The Current Distribution of the Multiparticle Hopping Asymmetric Diffusion Model

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 {pipe}S{pipe}-dimensional contour integrals over all S⊂{1,...,N} with {pipe}S{pipe}≥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.