Localization in Quantum Walks with a Single Lattice Defect: A Comparative Study

Abstract

We study how a single lattice defect in a discrete time quantum walk affects the return probability of a quantum particle. This defect at the starting position is modeled by a quantum coin that is distinct from the others over the lattice. This coin has a dependence on \(\omega\) which quantifies the intensity of the localization. For some sorts of lattice defects, we show how the localization can have a dependence just on \(\omega\) , and also, the polar \(\alpha\) and azimuth \(\beta\) angles of the initial qubit by numerical calculations. We propose a lattice defect whose localization has additional dependence on \(\beta +\omega\), leading to extra localization profiles. We compare the quantum walks with our lattice defect to the earlier ones, and we discuss their spreading and survival probability.