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

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dc.creatorPovolotsky, A. M.
dc.creatorMendes, J. F. F.
dc.date2004-11-22
dc.date2006-03-30
dc.date.accessioned2026-07-07T06:37:22Z
dc.date.available2026-07-07T06:37:22Z
dc.descriptionWe 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 $q<0$.
dc.description43 pages, 3 figures, final version, published in Journal Stat. Phys. in Online First, avalable at http://dx.doi.org/10.1007/s10955-006-9023-0
dc.identifierhttps://arxiv.org/abs/cond-mat/0411558
dc.identifierhttp://arxiv.org/abs/cond-mat/0411558
dc.identifierJ. Stat. Phys. 123, 125-166 (2006)
dc.identifierdoi:10.1007/s10955-006-9023-0
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/100369
dc.subjectStatistical Mechanics
dc.titleBethe ansatz solution of discrete time stochastic processes with fully parallel update
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