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Effective theory of systems coupled strongly to rapidly varying external sources

We consider quantum systems that interact strongly with a rapidly varying environment and derive a Schr\"odinger-like equation that describes the time evolution of the average wave function. We show that the corresponding Hamiltonian can be taken to be Hermitian provided all states are rotated using an appropriate-unitary transformation. The formalism is applied to a variety of systems and is compared and contrasted with related results describing stochastic resonances.