arXiv:0711.3762 [quant-ph]AbstractReferencesReviewsResources
Universal Behavior of Quantum Walks with Long-Range Steps
Oliver Muelken, Volker Pernice, Alexander Blumen
Published 2007-11-23Version 1
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 $\gamma\geq2$.
Comments: 4 pages, 3 figures
Journal: Phys. Rev. E 77, 021117 (2008)
Categories: quant-ph, cond-mat.stat-mech
Keywords: quantum walks, long-range steps, universal behavior, discrete line behave, mean square displacements
Tags: journal article
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