The steady state of the boundary-driven multiparticle asymmetric diffusion model

We consider the multiparticle asymmetric diffusion model (MADM) introduced by Sasamoto and Wadati with integrability preserving reservoirs at the boundaries. In contrast to the open asymmetric simple exclusion process the number of particles allowed per site is unbounded in the MADM. Taking inspiration from the stationary measure in the symmetric case, i.e. the rational limit, we first obtain the length 1 solution and then show that the steady state can be expressed as an iterated product of Jackson q-integrals. In the proof of the stationarity condition, we observe a cancellation mechanism that closely resembles the one of the matrix product ansatz. To our knowledge, the occupation probabilities in the steady state of the boundary-driven MADM were not available before.