Exact solution of an integrable non-equilibrium particle system

We consider the integrable family of symmetric boundary-driven interacting particle systems that arise from non-compact XXX Heisenberg model in one dimension with open boundaries. In contrast to well-known exclusion process, number particles at each site is unbounded. show a finite chain $N$ sites connected its ends two reservoirs can be solved exactly, i.e. factorial moments non-equilibrium steady-state written closed form for $N$. The solution relies on probabilistic arguments and techniques inspired by systems. It obtained steps: i) introduction dual absorbing process reducing problem particles; ii) dynamics exploiting symmetry Quantum Inverse Scattering Method. Long-range correlations are computed finite-volume system. exact allows prove direct computation that, thermodynamic limit, system approaches local equilibrium. A by-product algebraic construction mapping between steady state equilibrium reversible measure.