Nonlinear characterization of rotating transient stochastic dynamics

In this work we propose two theoretical schemes to characterize, through the mean passage time distribution, the nonlinear rotating transient stochastic dynamics: one is the quasi-deterministic approach valid for the long-time limit, and the other approach is valid for not so large times. The stochastic dynamics is represented by a rotating unstable Langevin-type dynamics in the presence of constant external force and is given in two x and y dynamical representations, such that y represents the transformed space of coordinates by means of a rotation matrix. The time characterization of the nonlinear system will be better described in the transformed space of coordinates y, because in this space the external force as well as the internal noise are rotational and the systematic force is derived from a potential. General and explicit results are obtained when we study those rotating systems of two variables. The theory is applied to detect weak and large optical signals in a rotating laser system as a prototype model.