Long time asymptotics of the totally asymmetric simple exclusion process

Abstract

We study the long time asymptotics of the relaxation dynamics of the totally asymmetric simple exclusion process on a ring. Evaluating the asymptotic amplitudes of the local currents by the algebraic Bethe ansatz method, we find the relaxation times starting from the step and alternating initial conditions are governed by different eigenvalues of the Markov matrix. In both cases, the scaling exponents of the leading asymptotic amplitudes with respect to the total number of sites are found to be -1. We also study the asymptotics of correlation functions such as the emptiness formation probability.

21 pages, 5 figures, revised version

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Cited by in corpus (10)

• Vertex models, TASEP and Grothendieck polynomials
• Finite-time fluctuations for the totally asymmetric exclusion process
• Riemann surfaces for KPZ with periodic boundaries
• Extrapolation methods and Bethe ansatz for the asymmetric exclusion process
• Current fluctuations and large deviations for periodic TASEP on the relaxation scale
• Perturbative solution for the spectral gap of the weakly asymmetric exclusion process
• Riemann surface for TASEP with periodic boundaries
• Relaxation dynamics of the asymmetric simple exclusion process with Langmuir kinetics on a ring
• Asymptotics for the norm of Bethe eigenstates in the periodic totally asymmetric exclusion process
• KPZ fluctuations in finite volume