Fluctuations and Transitions in the Absorptive Optical Bistability

  • J. C. Englund
  • W. C. Schieve
  • W. Zurek
  • R. F. Gragg


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.


Stochastic Differential Equation Passage Time Nucleation Theory Time Dependent Phenomenon Time Dependent Transition 
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Copyright information

© Plenum Press, New York 1981

Authors and Affiliations

  • J. C. Englund
    • 1
  • W. C. Schieve
    • 1
  • W. Zurek
    • 1
  • R. F. Gragg
    • 1
  1. 1.Center for Studies in Statistical Mechanics and ThermodynamicsUniversity of Texas at AustinAustinUSA

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