Dynamical phase transition in the two-point functions of the autonomous one-dimensional single-species reaction-diffusion systems

The evolution of the two-point functions of autonomous one-dimensional single-species reaction-diffusion systems with nearest-neighbor interaction and translationally-invariant initial conditions is investigated. It is shown that the dynamical phase structure of such systems consists of five phases. As an example, a one-parameter family is introduced which can be in each of these phases.Comment: 12 pages, 1 figure, LaTeX2

Phase transition in annihilation-limited processes

A system of particles is studied in which the stochastic processes are one-particle type-change (or one-particle diffusion) and multi-particle annihilation. It is shown that, if the annihilation rate tends to zero but the initial values of the average number of the particles tends to infinity, so that the annihilation rate times a certain power of the initial values of the average number of the particles remain constant (the double scaling) then if the initial state of the system is a multi-Poisson distribution, the system always remains in a state of multi-Poisson distribution, but with evolving parameters. The large time behavior of the system is also investigated. The system exhibits a dynamical phase transition. It is seen that for a k-particle annihilation, if k is larger than a critical value k_c, which is determined by the type-change rates, then annihilation does not enter the relaxation exponent of the system; while for k < k_c, it is the annihilation (in fact k itself) which determines the relaxation exponent.Comment: 10 page