Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2007-06-13
J. Stat. Mech. (2007) P08018
Physics
Condensed Matter
Statistical Mechanics
28 pages, 3 figures
Scientific paper
10.1088/1742-5468/2007/08/P08018
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.
Povolotsky Alexander M.
Priezzhev Vyatcheslav B.
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