Spectral Degeneracies in the Totally Asymmetric Exclusion Process

Details Spectral Degeneracies in the Totally Asymmetric Exclusion Process Spectral Degeneracies in the Totally Asymmetric Exclusion Process

2004-12-17

arxiv.org/abs/cond-mat/0412462v1

J. Stat. Phys 120 (2005) 779-798

Physics

Condensed Matter

Statistical Mechanics

19 pages, 1 figure

Scientific paper

10.1007/s10955-005-6972-7

We study the spectrum of the Markov matrix of the totally asymmetric exclusion process (TASEP) on a one-dimensional periodic lattice at ARBITRARY filling. Although the system does not possess obvious symmetries except translation invariance, the spectrum presents many multiplets with degeneracies of high order. This behaviour is explained by a hidden symmetry property of the Bethe Ansatz. Combinatorial formulae for the orders of degeneracy and the corresponding number of multiplets are derived and compared with numerical results obtained from exact diagonalisation of small size systems. This unexpected structure of the TASEP spectrum suggests the existence of an underlying large invariance group. Keywords: ASEP, Markov matrix, Bethe Ansatz, Symmetries.

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