Analytical study of an asymmetric 1D statistical model for chemical reactions

An analytical study is presented for the asymmetric FGZ reaction model, involving two different species A and B (only B can spontaneously desorb) in contact with a bath containing A and B with the same concentration. The expected values of the density and the pair correlation functions are calculated and their time behaviour is analysed in detail. This also allows to define an average time-dependent fragmentation index describing quantitatively the evolution of the topology (connectivity) of the clusters. In addition, when the system is doomed to end its evolution in the A-poisoned state, the distribution law P(T) of the times Tk at which this occurs is investigated numerically. It turns out that, in the case where a single isolated B is present in the initial state, this law is well enough represented by a stretched exponential in the log variable: P(T) = Cste exp[− α(1n T)ß].