### 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 {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.

Original language | English |
---|---|

Pages (from-to) | 50-72 |

Number of pages | 23 |

Journal | Journal of Statistical Physics |

Volume | 149 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2012 |

Externally published | Yes |

### Fingerprint

### Keywords

- ASEP
- Bethe ansatz
- KPZ universality
- TASEP
- Tracy-Widom distribution

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

**The Current Distribution of the Multiparticle Hopping Asymmetric Diffusion Model.** / Lee, Eunghyun.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 149, no. 1, pp. 50-72. https://doi.org/10.1007/s10955-012-0582-y

}

TY - JOUR

T1 - The Current Distribution of the Multiparticle Hopping Asymmetric Diffusion Model

AU - Lee, Eunghyun

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - ASEP

KW - Bethe ansatz

KW - KPZ universality

KW - TASEP

KW - Tracy-Widom distribution

UR - http://www.scopus.com/inward/record.url?scp=84867142059&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867142059&partnerID=8YFLogxK

U2 - 10.1007/s10955-012-0582-y

DO - 10.1007/s10955-012-0582-y

M3 - Article

VL - 149

SP - 50

EP - 72

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1

ER -