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

R. Voituriez

doi:10.1016/s0550-3213(01)00590-9

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

R. Voituriez

Université Paris Sud

Research output: Contribution to journal › Article › peer-review

Abstract

We study random walks on the three-strand braid group B₃, 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 B₃ as generalized magnetic translation operators for the problem of a quantum particle on the hyperbolic plane.

Original language	English
Pages (from-to)	675-688
Number of pages	14
Journal	Nuclear Physics B
Volume	621
Issue number	1-2
DOIs	https://doi.org/10.1016/s0550-3213(01)00590-9
Publication status	Published - 21 Jan 2002
Externally published	Yes

Keywords

Braid groups
Discrete magnetic Schrödinger operators
Hyperbolic geometry
Representation theory

Access to Document

10.1016/s0550-3213(01)00590-9

Cite this

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