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Register a new userMatrix product solution of the stationary states of two-species open zero range processes
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Using the matrix product ansatz, we obtain solutions of the steady-state distribution of the two-species open one-dimensional zero range process. Our solution is based on a conventionally employed constraint on the hop rates, which eventually allows us to simplify the constituent matrices of the ansatz. It is shown that the matrix at each site is given by the tensor product of two sets of matrices and the steady-state distribution assumes an inhomogeneous factorized form. Our method can be generalized to the cases of more than two species of particles.
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We present an explicit representation for the matrix product ansatz for some two-species TASEP with open boundary conditions. The construction relies on the integrability of the models, a property that constrains the possible rates at the boundaries. The realisation is built on a tensor product of copies of the DEHP algebras. Using this explicit construction, we are able to calculate the partition function of the models. The densities and currents in the stationary state are also computed. It leads to the phase diagram of the models. Depending on the values of the boundary rates, we obtain for each species shock waves, maximal current, or low/high densities phases.
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