Adsorption of reactive particles on a random catalytic chain: an exact solution

We study equilibrium properties of a catalytically activated annihilation A+A-->0 reaction taking place on a one-dimensional chain of length N (N--> infinity ) in which some segments (placed at random, with mean concentration p) possess special, catalytic properties. Annihilation reaction takes place as soon as any two A particles land onto two vacant sites at the extremities of the catalytic segment, or when any A particle lands onto a vacant site on a catalytic segment while the site at the other extremity of this segment is already occupied by another A particle. Noncatalytic segments are inert with respect to reaction and here two adsorbed A particles harmlessly coexist. For both "annealed" and "quenched" disorder in placement of the catalytic segments, we calculate exactly the disorder-averaged pressure per site. Explicit asymptotic formulas for the particle mean density and the compressibility are also presented.