Tuesday, April 23, 2013

1304.5781 (Jonathan M. Harrison et al.)

n-particle quantum statistics on graphs    [PDF]

Jonathan M. Harrison, Jonathan P. Keating, Jonathan M. Robbins, Adam Sawicki
We develop a full characterization of abelian quantum statistics on graphs. We explain how the number of anyon phases is related to connectivity. For 2-connected graphs the independence of quantum statistics with respect to the number of particles is proven. For non-planar 3-connected graphs we identify bosons and fermions as the only possible statistics, whereas for planar 3-connected graphs we show that one anyon phase exists. Our approach also yields an alternative proof of the structure theorem for the first homology group of n-particle graph configuration spaces. Finally, we determine the topological gauge potentials for 2-connected graphs.
View original: http://arxiv.org/abs/1304.5781

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