Hidden symmetries in the asymmetric exclusion process

Abstract

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.

16 pages

References in corpus (2)

• Bethe Ansatz calculation of the spectral gap of the asymmetric exclusion process
• Relaxation times in the ASEP model using a DMRG method

Cited by in corpus (8)

• The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
• Yang-Baxter integrable Lindblad equations
• Derivation of a Matrix Product Representation for the Asymmetric Exclusion Process from Algebraic Bethe Ansatz
• Spectral Degeneracies in the Totally Asymmetric Exclusion Process
• Spectrum of the totally asymmetric simple exclusion process on a periodic lattice -- first excited states
• Family of Commuting Operators for the Totally Asymmetric Exclusion Process
• Exact eigenspectrum of the symmetric simple exclusion process on the complete, complete bipartite, and related graphs
• KPZ fluctuations in finite volume