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

References in corpus (8)

• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• Fluctuation properties of the TASEP with periodic initial configuration
• Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
• Relaxation dynamics in the gapped XXZ spin-1/2 chain
• Current Distribution and random matrix ensembles for an integrable asymmetric fragmentation process
• Eigenvectors of open XXZ and ASEP models for a class of non-diagonal boundary conditions
• Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition
• Spectrum in multi-species asymmetric simple exclusion process on a ring