Determinant solution for the totally asymmetric exclusion process with parallel update

Abstract

We consider the totally asymmetric exclusion process in discrete time with\nthe parallel update. Constructing an appropriate transformation of the\nevolution operator, we reduce the problem to that solvable by the Bethe ansatz.\nThe non-stationary solution of the master equation for the infinite 1D lattice\nis obtained in a determinant form. Using a modified combinatorial treatment of\nthe Bethe ansatz, we give an alternative derivation of the resulting\ndeterminant expression.\n