Abstract
From a previously suggested stochastic differential equation (S.D.E.), the fluctuations in amplitude, x, both in and out of the steady state are described for the absorptive bistability. The Stratonovic Fokker-Planck (F.P.) equation obtained is utilized to develop a theory of switching between locally stable states of amplitude x. This approach is a generalization of Kramers’ early work and the ideas of nucleation theory to the situation of non-constant diffusion, an interesting characteristic of the optical bistability. The importance of fluctuations (noise) is emphasized in switching. This result is compared to the approximation of Kramers and Landauer-Swanson. Also, comparisons are made to mean first passage estimates, and a recent work of Hanggi, Bulsara and Janda. The important question of the dominance of the low eigenvalue of the F.P. equation is investigated numerically by the development of a variational eigenvalue calculation for the bistability. The one eigenvalue approximation is found to hold for a wide range of y values and it is found that the variational treatment and the above theory agree well. Critical slowing is seen for c = 4, q = 0.01. The numerical algorithm may readily be applied to other one-dimensional bistable models.
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Englund, J.C., Schieve, W.C., Zurek, W., Gragg, R.F. (1981). Fluctuations and Transitions in the Absorptive Optical Bistability. In: Bowden, C.M., Ciftan, M., Robl, H.R. (eds) Optical Bistability. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-3941-0_19
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