Stochastic chaos in a class or Fokker-Planck equations

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Abstract
We show that a large class of Fokker-Planck equations, like the Schrödinger equation, can exhibit a transition in their spectral statistics as a coupling parameter is varied. We assert that this transition is connected to the transition to nonintegrability in a particular set of Hamilton’s equations. In the case of the Schrödinger equation, this transition is known to be a fingerprint of the underlying classical dynamics. However, the Hamilton’s equations describing the transition in the Fokker-Planck spectrum have no direct physical relation to the underlying dynamics of the Fokker-Planck equation, and consequently have no such simple physical interpretation.

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