The decay process of rotating unstable systems through the passage time distribution

In this work we propose a general scheme to characterize, through the passage time distribution, the decay process of rotational unstable systems in the presence of external forces of large amplitude. The formalism starts with a matricial Langevin type equation formulated in the context of two dynamical representations given, respectively, by the vectors x and y, both related by a time dependent rotation matrix. The transformation preserves the norm of the vector and decouples the set of dynamical equations in the transformed space y. We study the dynamical characterization of the systems of two variables and show that the statistical properties of the passage time distribution are essentially equivalent in both dynamics. The theory is applied to the laser system studied in Dellunde et al. (Opt. Commun. 102 (1993) 277), where the effect of large injected signals on the transient dynamics of the laser has been studied in terms of complex electric field. The analytical results are compared with numerical simulation.