Random walks on the braid group B3 and magnetic translations in hyperbolic geometry

被引：5
|
作者：
Voituriez, R [1 ]
机构：
[1] Univ Paris 11, Lab Phys Theor & Modeles Stat, F-91405 Orsay, France
来源：
NUCLEAR PHYSICS B | 2002年 / 621卷 / 03期
关键词：
braid groups; discrete magnetic Schrodinger operators representation theory; hyperbolic geometry;
D O I：
10.1016/S0550-3213(01)00590-9
中图分类号：
O412 [相对论、场论]; O572.2 [粒子物理学];
学科分类号：
摘要：
We study random walks on the three-strand braid group B-3, and in particular compute the drift, or average topological complexity of a random braid, as well as the probability of trivial entanglement. These results involve the study of magnetic random walks on hyperbolic graphs (hyperbolic Harper-Hofstadter problem), what enables to build a faithful representation of B-3 as generalized magnetic translation operators for the problem of a quantum particle on the hyperbolic plane. (C) 2002 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：675 / 688
页数：14
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