Weak external fluctuations on the rotating unstable Langevin-type dynamics

The matrix formalism of quasi-deterministic (QD) approach is developed to characterize, through the statistical properties of the passage time distributions, the rotating unstable Langevin-type dynamics under the influence of weak external fluctuations. The theory is developed for those two variable systems by assuming a phase diffusion model for the fluctuating external force. The proposal is applied to the same laser system studied by Dellunde et al. [Opt. Commun. 109 (1994) 435] and shows the conditions, in the appropriate dynamical representation, under which the rotational effects of the laser system are not exhibited in the theoretical description of this reference.