Phase Transition and Shock in a One-Dimensional Reaction-Diffusion Model
There is a one-dimensional model in which particles undergo many different reactions such as diffusion, coagulation and decoagulation. One boundary of chain is open to particles’ entry and exit. The aim is inspecting different phases in parameters space of model, probing phase transition point, and calculating quantities like density distribution function in each phase, particles’ flow and particles’ correlation functions in each site of lattice. To solve these kind of problems, different approaches such as mean field approximation, bethe's Ansatz, vacant sites formalism and computer simulation have extended but here matrix product Ansatz way was used to solve the model. Results have revealed high density and low density phases for model for particles' density of course with a constraint on parameters. A traveling shock is seen that moves in the body of lattice before attaching to steady state, too.