caa a22 4500 467891729 CHVBK 20180406152751.0 cr unu---uuuuu 170328e20060401xx s 000 0 eng 10.1007/s10955-006-9023-0 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9023-0 Bethe Ansatz Solution of Discrete Time Stochastic Processes with Fully Parallel Update [Elektronische Daten] [A. Povolotsky, J. Mendes] 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 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→ 1 when q < 0. Springer Science + Business Media, Inc., 2006 Asymmetric exclusion process nationallicence Bethe ansatz nationallicence cellular automata nationallicence Povolotsky A. Physics Department, University of Aveiro, Campus de Santiago, 3810-193, Aveiro, Portugal aut Mendes J. Physics Department, University of Aveiro, Campus de Santiago, 3810-193, Aveiro, Portugal aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 123/1(2006-04-01), 125-166 0022-4715 123:1<125 2006 123 10955 https://doi.org/10.1007/s10955-006-9023-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9023-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Povolotsky A. Physics Department, University of Aveiro, Campus de Santiago, 3810-193, Aveiro, Portugal aut NATIONALLICENCE 700 1- Mendes J. Physics Department, University of Aveiro, Campus de Santiago, 3810-193, Aveiro, Portugal aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 123/1(2006-04-01), 125-166 0022-4715 123:1<125 2006 123 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer