n-particle quantum statistics on graphs
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 iden...
| Main Authors: | , , , |
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| Format: | Journal article |
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Springer
2014
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| _version_ | 1797073687283761152 |
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| author | Harrison, JM Keating, JP Robbins, JM Sawicki, A |
| author_facet | Harrison, JM Keating, JP Robbins, JM Sawicki, A |
| author_sort | Harrison, JM |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T23:25:38Z |
| format | Journal article |
| id | oxford-uuid:6a478dd6-baa6-4956-957d-77a3bf35bde3 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T23:25:38Z |
| publishDate | 2014 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:6a478dd6-baa6-4956-957d-77a3bf35bde32022-03-26T18:56:23Zn-particle quantum statistics on graphsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:6a478dd6-baa6-4956-957d-77a3bf35bde3Symplectic Elements at OxfordSpringer2014Harrison, JMKeating, JPRobbins, JMSawicki, AWe 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. |
| spellingShingle | Harrison, JM Keating, JP Robbins, JM Sawicki, A n-particle quantum statistics on graphs |
| title | n-particle quantum statistics on graphs |
| title_full | n-particle quantum statistics on graphs |
| title_fullStr | n-particle quantum statistics on graphs |
| title_full_unstemmed | n-particle quantum statistics on graphs |
| title_short | n-particle quantum statistics on graphs |
| title_sort | n particle quantum statistics on graphs |
| work_keys_str_mv | AT harrisonjm nparticlequantumstatisticsongraphs AT keatingjp nparticlequantumstatisticsongraphs AT robbinsjm nparticlequantumstatisticsongraphs AT sawickia nparticlequantumstatisticsongraphs |