Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2004-01-15
Phys. Rev. E 69, 061109 (2004)
Physics
Condensed Matter
Statistical Mechanics
7 pages, Revtex4, mistypes corrected
Scientific paper
10.1103/PhysRevE.69.061109
The eigenfunctions and eigenvalues of the master-equation for zero range process with totally asymmetric dynamics on a ring are found exactly using the Bethe ansatz weighted with the stationary weights of particle configurations. The Bethe ansatz applicability requires the rates of hopping of particles out of a site to be the $q$-numbers $[n]_q$. This is a generalization of the rates of hopping of noninteracting particles equal to the occupation number $n$ of a site of departure. The noninteracting case can be restored in the limit $q\to 1$. The limiting cases of the model for $q=0,\infty$ correspond to the totally asymmetric exclusion process, and the drop-push model respectively. We analyze the partition function of the model and apply the Bethe ansatz to evaluate the generating function of the total distance travelled by particles at large time in the scaling limit. In case of non-zero interaction, $q \ne 1$, the generating function has the universal scaling form specific for the Kardar-Parizi-Zhang universality class.
No associations
LandOfFree
Bethe ansatz solution of zero-range process with nonuniform stationary state 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 zero-range process with nonuniform stationary state, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bethe ansatz solution of zero-range process with nonuniform stationary state will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-299809