Matricial formalism of transient dynamics: I. The presence of constant external forces

An alternative method in terms of a matricial formulation of quasideterministic (QD) approach and its connection with the nonlinear relaxation times (NLRT) has recently been proposed by (Jiménez-Aquino, 1997), to characterize the decay of unstable states of nonlinear systems, in the context of Gaussian white noise (GWN). The objective of this paper is to extend the method to the study of transient stochastic dynamics in the presence of a constant external force. In this matricial scheme, besides the influence of internal fluctuations and of the external force in the dynamical relaxation of the system, we also study the effect of fluctuations of initial conditions. The theory is explicitly applied to general systems of the two physical variables, and particularly to the study of a laser system in the presence of weak optical signals.