Universal behavior of quantum walks with long-range steps

被引：16

作者：

Muelken, Oliver ^{[1
]}

Pernice, Volker ^{[1
]}

Blumen, Alexander ^{[1
]}

机构：

[1] Univ Freiburg, D-79104 Freiburg, Germany

来源：

PHYSICAL REVIEW E | 2008年 / 77卷 / 02期

关键词：

D O I：

10.1103/PhysRevE.77.021117

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

Continuous-time 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 >= 2. This is in contrast to classical random walks, which for gamma>3 belong to a different universality class than for gamma <= 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 >= 2.

引用

页数：5

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