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.