A one-dimensional model on a line of length L is investigated, which involves particle diffusion as well as single particle annihilation. There are also creation and annihilation at the boundaries. The static and dynamical behaviors of the system are studied. It is seen that the system could exhibit a dynamical phase transition. For small drift velocities, the relaxation time does not depend on the absorption rates at the boundaries. This is the fast phase. For large velocities, the smaller of the absorption rates at boundaries enter the relaxation rate and makes it longer. This is the slow phase. Finally, the effect of a random particle creation in the bulk is also investigated.
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