Bethe ansatz solution of discrete time stochastic processes with fully parallel update

Details Bethe ansatz solution of discrete time stochastic processes with fully parallel update Bethe ansatz solution of discrete time stochastic processes with fully parallel update

2004-11-22

arxiv.org/abs/cond-mat/0411558v3

J. Stat. Phys. 123, 125-166 (2006)

Physics

Condensed Matter

Statistical Mechanics

43 pages, 3 figures, final version, published in Journal Stat. Phys. in Online First, avalable at http://dx.doi.org/10.1007/s1

Scientific paper

10.1007/s10955-006-9023-0

We present the Bethe ansatz solution for the discrete time zero range and asymmetric exclusion processes with fully parallel dynamics. The model depends on two parameters: $p$, the probability of single particle hopping, and $q$, the deformation parameter, which in the general case, $|q|<1$, is responsible for long range interaction between particles. The particular case $q=0$ corresponds to the Nagel-Schreckenberg traffic model with $v_{\mathrm{max}}=1$. As a result, we obtain the largest eigenvalue of the equation for the generating function of the distance travelled by particles. For the case $q=0$ the result is obtained for arbitrary size of the lattice and number of particles. In the general case we study the model in the scaling limit and obtain the universal form specific for the Kardar-Parisi-Zhang universality class. We describe the phase transition occurring in the limit $p\to 1$ when $q<0$.

Affiliated with

Also associated with

No associations

Rating

Bethe ansatz solution of discrete time stochastic processes with fully parallel update does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Bethe ansatz solution of discrete time stochastic processes with fully parallel update, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bethe ansatz solution of discrete time stochastic processes with fully parallel update will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-167916