Time scales in rotating unstable Langevin-type dynamics

In this Rapid Communication we propose a different and general characterization of rotating, unstable Langevin-type dynamics in the presence of an external force in the context of two dynamical representations [formula presented] and [formula presented] using the passage time distribution. Here [formula presented] is the transformed space of coordinates obtained by means of a time-dependent rotation matrix. The Langevin dynamics in the new [formula presented] space defines an interesting concept of external force and internal noise due to rotation. The theory is applied to the characterization of rotational unstable systems of two (such as the laser system) and three variables, and stimulates its application in other fields, for instance, in plasma physics.