7 research outputs found
Exactly solvable models through the empty interval method
The most general one dimensional reaction-diffusion model with
nearest-neighbor interactions, which is exactly-solvable through the empty
interval method, has been introduced. Assuming translationally-invariant
initial conditions, the probability that consecutive sites are empty
(), has been exactly obtained. In the thermodynamic limit, the large-time
behavior of the system has also been investigated. Releasing the translational
invariance of the initial conditions, the evolution equation for the
probability that consecutive sites, starting from the site , are empty
() is obtained. In the thermodynamic limit, the large time behavior of
the system is also considered. Finally, the continuum limit of the model is
considered, and the empty-interval probability function is obtained.Comment: 12 pages, LaTeX2
Phase transition in an asymmetric generalization of the zero-temperature Glauber model
An asymmetric generalization of the zero-temperature Glauber model on a
lattice is introduced. The dynamics of the particle-density and specially the
large-time behavior of the system is studied. It is shown that the system
exhibits two kinds of phase transition, a static one and a dynamic one.Comment: LaTeX, 9 pages, to appear in Phys. Rev. E (2001
Multispecies reaction-diffusion systems
Multispecies reaction-diffusion systems, for which the time evolution
equation of correlation functions become a closed set, are considered. A formal
solution for the average densities is found. Some special interactions and the
exact time dependence of the average densities in these cases are also studied.
For the general case, the large time behaviour of the average densities has
also been obtained.Comment: LaTeX file, 15 pages, to appear in Phys. Rev.
Phase transition in an asymmetric generalization of the zero-temperature q-state Potts model
An asymmetric generalization of the zero-temperature q-state Potts model on a
one dimensional lattice, with and without boundaries, has been studied. The
dynamics of the particle number, and specially the large time behavior of the
system has been analyzed. In the thermodynamic limit, the system exhibits two
kinds of phase transitions, a static and a dynamic phase transition.Comment: 11 pages, LaTeX2
Autonomous multispecies reaction-diffusion systems with more-than-two-site interactions
Autonomous multispecies systems with more-than-two-neighbor interactions are
studied. Conditions necessary and sufficient for closedness of the evolution
equations of the -point functions are obtained. The average number of the
particles at each site for one species and three-site interactions, and its
generalization to the more-than-three-site interactions is explicitly obtained.
Generalizations of the Glauber model in different directions, using generalized
rates, generalized number of states at each site, and generalized number of
interacting sites, are also investigated.Comment: 9 pages, LaTeX2