1207.4106 (J. Ricardo G. Mendonça)
J. Ricardo G. Mendonça
We cast the infinitesimal generator of the symmetric simple exclusion process on a graph as a quantum spin-1/2 ferromagnetic Heisenberg model and show that its eigenspectrum can be obtained by elementary techniques on the complete, complete bipartite, and related multipartite graphs. Some of the resulting infinitesimal generators are formally identical to homogeneous as well as mixed higher spins models. The degeneracies of the eigenspectra are described in detail, and we give a neat derivation of the outer multiplicities appearing in the Clebsch-Gordan series for arbitrary spin-s representations of the SU(2) not easily found elsewhere. We mention in passing how our results fit within the related questions of a ferromagnetic ordering of energy levels and a conjecture according to which the spectral gaps of the random walk and the interchange process on finite simple graphs must be equal.
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http://arxiv.org/abs/1207.4106
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