Statistical dynamics of a non-Abelian anyonic quantum walk
arXiv:1009.0813 · doi:10.1103/PhysRevLett.106.230404
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.
7 pages, 5 figures