Perturbative calculation of one-point functions of one-dimensional single-species reaction-diffusion systems

Perturbations around autonomous one-dimensional single-species reaction-diffusion systems are investigated. It is shown that the parameter space corresponding to the autonomous systems is divided into two parts: In one part, the system is stable against the perturbations, in the sense that largest relaxation time of the one-point functions changes continuously with perturbations. In the other part, however, the system is unstable against perturbations, so that any small perturbation drastically modifies the large-time behavior of the one-point functions.