FIRST-ORDER CORRECTION TO THE UNIFIED COLORED-NOISE APPROXIMATION ANDDYE-LASER TRANSIENTS

We develop a first-order theory of the unified colored-noise approxima tion. It can be applied to general multidimensional systems driven by colored noise (the Ornstein-Uhlenbeck noise). A general formula for th e first-order correction is derived, which is used for investigating t he transient process of a dye laser. For the colored cubic model and c olored gain-noise model of a dye laser, the Fokker-Planck equations ar e derived based on the general formula of first-order theory. The firs t-order corrections of the mean first-passage times for the models are obtained. We compare the results with numerical simulations, and show that the present results have greatly improved the results obtained b y the original unified colored-noise approximation.