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

Useful dynamical processes often begin through barrier-crossing dynamical transitions; engineering system dynamics in order to make such transitions reliable 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.

Hamiltonian active particles in an environment.

We examine a Hamiltonian system which represents an active particle that can move against an opposing external force by drawing energy from an internal depot while immersed in a noisy and dissipative environment. The Hamiltonian consists of two subsystems, one representing the active particle's motion and the other its depot of "fuel." We show that although the active particle loses some of its energy to dissipation from the environment, dissipation can also help to stabilize the dynamical process that makes the particle active.