On the weak-noise limit of Fokker-Planck models |
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Authors: | R Graham T Tél |
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Institution: | (1) Fachbereich Physik, Universität Essen, D-4300 Essen 1, West Germany |
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Abstract: | The weak-noise limit of Fokker-Planck models leads to a set of nonlinear Hamiltonian canonical equations. We show that the existence of a nonequilibrium potential in the weak-noise limit requires the existence of whiskered tori in the Hamiltonian system and, therefore, the complete integrability of the latter. A specific model is considered, where the Hamiltonian system in the weak-noise limit is not integrable. Two different perturbative solutions are constructed: the first solution describes analytically the breakdown of the whiskered tori due to the appearance of wild séparatrices; the second solution allows the analytic construction of an approximate nonequilibrium potential and an asymptotic expression for the probability density in the steady state.On leave from Institute for Theoretical Physics, Eötvös University, Budapest, Hungary. |
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Keywords: | Fokker-Planck processes dynamical systems nonequilibrium potentials weak-noise limit integrability of Hamiltonian systems whiskered tori |
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