This title appears in the Scientific Report :
2005
Please use the identifier:
http://dx.doi.org/10.1007/s10955-004-8819-z in citations.
Current distribution and random matrix ensembles for an integrable asymmetric fragmentation process
Current distribution and random matrix ensembles for an integrable asymmetric fragmentation process
We calculate the time-evolution of a discrete-time fragmentation process in which clusters of particles break up and reassemble and move stochastically with size-dependent rates. In the continuous-time limit the process turns into the totally asymmetric simple exclusion process (only pieces of size...
| Personal Name(s): | Rakos, A. |
|---|---|
| Schütz, G. M. | |
| Contributing Institute: |
Theorie II; IFF-TH-II |
| Published in: | Journal of statistical physics, 118 (2005) |
| Imprint: |
New York, NY [u.a.]
Springer Science + Business Media B.V.
2005
|
| DOI: |
10.1007/s10955-004-8819-z |
| Document Type: |
Journal Article |
| Research Program: |
Kondensierte Materie |
| Series Title: |
Journal of Statistical Physics
118 |
| Subject (ZB): | |
| Publikationsportal JuSER |
|
We calculate the time-evolution of a discrete-time fragmentation process in which clusters of particles break up and reassemble and move stochastically with size-dependent rates. In the continuous-time limit the process turns into the totally asymmetric simple exclusion process (only pieces of size 1 break off a given cluster). We express the exact solution of the master equation for the process in terms of a determinant which can be derived using the Bethe ansatz. From this determinant we compute the distribution of the current across an arbitrary bond which after appropriate scaling is given by the distribution of the largest eigenvalue of the Gaussian unitary ensemble of random matrices. This result confirms universality of the scaling form of the current distribution in the KPZ universality class and suggests that there is a link between integrable particle systems and random matrix ensembles. |