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arXiv · 0711.3762

Universal Behavior of Quantum Walks with Long-Range Steps

Oliver Muelken·Volker Pernice·Alexander Blumen
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Abstract

Quantum walks with long-range steps $R^{-γ}$ ($R$ being the distance between sites) on a discrete line behave in similar ways for all $γ\geq2$. This is in contrast to classical random walks, which for $γ>3$ belong to a different universality class than for $γ\leq 3$. 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 $γ=2$, 4, and with nearest neighbor steps. We interpolate this result to arbitrary $γ\geq2$.

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Oliver Muelken, Volker Pernice, Alexander Blumen. 2007-11-23. Universal Behavior of Quantum Walks with Long-Range Steps. https://doi.org/10.1103/physreve.77.021117

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