Theory of resonantly activated rate processes

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Abstract
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 α. In the conditions of the aforementioned experiment this theory predicts the shift from the natural frequency to be 2α (with an agreement with experiment of ±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 α. Analytical predictions on the friction region where this transition takes place are made.