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arXiv · 2207.02768

Open system control of dynamical transitions under the generalized Kruskal-Neishtadt-Henrard theorem

Diego M. Fieguth·James R. Anglin
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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.

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Diego M. Fieguth, James R. Anglin. 2022-07-06. Open system control of dynamical transitions under the generalized Kruskal-Neishtadt-Henrard theorem. https://doi.org/10.1103/physreve.107.034209

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