Finite correlation time effects in nonequilibrium phase transitions: I. Dynamic equation and steady state properties

We determine an approximate renormalized equation of evolution for an arbitrary nonlinear single-degree-of-freedom system externally driven by Gaussian parametric fluctuations of finite correlation time. The renormalization scheme used here gives a second order equation with a time-and-state-dependent “diffusion coefficient”. We are able to calculate the diffusion coefficient in closed form. The steady-state distribution can easily be obtained from the evolution equation. We are thus able to determine the parameter dependence of the steady-state distribution and, in particular, the influence of a correlation time of the fluctuations, which does not vanish, on the steady-state distribution.