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We consider a process in which there are two types of particles, A
and B, on an infinite one-dimensional lattice. The particles hop
to their adjacent sites, like the totally asymmetric exclusion
process (ASEP), and have also the following interactions:
$A+B-->B+B and B+A-->B+B$, which all occur with equal rate. We
study this process by imposing four boundary conditions on the
ASEP master equation. It is shown that this model is integrable,
in the sense that its N-particle S matrix is factorized into a
product of two-particle S matrices and, more importantly, the
two-particle S matrix satisfies the quantum Yang-Baxter equation.
Using the coordinate Bethe-ansatz, the N-particle wave functions
and the two-particle conditional probabilities are found exactly.
Further, by imposing four reasonable physical conditions on
two-species diffusion-reaction processes (where the most important
ones are the equality of the reaction rates and the conservation
of the number of particles in each reaction), we show that among
the 4096 types of interactions which have these properties and can
be modeled by a master equation and an appropriate set of boundary
conditions, there are only 28 independent interactions which are
integrable. We find all these interactions and also their
corresponding wave functions. Some of these may be new solutions
of the quantum Yang-Baxter equation.
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