Spectrum in multi-species asymmetric simple exclusion process on a ring

2009/04/09 by Chikashi Arita, Atsuo Kuniba, Kazumitsu Sakai +1 · 1 citation
Physics and Astronomy · Mathematics · #math-ph #cond-mat.stat-mech #math.MP #nlin.SI

paper · pdf · doi:10.1088/1751-8113/42/34/345002

published as J. Phys. A: Math. Theor. 42 (2009) 345002 · 46 pages, 9 figures

arxiv created 2009/04/09 · arxiv updated 2009/12/01

Abstract

The spectrum of 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.

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