Discrete-time quantum walks generated by aperiodic fractal sequence of space coin operators

Abstract: Properties of one dimensional discrete-time quantum walks are sensitive to the presence of inhomogeneities in the substrate, which can be generated by defining position dependent coin operators. Deterministic aperiodic sequences of two or more symbols provide ideal environments where these properties can be explored in a controlled way. This work discusses a two-coin model resulting from the construction rules that lead to the usual fractal Cantor set. Although the fraction of the less frequent coin $\rightarrow 0$ as the size of the chain is increased, it leaves peculiar properties in the walker dynamics. They are characterized by the wave function, from which results for the probability distribution and its variance, as well as the entanglement entropy were obtained. A number of results for different choices of the two coins are presented. The entanglement entropy has shown to be very sensitive to uncover subtle quantum effects present in the model.