Rotating unstable Langevin-type dynamics: Linear and nonlinear mean passage time distributions

To characterize the decay process of linear rotating unstable Langevin-type dynamics in the presence of constant external force, through the mean passage time distribution, two theoretical descriptions are proposed: one is called the Quasideterministic (QD) approach described in the limit of long times, and the other approach is formulated for not so long times. Both theories are matrix based and formulated in two x and y dynamical representations, y being the transformed space of coordinates by means of a time-dependent rotation matrix. In the y dynamical representation the noise as well as the external force are rotational. The QD approach is studied when the dynamics is not influenced by the external force and when it is influenced by it. In the absence of this force, the theory is given for n variables and leads to the same results as those obtained in the characterization of nonrotating unstable systems; a fact that is better understood in the space of coordinates y. In the presence of the external force, the characterization is given for two variables and it is only valid for weak amplitude forces. For large amplitudes, the dynamics is almost dominated by the deterministic rotational evolution; then the QD approach is no longer valid and therefore the other approach is required. The theory in this case is general and verified for systems of two and three variables. In the case of two variables we study a laser system and use the experimental data of this system to compare with both theoretical and simulation results. In the case of three variables, the theory foresees application in other fields, for instance, in plasma physics. We also study the time characterization of the nonlinear rotating unstable systems and show in general that the nonlinear correction to the linear case is a quantity evaluated in the deterministic limit. The same laser system studied in the linear case is used as a prototype model.