Determinant solution for the Totally Asymmetric Exclusion Process with parallel update II. Ring geometry

Abstract

Using the Bethe ansatz we obtain the determinant expression for the time dependent transition probabilities in the totally asymmetric exclusion process with parallel update on a ring. Developing a method of summation over the roots of Bethe equations based on the multidimensional analogue of the Cauchy residue theorem, we construct the resolution of the identity operator, which allows us to calculate the matrix elements of the evolution operator and its powers. Representation of results in the form of an infinite series elucidates connection to other results obtained for the ring geometry. As a byproduct we also obtain the generating function of the joint probability distribution of particle configurations and the total distance traveled by the particles.

28 pages, 3 figures

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Cited by in corpus (11)

• Slow relaxation and aging kinetics for the driven lattice gas
• Spectrum of the totally asymmetric simple exclusion process on a periodic lattice -- first excited states
• The propagator of the attractive delta-Bose gas in one dimension
• Spectrum of the totally asymmetric simple exclusion process on a periodic lattice - bulk eigenvalues
• Integral formulas of ASEP and $q$-TAZRP on a ring
• Current fluctuations and large deviations for periodic TASEP on the relaxation scale
• Perturbative solution for the spectral gap of the weakly asymmetric exclusion process
• Asymptotics for the norm of Bethe eigenstates in the periodic totally asymmetric exclusion process
• On the blockage problem and the non-analyticity of the current for the parallel TASEP on a ring
• Generalized Green Functions and current correlations in the TASEP
• KPZ fluctuations in finite volume