The current distribution of the multiparticle hopping asymmetric diffusion model

Details The current distribution of the multiparticle hopping asymmetric diffusion model The current distribution of the multiparticle hopping asymmetric diffusion model

2012-03-02

arxiv.org/abs/1203.0501v1

Physics

Mathematical Physics

27 pages

Scientific paper

In this paper we treat the \textit{multiparticle hopping asymmetric diffusion model} (MADM) on $\mathbb{Z}$ 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 $\mathbb{P}(x_m(t) =x)$, the probability that the $m$th particle from the left is at $x$ at time $t$. The probability $\mathbb{P}(x_m(t) =x)$ is expressed as the sum of $|S|$-dimensional contour integrals over all $S \subset \{1,...,N\}$ with $|S| \geq m$, 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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