One-dimensional quantum walks with one defect

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 at the origin

Resolvent Methods for Quantum Walks with an Application to a Thue-Morse Quantum Walk

In this expository note, we discuss spatially inhomogeneous quantum walks in one dimension and describe a genre of mathematical methods that enables one to translate information about the time-independent eigenvalue equation for the unitary generator into dynamical estimates for the corresponding quantum walk. To illustrate the general methods, we show how to apply them to a 1D coined quantum walk whose coins are distributed according to an element of the Thue--Morse subshift.Comment: This paper is part of the proceedings volume for the Workshop on "Quantum Simulation and Quantum Walks" held in Yokohama, Japan in November of 201