Localization of a multi-dimensional quantum walk with one defect

13 Mar 2017  ·  Fuda Toru, Funakawa Daiju, Suzuki Akito ·

In this paper, we introduce a multidimensional generalization of Kitagawa's split-step discrete-time quantum walk, study the spectrum of its evolution operator for the case of one defect coins, and prove localization of the walk. Using a spectral mapping theorem, we can reduce the spectral analysis of the evolution operator to that of a discrete Schr\"{o}dinger operator with variable coefficients, which is analyzed using the Feshbach map...

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Mathematical Physics Mathematical Physics Spectral Theory