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Solution of a One-Dimensional Reaction-Diffusion Model with Spatial Asymmetry

We study classical particles on the sites of an open chain which diffuse, coagulate and decoagulate preferentially in one direction. The master equation is expressed in terms of a spin one-half Hamiltonian $H$ and the model is shown to be completely solvable if all processes have the same asymmetry. The relaxational spectrum is obtained directly from $H$ and via the equations of motion for strings of empty sites. The structure and the solvability of these equations are investigated in the general case. Two phases are shown to exist for small and large asymmetry, respectively, which differ in their stationary properties.