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arXiv · 1009.0813

Statistical dynamics of a non-Abelian anyonic quantum walk

Lauri Lehman·Vaclav Zatloukal·Gavin K. Brennen·Jiannis K. Pachos·Zhenghan Wang
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Abstract

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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Lauri Lehman, Vaclav Zatloukal, Gavin K. Brennen, Jiannis K. Pachos, Zhenghan Wang. 2010-09-04. Statistical dynamics of a non-Abelian anyonic quantum walk. https://doi.org/10.1103/physrevlett.106.230404

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