A family of one-dimensional multi-species reaction-diffusion processes on a lattice is introduced. It is shown that these processes are exactly solvable, provided a nonspectral matrix equation is satisfied. Some general remarks on the solutions to this equation, and some special solutions are given. The large-time behavior of the conditional probabilities of such systems are also investigated.
We consider a two-parameter family of asymmetric exclusion processes for particles living on a continuous one-dimensional space. Using the Bethe ansatz, the exact solution to the master equation, and from that the drift and the diffusion rate in the two particle sector, are obtained.
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