Random walks on the braid group B_3 and magnetic translations in hyperbolic geometry

Details Random walks on the braid group B_3 and magnetic translations in hyperbolic geometry Random walks on the braid group B_3 and magnetic translations in hyperbolic geometry

2001-03-06

arxiv.org/abs/math-ph/0103008v2

Nucl.Phys. B621 (2002) 675-688

Physics

Mathematical Physics

17 pages, 2 figures, accepted in Nuclear Physics B

Scientific paper

10.1016/S0550-3213(01)00590-9

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.

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