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


  • 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 in the small-noise high-barrier limit is shown to follow rrr, where Tp=, 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. 1984 The American Physical Society.

published proceedings

  • Physical Review A

author list (cited authors)

  • Shenoy, S. R., & Agarwal, G. S.

citation count

  • 45

complete list of authors

  • Shenoy, Subodh R||Agarwal, GS

publication date

  • March 1984