Resonant activation: Potential vs. temperature fluctuations

Abstract

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.

Escape process and stochastic resonance under noise intensity fluctuation

“…This correspondence can qualitatively explain the occurrence of the RA phenomenon in the present model. RA induced by a noise intensity fluctuation has been reported previously [33]; it was realized by the random telegraph process. As expected, the ρ = 0.01 case shows a very small RA effect because the noise intensity fluctuation is very weak in this case.…”

Thermally activated escape far from equilibrium: A unified path-integral approach

“…8a) these are reactions proceeding in twosteps via an intermediate (metastable state x s 2 ). Temperature pulses could be generated, among others [32][33][34][35]29,[36][37][38][39], by means of a flashing black body radiator. More realistic are short laser pulses [71,72], whose basic effects (on the reacting molecules and their environment) may still be roughly modeled by a temperature pulse.…”

“…In the present work we have investigated the thermally activated escape of a one-dimensional overdamped Brownian particle over a potential barrier for weak noise and rather general timedependences of the potential, the temperature [32][33][34][35]29,[36][37][38][39], and the dissipation coefficient [39,40], including periodic, nonperiodic and time-independent set ups as special cases. The time-dependent escape rate readily follows from the propagator from the stable to the unstable deterministic orbit, thus naturally suggesting to employ path-integral methods.…”

“…As a particularly interesting specific application of the general formalism, we finally consider the case of a static potential and a time-dependent temperature [32][33][34][35]29,[36][37][38][39]. Adapting our approach to the case of a potential with two metastable potential wells, we demonstrate that for suitably chosen, but still fairly simple and generic such potential landscapes, the net escape rate may be substantially reduced by temporally increasing the temperature above its unperturbed, constant level.…”

“…In the last decades, elaborate experimental techniques have made it possible to observe systems at the nano-scale -where thermal noise is particularly important -and at the same time perturb them in a controlled way from outside -either directly, resulting in time-dependent forces (or potentials), or indirectly (via the thermal environment) giving rise to time-dependent temperatures [32][33][34][35]29,[36][37][38][39], dissipation coefficients [39,40], or multiple noise processes [41]. In either case, this leads to new interesting far from equilibrium conditions and effects.…”