CO2 laser with swept pump parameter: The nonlinear regime

Moment evolution and level-crossing statistics in dichotomous and multilevel flows with time-dependent control parameters

We study the dynamics of the first two moments and of threshold crossings by the stochastic trajectory in dichotomous diffusion x=xi(t), where xi(t) is a dichotomous Markov process. The transition rate of the latter is regarded as a control parameter and allowed to have specified time variations. The stabilizing or destabilizing effect of this variation is demonstrated, and qualitative changes in the statistical properties of the system are shown to occur. The analysis is then extended to linear dichotomous flow, and to a generalization of dichotomous diffusion in which x is driven by a multilevel Markov noise.

Passage through a barrier with a slowly increasing control parameter

A bistable system subjected to noise and a slow increase of the parameter controlling the instability is studied, with emphasis on the kinetics of the transitions across the barrier separating the stable states. It is shown that the presence of a ramp in the control parameter may considerably affect the distribution of probability mass on the two sides of the barrier as compared to the predictions of the classical Kramers theory.