Exact Relaxation Dynamics in the Totally Asymmetric Simple Exclusion Process

Abstract

The relaxation dynamics of the one-dimensional totally asymmetric simple exclusion process on a ring is considered in the case of step initial condition. Analyzing the time evolution of the local particle densities and currents by the Bethe ansatz method, we examine their full relaxation dynamics. As a result, we observe peculiar behaviors, such as the emergence of a ripple in the density profile and the existence of the excessive particle currents. Moreover, by making a finite-size scaling analysis of the asymptotic amplitudes of the local densities and currents, we find the scaling exponents with respect to the total number of sites to be -3/2 and -1 respectively.

5 pages, 8 figures, v2: finite-size scaling of asymptotic amplitudes added, v3: minor revision

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Cited by in corpus (9)

• Vertex models, TASEP and Grothendieck polynomials
• Transport on a Lattice with Dynamical Defects
• Riemann surfaces for KPZ with periodic boundaries
• Long time asymptotics of the totally asymmetric simple 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