Universal Behavior of Quantum Walks with Long-Range Steps

Abstract

Quantum walks with long-range steps $R^{-\gamma }$ ($R$ being the distance between sites) on a discrete line behave in similar ways for all $\gamma \ge 2$. This is in contrast to classical random walks, which for $\gamma >3$ belong to a different universality class than for $\gamma \le 3$. We show that the average probabilities to be at the initial site after time $t$ as well as the mean square displacements are of the same functional form for quantum walks with $\gamma =2$, 4, and with nearest neighbor steps. We interpolate this result to arbitrary $\gamma \ge 2$.

4 pages, 3 figures

References in corpus (1)

• Survival Probabilities in Coherent Exciton Transfer with Trapping

Cited by in corpus (2)

• Coherent exciton transport and trapping on long-range interacting cycles
• Slow Excitation Trapping in Quantum Transport with Long-Range Interactions