Statistical dynamics of a non-Abelian anyonic quantum walk

Details Statistical dynamics of a non-Abelian anyonic quantum walk Statistical dynamics of a non-Abelian anyonic quantum walk

2010-09-04

arxiv.org/abs/1009.0813v1

Phys.Rev.Lett.106:230404,2011

Physics

Quantum Physics

7 pages, 5 figures

Scientific paper

10.1103/PhysRevLett.106.230404

We study the single particle dynamics of a mobile non-Abelian anyon hopping around many pinned anyons on a surface. The dynamics is modelled by a discrete time quantum walk and the spatial degree of freedom of the mobile anyon becomes entangled with the fusion degrees of freedom of the collective system. Each quantum trajectory makes a closed braid on the world lines of the particles establishing a direct connection between statistical dynamics and quantum link invariants. We find that asymptotically a mobile Ising anyon becomes so entangled with its environment that its statistical dynamics reduces to a classical random walk with linear dispersion in contrast to particles with Abelian statistics which have quadratic dispersion.

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