Asymptotic Properties of Generalized Eigenfunctions for Multi-dimensional Quantum Walks
نویسندگان
چکیده
We construct a distorted Fourier transformation associated with the multi-dimensional quantum walk. In order to avoid complication of notations, almost all our arguments are restricted two dimensional walks (2DQWs) without loss generality. The characterizes generalized eigenfunctions time evolution operator QW. 2DQW which will be considered in this paper has an anisotropy due definition shift for free Then we define anisotropic Banach space as modified Agmon-H\"{o}rmander's $\mathcal{B}^*$ and derive asymptotic behavior at infinity these spaces. scattering matrix appears expansion eigenfunctions.
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ژورنال
عنوان ژورنال: Annales Henri Poincaré
سال: 2021
ISSN: ['1424-0661', '1424-0637']
DOI: https://doi.org/10.1007/s00023-021-01131-3