n-Particle Quantum Statistics on Graphs
- 491 Downloads
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.
KeywordsHomology Group Gauge Potential Star Graph Central Vertex Independent Cycle
- 2.Souriau J.M.: Structure des systmes dynamiques. Dunod, Paris (1970)Google Scholar
- 3.Wilczek, F. (ed.): Fractional Statistics and Anyon Superconductivity. World Scientific, Singapore (1990)Google Scholar
- 8.Berkolaiko, G., Kuchment, P.: Introduction to Quantum Graphs. Mathematical Surveys and Monographs, vol. 186. AMS, Providence (2013)Google Scholar
- 13.Tutte, W.T.: Graph Theory. Cambridge University Press, New York (2001)Google Scholar
- 15.Abrams, A.: Configuration spaces and braid groups of graphs. Ph.D. thesis, UC Berkeley (2000)Google Scholar
- 16.Nakahara, M.: Geometry, Topology, and Physics. Hilger, London (1990)Google Scholar
Open AccessThis article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.