Chikashi Arita et al 2009 J. Phys. A: Math. Theor. 42 345002 doi:10.1088/1751-8113/42/34/345002
Chikashi Arita1, Atsuo Kuniba2, Kazumitsu Sakai2 and Tsuyoshi Sawabe3
Show affiliationsThe spectrum of the Hamiltonian (Markov matrix) of a multi-species asymmetric simple exclusion process on a ring is studied. The dynamical exponent concerning the relaxation time is found to coincide with the one-species case. It implies that the system belongs to the Kardar–Parisi–Zhang or Edwards–Wilkinson universality classes depending on whether the hopping rate is asymmetric or symmetric, respectively. Our derivation exploits a poset structure of the particle sectors, leading to a new spectral duality and inclusion relations. The Bethe ansatz integrability is also demonstrated.
15A24 Matrix equations and identities
15A18 Eigenvalues, singular values, and eigenvectors
15A30 Algebraic systems of matrices (See also 16S50, 20Gxx, 20Hxx)
Issue 34 (28 August 2009)
Received 8 April 2009, in final form 30 June 2009
Published 31 July 2009
Chikashi Arita et al 2009 J. Phys. A: Math. Theor. 42 345002
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