title: Hamiltonian analogs of combustion engines: A systematic exception to adiabatic decoupling.
abstract: Workhorse theories throughout all of physics derive effective Hamiltonians to describe slow time evolution, even though low-frequency modes are actually coupled to high-frequency modes. Such effective Hamiltonians are accurate because of adiabatic decoupling: the high-frequency modes "dress" the low-frequency modes, and renormalize their Hamiltonian, but they do not steadily inject energy into the low-frequency sector. Here, however, we identify a broad class of dynamical systems in which adiabatic decoupling fails to hold, and steady energy transfer across a large gap in natural frequency ("steady downconversion") instead becomes possible, through nonlinear resonances of a certain form. Instead of adiabatic decoupling, the special features of multiple time scale dynamics lead in these cases to efficiency constraints that somewhat resemble thermodynamics.
authors.affiliation: State Research Center OPTIMAS and Fachbereich Physik, Technische Univerität Kaiserslautern, D-67663 Kaiserslautern, Germany.
authors.forename: Lukas
authors.initials: L
authors.lastname: Gilz
authors.affiliation: State Research Center OPTIMAS and Fachbereich Physik, Technische Univerität Kaiserslautern, D-67663 Kaiserslautern, Germany.
authors.forename: Eike
authors.initials: E
authors.lastname: Thesing
authors.affiliation: State Research Center OPTIMAS and Fachbereich Physik, Technische Univerität Kaiserslautern, D-67663 Kaiserslautern, Germany.
authors.forename: James R
authors.initials: JR
authors.lastname: Anglin