Explicit construction of an autonomous Hamiltonian system exhibiting continual directed flow

We construct a prototypical example of a spatially-open autonomous Hamiltonian system in which localised, but otherwise unbiased, ensembles of initial conditions break spatio-temporal symmetries in the subsequent ensemble dynamics, despite time reversal symmetry of the equations of motion. Together with transient chaos, this provides the mechanism for the occurrence of a current. Transporting trajectories pass through transient chaos and subsequently cross surfaces of no-return, after which they perform solely regular motion so that the current is of continual ballistic nature.

► An autonomous Hamiltonian system of 2 integrable subsystems coupled locally.
► Trajectories escape potential wells, via transient chaos, to transporting motion.
► Localised initial conditions break symmetries, leading to a current.
► Surfaces of no return are constructed demonstrating that transport is continual.