Controllability for chains of dynamical scatterers
Jean-Pierre Eckmann, Philippe Jacquet · Nonlinearity · 2007
In this paper, we consider a class of mechanical models which consists of a linear chain of identical chaotic cells, each of which has two small lateral holes and contains a freely rotating disc at its centre. Particles are injected at characteristic temperatures and rates from stochastic heat baths located at both ends of the chain. Once in the system, the particles move freely within the cells and will experience elastic collisions with the outer boundary of the cells as well as with the discs. They do not interact with each other but can transfer energy from one to another through collisions with the discs. The state of the system is defined by the positions and velocities of the particles and by the angular positions and angular velocities of the discs. We show that each model in this class is controllable with respect to the baths, i.e. we prove that the action of the baths can drive the system from any state to any other state in a finite time. As a consequence, one obtains the existence of, at most, one regular invariant measure characterizing its states (out of equilibrium).