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Localization for a one-dimensional split-step quantum walk with bound states robust against perturbations

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 نشر من قبل Akito Suzuki
 تاريخ النشر 2018
  مجال البحث فيزياء
والبحث باللغة English




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For given two unitary and self-adjoint operators on a Hilbert space, a spectral mapping theorem was proved in cite{HiSeSu}. In this paper, as an application of the spectral mapping theorem, we investigate the spectrum of a one-dimensional split-step quantum walk. We give a criterion for when there is no eigenvalues around $pm 1$ in terms of a discriminant operator. We also provide a criterion for when eigenvalues $pm 1$ exist in terms of birth eigenspaces. Moreover, we prove that eigenvectors from the birth eigenspaces decay exponentially at spatial infinity and that the birth eigenspaces are robust against perturbations.



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