Adiabatic Elimination by the Eigenfunction Expansion Method

The systematic adiabatic elimination method is formulated using the eigenfunction expansion method, in terms of the small parameter γ−1, which is the time scale for a fast variable. This method is applied to the linear processes with some examples of an optical system and a chemical reaction model. We also apply this method to the colored noise problems, to obtain the lowest correction of the effect of the memory.