n-particle quantum statistics on graphs
Mathematical Physics
2016-01-19 v1 Algebraic Topology
math.MP
Abstract
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.
Cite
@article{arxiv.1304.5781,
title = {n-particle quantum statistics on graphs},
author = {Jonathan M. Harrison and Jonathan P. Keating and Jonathan M. Robbins and Adam Sawicki},
journal= {arXiv preprint arXiv:1304.5781},
year = {2016}
}
Comments
34 pages, 21 figures