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Electronic analog experiments on escape over a fluctuating potential barrier are performed for the case when the fluctuations are caused by Ornstein-Uhlenbeck noise (OUN). In its dependence on the relation between the two OUN parameters (the correlation time tau and noise strength Q) the nonmonotonic variation of the mean escape time T as a function of tau can exhibit either a minimum (resonant activation), or a maximum (inhibition of activation), or both these effects. The possible resonant nature of these features is discussed. We claim that T is not a good quantity to describe the resonancelike character of the problem. Independently of the specific relation between the OUN parameters, the resonance manifests itself as a maximal lowering of the potential barrier during the escape event, and it appears for tau of the order of the relaxation time toward the metastable state.

The phenomenon of stochastic resonance is predicted in a monostable system displaying transient bimodality during the evolution. The signal-to-noise ratio as a function of the noise intensity calculated within the rate equation theory with many simplifying assumptions exhibits a promising peak. The numerical simulations are also reported.

The behaviour of a quantum kicked top subject to a dissipation mechanism is considered. Following Gisin and Percival (1992 J. Phys. A: Math. Gen. 25 5677) the dissipation is described by means of a diffusion process acting on the vector state; thus the dynamics is given by the stochastic Schrodinger equation. This approach allows one to treat numerically much larger quantum systems than with the use of a density operator. The calculations presented demonstrate an essential similarity between the classical and quantum counterparts of the top, the better the similarity the greater the quantum size of the problem. This concerns both the regular and chaotic behaviour of the top.

The problem of an escape over a fluctuating potential barrier is considered. The results of the analogue electronic experiment confirm the predictions about the dependence of the occurrence of the phenomena of resonant activation and inhibition of activation on the relation between the barrier noise parameters. We propose a new interpretation of the noise-induced resonance in this problem. A simple theoretical description valid for any correlation time is given.

We analyse a relaxation process from an unstable state during which transient multimodality occurs. This phenomenon is investigated experimentally on an electronic analogue circuit which mimics an overdamped bistable oscillator described by a sixth--order polynomial U(x) and is driven by a Gaussian white noise. The measured times and positions at which new maxima appear in the probability distribution function agree well with the theoretical predictions. It is shown that the shape of the potential guarantees the existence of two different time scales, allowing for the coexistence of three probability distribution peaks during a sizeable interval of time, even though there is no long "flat" region in the potential where U'(x) is very small. Finally, the concept of marginality with reference to unsteady states is discussed.

The thermal activation over a potential barrier in a stochastically modified system is analyzed. If colored noise perturbs the potential one can observe the famous resonant activation phenomenon. We compare this effect with the results caused by correlated fluctuations of the temperature. For high potential barrier stochastic variations of temperature lead to resonant activation as well. However, for low-barrier or barrierless evolution this effect disappears. We formulate an analytical condition separating these cases and present a physical interpretation of both types of behavior.

Starting from a Langevin equation with stationary gaussian noise of arbitrary correlation time, a corresponding Fokker-Planck equation is derived under the condition of small noise strength.