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Non-stationary probabilities for the asymmetric exclusion process on a ring

V. B. Priezzhev

PramanaJun 1, 200518 citations

Exact Nonstationary Probabilities in the Asymmetric Exclusion Process on a Ring

V. B. Priezzhev

The complete solution of the master equation for a system of interacting particles of finite density is presented. By using a new form of the Bethe ansatz, the totally asymmetric exclusion process on a ring is solved for arbitrary initial conditions and time intervals.

arXiv:cond-mat/0211052Physical Review LettersAug 1, 200364 citations

Long time asymptotics of the totally asymmetric simple exclusion process

Kohei Motegi, Kazumitsu Sakai, Jun Sato

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 that 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.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 that 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.

arXiv:1207.6156Journal of Physics A Mathematical and TheoreticalOct 29, 201218 citations

A Two-Parametric Family of Asymmetric Exclusion Processes and Its Exact Solution

M. Alimohammadi, Vahid Karimipour, Mohammad Khorrami

arXiv:cond-mat/9805155Journal of Statistical PhysicsOct 1, 199966 citations

Duality relations for asymmetric exclusion processes

Gunter Markus Schutz

Journal of Statistical PhysicsMar 1, 1997100 citations

Determinant solution for the totally asymmetric exclusion process with parallel update

Alexander M. Povolotsky, V. B. Priezzhev

We consider the totally asymmetric exclusion process in discrete time with the parallel update. Constructing an appropriate transformation of the evolution operator, we reduce the problem to that solvable by the Bethe ansatz. The nonstationary solution of the master equation for the infinite 1D lattice is obtained in a determinant form. Using a modified combinatorial treatment of the Bethe ansatz, we give an alternative derivation of the resulting determinant expression.

arXiv:cond-mat/0605150Journal of Statistical Mechanics Theory and ExperimentJul 12, 200639 citations

Nonstationary probabilities and time correlation functions for an asymmetric exclusion process

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