PMID: 15244542Jul 13, 2004Paper

Bethe ansatz solution of zero-range process with nonuniform stationary state

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
A M Povolotsky

Abstract

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-->1. The limiting cases of the model for q=0, infinity 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 traveled by particles at large time in the scaling limit. In case of nonzero interaction, q not equal 1, the generating function has the universal scaling form specific for the Kardar-Parizi-Zhang universality class.

References

Oct 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·D Kim
Mar 3, 1986·Physical Review Letters·M KardarY C Zhang
Sep 30, 1991·Physical Review Letters·J Krug
Aug 11, 2001·Physical Review Letters·V B PriezzhevC K Hu
Apr 24, 2002·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·D S Lee, D Kim

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Citations

Mar 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A E DerbyshevV B Priezzhev

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