Solution of a class of one-dimensional reaction-diffusion models in disordered media

We study a one-dimensional class of reaction-diffusion models on a $10$-parameter manifold. The equations of motion of the correlation functions close on this manifold. We compute exactly the long-time behavior of the density and correlation functions for quenched-disordered systems. The quenched disorder consists of disconnected domains of reaction. We first consider the case where the disorder comprises a superposition, with different probabilistic weights of finite segments, with periodic boundary conditions. We then pass to the case of finite segments with open boundary conditions: we solve the ordered dynamics on a open lattice with the help of the dynamical matrix ansatz and investigate further its disordered version.