Abstract
The adiabatic elimination of fast variables from overdamped stochastic processes by functional integration is demonstrated. Adiabatic elimination entails the evaluation of a reduced evolution operator from the full evolution equation. For Fokker-Planck processes, the reduced evolution operator may be expressed as a ground-state expectation, and it is shown how this is represented as a coherent state path integral. The elimination is then achieved by functionally integrating out all reference to the fast variables. The end result is a decoupling of the full evolution equation into separate equations for the fast and slow variables. The method is demonstrated for Brownian motion, and for a system with multiplicative colored noise.
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