We define a family of asymmetric processes for particles on a one-dimensional lattice, depending on a continuous parameter lambda is an element of [0,1], interpolating between the completely asymmetric processes (for lambda=1) and the n=1 drop-push models (for lambda=0). For arbitrary lambda, the model describes an exclusion process, in which a particle pushes its right neighboring particles to the right, with rates depending on the number of these particles. Using the Bethe ansatz, we obtain the exact solution of the master equation. [References: 14]
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