Journal
REVIEWS IN MATHEMATICAL PHYSICS
Volume 24, Issue 2, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0129055X1250002X
Keywords
Quantum walks; localization; CGMV method; CMV matrices; scalar and matrix Laurent orthogonal polynomials on the unit circle
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Funding
- Office of Energy Research, USDOE [DE-AC03-76SF00098]
- Ministry of Science and Innovation of Spain [MTM2008-06689-C02-01]
- European Regional Development Fund (ERDF)
- Diputacion General de Aragon (Spain) [E-64]
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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.
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