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ONE-DIMENSIONAL QUANTUM WALKS WITH ONE DEFECT

M. J. CANTERO

Department of Mathematics, University of California, Berkeley, CA, 94720, USA

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F. A. GRÜNBAUM

Departamento de Matemática Aplicada, Universidad de Zaragoza, Zaragoza, Spain

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L. MORAL

Department of Mathematics, University of California, Berkeley, CA, 94720, USA

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, and

L. VELÁZQUEZ

Department of Mathematics, University of California, Berkeley, CA, 94720, USA

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https://doi.org/10.1142/S0129055X1250002XCited by:36 (Source: Crossref)

Abstract

The CGMV method allows for the general discussion of localization properties for the states of a one-dimensional quantum walk, both in the case of the integers and in the case of the nonnegative integers. Using this method we classify, according to such localization properties, all the quantum walks with one defect at the origin, providing explicit expressions for the asymptotic return probabilities to the origin.

Keywords:

AMSC: 81P68, 47B36, 42C05

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