Three-state model and chemical reactions

A three-state model is formulated in terms of raising and lowering operators. As an application, cyclic chemical reactions with three different species in the solid state are studied. The evolution equations for the densities and for the correlation functions can be derived starting from a master equation in a generalized Fock space representation on a lattice. Such a description guarantees the consideration of the excluded volume effect. In contrast to the classical kinetic behaviour, the system offers stable and unstable regimes depending on the averaged composition ratio.