Open system control of dynamical transitions under the generalized Kruskal-Neishtadt-Henrard theorem
Classical Physics
2023-03-29 v1
Abstract
Useful dynamical processes often begin through barrier-crossing dynamical transitions; engineering system dynamics in order to make such transitions reliably is therefore an important task for biological or artificial microscopic machinery. Here we first show by example that adding even a small amount of back-reaction to a control parameter, so that it responds to the system's evolution, can significantly increase the fraction of trajectories that cross a separatrix. We then explain how a post-adiabatic theorem due to Neishtadt can quantitatively describe this kind of enhancement without having to solve the equations of motion, allowing systematic understanding and design of a class of self-controlling dynamical systems.
Keywords
Cite
@article{arxiv.2207.02768,
title = {Open system control of dynamical transitions under the generalized Kruskal-Neishtadt-Henrard theorem},
author = {Diego M. Fieguth and James R. Anglin},
journal= {arXiv preprint arXiv:2207.02768},
year = {2023}
}