Séminaire du LPTMS: Jon Harrison


14:30 - 15:30

LPTMS, salle 201, 2ème étage, Bât 100, Campus d'Orsay
15 Rue Georges Clemenceau, Orsay, 91405
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New forms of quantum statistics on graphs

Jon Harrison, Baylor University

We consider the quantum statistics of indistinguishable particles on a graph. In three dimensions quantum states are symmetric or anti-symmetric under exchange of pairs of identical particles, corresponding to Bose-Einstein or Fermi-Dirac statistics respectively. Restricting the particles totwo dimensions topologically inequivalent exchange paths correspond to elements of the braid group instead of the symmetric group. This opens up the possibility of Anyon statistics on a surface, characterized by a single free choice of an exchange phase. We consider the case when the particles are further restricted to lie on a quasi-one-dimensional network; a graph. For sufficiently complex graphs new forms of statistics emerge. Quantum statistics of indistinguishable particles on graphs may be characterized by multiple independent free Anyon phases and discrete-valued phases. Possible applications of the new forms of quantum statistics include topological quantum computing, the fractional quantum Hall effect, superconductivity, topological insulators and molecular physics. This is work with JP Keating and JM Robbins at Bristol University. Proc. R. Soc. A doi:10.1098/rspa.2010.0254

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