State selection at points of instability

McKane, Alan; Short, Hiroko; Tarlie, Martin
February 2000
AIP Conference Proceedings;2000, Vol. 502 Issue 1, p278
Academic Journal
We consider the problem of state selection for a stochastic system, initially in an unstable stationary state, when multiple metastable states compete for occupation. The problem is formulated in terms of coupled Langevin equations with Gaussian white noise of strength D. We first discuss some simple approximation schemes which give an indication of the general features of the solution. The results of these methods are in qualitative, but not quantitative, agreement with computer simulations. We then reformulate the problem in terms of path-integrals and use an approximate scheme, which is valid for small D, to derive accurate formulas for state-selection probabilities. The method is illustrated on relatively simple systems, but it is sufficiently general that it is applicable to a wide variety of problems. © 2000 American Institute of Physics.


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