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

In this work we propose a general scheme to characterize, through the passa ge time distribution, the decay process of rotational unstable systems in t he presence of external forces of large amplitude. The formalism starts wit h a matricial Langevin type equation formulated in the context of two dynam ical representations given, respectively, by the vectors x and y, both rela ted by a time dependent rotation matrix. The transformation preserves the n orm of the vector and decouples the set of dynamical equations in the trans formed space y. We study the dynamical characterization of the systems of t wo variables and show that the statistical properties of the passage time d istribution are essentially equivalent in both dynamics. The theory is appl ied 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 anal ytical results are compared with numerical simulation. (C) 2001 Elsevier Sc ience B.V. All rights reserved.