First-passage times and hysteresis in multivariable stochastic processes: The two-mode ring laser

Subodh R. Shenoy and G. S. Agarwal
Phys. Rev. A 29, 1315 – Published 1 March 1984
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Abstract

The decay of metastable states of a system obeying an n-variable Fokker-Planck equation is considered by evaluating the mean first-passage time Tp using the asymptotic method of Schuss and Matkowsky. The statistics of the first-passage time τ in the small-noise high-barrier limit is shown to follow τrr!τr, where Tp=τ, independent of the number of degrees of freedom, n. The time Tp in the low-barrier, high-noise limit is also calculated. The hysteresis window for the control-parameter sweep rate is generalized to multivariate systems. These general results are applied to a model of a two-mode laser, where n=4. A comparison with recent results of Mandel and co-workers is made, and experimental tests of the predictions are suggested.

  • Received 8 June 1983

DOI:https://doi.org/10.1103/PhysRevA.29.1315

©1984 American Physical Society

Authors & Affiliations

Subodh R. Shenoy and G. S. Agarwal

  • School of Physics, University of Hyderabad, Hyderabad 500134, Andhra Pradesh, India

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Issue

Vol. 29, Iss. 3 — March 1984

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