The current distribution of the multiparticle hopping asymmetric diffusion model

Abstract

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 $|S|\ge m$, 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.

27 pages

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Cited by in corpus (6)

• On integrability of zero-range chipping models with factorized steady state
• The $q$-Hahn asymmetric exclusion process
• Exact Formulas of the Transition Probabilities of the Multi-Species Asymmetric Simple Exclusion Process
• The transition probability and the probability for the left-most particle's position of the q-TAZRP
• On the TASEP with Second Class Particles
• Some conditional probabilities in the TASEP with second class particles