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ONE-DIMENSIONAL QUANTUM WALKS WITH ONE DEFECT

Profile image of M. CanteroM. CanteroProfile image of Alberto GrunbaumAlberto Grunbaum

2012, Reviews in Mathematical Physics

https://doi.org/10.1142/S0129055X1250002X
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45 pages

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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 non negative 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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