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arXiv:2009.05336 · Annales Henri Poincaré

Spectral and Scattering Properties of Quantum Walks on Homogenous Trees of Odd Degree

Rafael Tiedra de Aldecoa

Published Jun 3, 2021• 3 citations
arXivHTMLPDF
DOI
10.1007/s00023-021-01066-9

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We study discrete-time quantum walks on a half line by means of spectral analysis. Cantero et al. showed that the CMV matrix, which gives a recurrence relation for the orthogonal Laurent polynomials on the unit circle, expresses the dynamics of the quantum walk. Using the CGMV method introduced by them, the name is taken from their initials, we obtain the spectral measure for the quantum walk. As a corollary, we give another proof for localization of the quantum walk on homogeneous trees shown by Chisaki et al.
We study discrete-time quantum walks on a half line by means of spectral analysis. Cantero et al. [1] showed that the CMV matrix, which gives a recurrence relation for the orthogonal Laurent polynomials on the unit circle [2], expresses the dynamics of the quantum walk. Using the CGMV method introduced by them, the name is taken from their initials, we obtain the spectral measure for the quantum walk. As a corollary, we give another proof for localization of the quantum walk on homogeneous trees shown by Chisaki et al. [3].