Universal Behavior of Quantum Walks with Long-Range Steps

Details Universal Behavior of Quantum Walks with Long-Range Steps Universal Behavior of Quantum Walks with Long-Range Steps

2007-11-23

arxiv.org/abs/0711.3762v1

Phys. Rev. E 77, 021117 (2008)

Physics

Quantum Physics

4 pages, 3 figures

Scientific paper

10.1103/PhysRevE.77.021117

Quantum walks with long-range steps $R^{-\gamma}$ ($R$ being the distance between sites) on a discrete line behave in similar ways for all $\gamma\geq2$. This is in contrast to classical random walks, which for $\gamma >3$ belong to a different universality class than for $\gamma \leq 3$. 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 $\gamma\geq2$.

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