Abstract
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 2connected graphs the independence of quantum statistics with respect to the number of particles is proven. For nonplanar 3connected graphs we identify bosons and fermions as the only possible statistics, whereas for planar 3connected 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 nparticle graph configuration spaces. Finally, we determine the topological gauge potentials for 2connected graphs.
We explain how the number of anyon phases is related to connectivity. For 2connected graphs the independence of quantum statistics with respect to the number of particles is proven. For nonplanar 3connected graphs we identify bosons and fermions as the only possible statistics, whereas for planar 3connected 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 nparticle graph configuration spaces. Finally, we determine the topological gauge potentials for 2connected graphs.
Original language  English 

Pages (fromto)  1293–1326 
Number of pages  34 
Journal  Communications in Mathematical Physics 
Volume  33 
Issue number  3 
DOIs  
Publication status  Published  6 Jun 2014 
Keywords
 quantum graphs
 quantum statistics
 topology of configurations spaces
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Profiles

Professor Jonathan M Robbins
 School of Mathematics  Head of School, Professor of Mathematics
 Applied Mathematics
 Mathematical Physics
Person: Academic , Member, Professional and Administrative