Hidden symmetries in the asymmetric exclusion process

Details Hidden symmetries in the asymmetric exclusion process Hidden symmetries in the asymmetric exclusion process

2004-12-14

arxiv.org/abs/cond-mat/0412353v1

JSTAT (2004) P12001

Physics

Condensed Matter

Statistical Mechanics

16 pages

Scientific paper

10.1088/1742-5468/2004/12/P12001

We present a spectral study of the evolution matrix of the totally asymmetric exclusion process on a ring at half filling. The natural symmetries (translation, charge conjugation combined with reflection) predict only two fold degeneracies. However, we have found that degeneracies of higher order also exist and, as the system size increases, higher and higher orders appear. These degeneracies become generic in the limit of very large systems. This behaviour can be explained by the Bethe Ansatz and suggests the presence of hidden symmetries in the model. Keywords: ASEP, Markov matrix, symmetries, spectral degeneracies, Bethe Ansatz.

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