The Current Distribution of the Multiparticle Hopping Asymmetric Diffusion Model |
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Authors: | Eunghyun Lee |
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Affiliation: | 1.Department of Mathematics and Statistics,University of Helsinki,Helsinki,Finland |
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Abstract: | In this paper we treat the multiparticle hopping asymmetric diffusion model (MADM) on ℤ introduced by Sasamoto and Wadati in 1998. The transition probability of the MADM with N particles is provided by using the Bethe ansatz. The transition probability is expressed as the sum of N-dimensional contour integrals of which contours are circles centered at the origin with restrictions on their radii. By using the transition probability we find ℙ(x m (t)=x), the probability that the mth particle from the left is at x at time t. The probability ℙ(x m (t)=x) is expressed as the sum of |S|-dimensional contour integrals over all S⊂{1,…,N} with |S|≥m, and is used to give the current distribution of the system. The mapping between the MADM and the pushing asymmetric simple exclusion process (PushASEP) is discussed. |
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