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The Current Distribution of the Multiparticle Hopping Asymmetric Diffusion Model

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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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Notes

  1. Here q is not related to the q in the rate ql n .

  2. In the PushASEP in [4], the pushing can occur in only one direction, so we will call it the one-sided PushASEP.

  3. In general, for any product of S-matrices with a certain condition, if there is no S-matrix that satisfies the condition, then the product is defined to be 1 in this paper.

  4. The authors corrected the error in the erratum [21].

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Acknowledgements

This work was supported by European Research Council.

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  1. Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland

    Eunghyun Lee

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  1. Eunghyun Lee
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Lee, E. The Current Distribution of the Multiparticle Hopping Asymmetric Diffusion Model. J Stat Phys 149, 50–72 (2012). https://doi.org/10.1007/s10955-012-0582-y

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