Exact Relaxation Dynamics in the Totally Asymmetric Simple Exclusion Process

Details Exact Relaxation Dynamics in the Totally Asymmetric Simple Exclusion Process Exact Relaxation Dynamics in the Totally Asymmetric Simple Exclusion Process

2012-01-13

arxiv.org/abs/1201.2749v3

Phys. Rev. E 85 (2012) 042105

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1103/PhysRevE.85.042105

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.

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