Resonant Activation Phenomenon Research Articles

Properties of resonant activation phenomena

The phenomenon of resonant activation of a Brownian particle over a fluctuating barrier is revisited. We discuss the important distinctions between barriers that can fluctuate among "up" and "down" configurations, and barriers that are always "up" but that can fluctuate among different heights. A resonance as a function of the barrier fluctuation rate is found in both cases, but the nature and physical description of these resonances is quite distinct. The nature of the resonances, the physical basis for the resonant behavior, and the importance of boundary conditions are discussed in some detail. We obtain analytic expressions for the escape time over the barrier that explicitly capture the minima as a function of the barrier fluctuation rate, and show that our analytic results are in excellent agreement with numerical results.

Non-Markov noise in barrier-fluctuation model

We investigate the thermally activated escape of a particle over a potential barrier whose height fluctuates between two values. The barrier-switching process is constructed as a semi-Markov alternating process: the times at which a change of the barrier state can occcur form a general renewal process and the probability of leaving a state depends on the time the barrier resides in the state before the jump. During the interjump interval, the barrier is fixed in one of the two states and the crossing dynamics is described by a general (not necessarily exponential) decay law. We give the general formulae describing the averaged escape dynamics, where the averaging runs over all possible histories of the switching process. Using the above device of the selective residence times, the recently discussed phenomenon of resonant activation (a minimal averaged lifetime of the particle in the potential well) emerges also within the framework of the conventional exponential escape dynamics.

Characterizing the dynamics of stochastic bistable systems by measures of complexity

The dynamics of noisy bistable systems is analyzed by means of Lyapunov exponents and measures of complexity. We consider both the classical Kramers problem with additive white noise and the case when the barrier fluctuates due to additional external colored noise. In the case of additive noise we calculate the Lyapunov exponents and all measures of complexity analytically as functions of the noise intensity or the mean escape time, respectively. For the problem of a fluctuating barrier the usual description of the dynamics with the mean escape time is not sufficient. The application of the concept of measures of complexity allows us to describe the structures of motion in more detail. Most complexity measures indicate the value of the correlation time at which the phenomenon of resonant activation occurs with an extremum.

Resonant activation in a bistable system.

The analog simulation of an overdamped Brownian particle in a quartic double-well potential driven by an external (either Gaussian or dichotomic) multiplicative noise is performed with special focus on the phenomenon of resonant activation. Such an effect is shown to occur on increasing the correlation time of the multiplicative noise, while keeping the noise variance constant. The asymptotic behavior of the relevant escape times for large noise correlation time and large variance is also investigated. Simple qualitative arguments are produced to justify the results thus obtained. Furthermore, the traversal barrier, that is the effective barrier at the time the system switches state, is shown to have a minimum for a certain value of the noise correlation time, though not always in coincidence with the relevant resonant activation value. \textcopyright{} 1996 The American Physical Society.

Thermally activated escape controlled by colored multiplicative noise

Thermally driven escape over a barrier which fluctuates with Gaussian statistics is studied by means of analog simulation. The phenomenon of resonant activation [C.R. Doering and J.C. Gadoua, Phys. Rev. Lett. 69 (1992) 2318] occurs when the correlation-time of the barrier fluctuations is increased without changing the amplitude. The dependence of the relevant escape time on the fluctuation variance exhibits a number of properties, independent of the potential shape, which eluded previous investigations.

Theory of resonantly activated rate processes.

The very recent experimental results on the new phenomenon of resonant activation in current-biased Josephson junctions [M. H. Devoret, J. M. Martinis, D. Esteve, and J. Clarke, Phys. Rev. Lett. 53, 1260 (1984)] are completely accounted for via a theoretical approach which settles the problem of determining the rate of escape of a highly inertial Brownian particle from a potential well in the presence of a radiation field. To get this very satisfactory agreement with experiment a theory was developed, the main features of which are as follows. (1) The subtle problem of elimination of irrelevant variables is dealt with by devoting special attention to the case where the time scale of the system of interest is not well separated from that of the irrelevant variables. (2) A perturbation approach is used which, in the absence of stochastic force, is proved to coincide with the well-known method of multiple time scales. (3) It is assumed that the process of excitation-relaxation within the well is much faster than the process of escape from the well itself. The theory of this paper predicts analytically the frequency position for the maximum escape rate in terms of a suitable renormalized anharmonicity parameter \ensuremath{\alpha}. In the conditions of the aforementioned experiment this theory predicts the shift from the natural frequency to be 2\ensuremath{\alpha} (with an agreement with experiment of \ifmmode\pm\else\textpm\fi{}1%). Furthermore, theory predicts that if the friction is lowered, a new phenomenon takes place: the shift of the maximum from the natural frequency is reduced to \ensuremath{\alpha}. Analytical predictions on the friction region where this transition takes place are made.