schrödinger Operators with Electric Fields. J Stat Phys 173, 140–162 (2018). https://doi.org/10.1007/s10955-018-2126-6
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DOI: https://doi.org/10.1007/s10955-018-2126-6