Anyons in One Dimension

Martin Greiter

doi:10.37282/991819.22.27

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arXiv · 2112.08021

Anyons in One Dimension

Martin Greiter

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Abstract

I give a non-technical account of fractional statistics in one dimension. In systems with periodic boundary conditions, the crossing of anyons is always uni-directional, and the fractional phase $\theta$ acquired by the anyons gives rise to fractional shifts in the spacings of the relative momenta, ${\Delta p =2\pi\hbar/L\, (|\theta|/\pi+n)}$. The fractional shift $\theta/\pi$ is a good quantum number of interacting anyons, even though the single particle momenta, and hence the non-negative integers $n$, are generally not.

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Martin Greiter. 2021-12-15. Anyons in One Dimension. https://doi.org/10.37282/991819.22.27

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