Work

n-Particle Quantum Statistics on Graphs

Year: 2014

Type: article

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.

Source: Communications in Mathematical Physics

DOI: 10.1007/s00220-014-2091-0

Authors: J. M. Harrison, J. P. Keating, J. M. Robbins, A. Sawicki

Institutions: Baylor University, University of Bristol, Center for Theoretical Physics, Polish Academy of Sciences

Language: English

Topic: Quantum Mechanics and Applications

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: Baylor University, University of Bristol