Workhorse theories throughout all of physics derive effective Hamiltonians todescribe slow time evolution, even though low-frequency modes are actuallycoupled to high-frequency modes. Such effective Hamiltonians are accuratebecause of \textit{adiabatic decoupling}: the high-frequency modes `dress' thelow-frequency modes, and renormalize their Hamiltonian, but they do notsteadily inject energy into the low-frequency sector. Here, however, weidentify a broad class of dynamical systems in which adiabatic decoupling failsto hold, and steady energy transfer across a large gap in natural frequency(`steady downconversion') instead becomes possible, through nonlinearresonances of a certain form. Instead of adiabatic decoupling, the specialfeatures of multiple time scale dynamics lead in these cases to efficiencyconstraints that somewhat resemble thermodynamics.
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