# Hamiltonian analogs of combustion engines: a systematic exception to adiabatic decoupling

## TL;DR

This paper identifies a class of dynamical systems where the usual adiabatic decoupling fails, allowing steady energy transfer across frequency gaps, resembling thermodynamic efficiency constraints.

## Contribution

It introduces a systematic class of Hamiltonian systems that violate adiabatic decoupling, enabling steady downconversion through nonlinear resonances.

## Key findings

- Adiabatic decoupling can fail in certain Hamiltonian systems.
- Steady energy transfer across frequency gaps is possible.
- Efficiency constraints resemble thermodynamic principles.

## 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 \textit{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.