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 |
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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.
In: Journal of Statistical Physics, Vol. 149, No. 1, 2012, p. 50-72.Research output: Contribution to journal › Article
}
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 -