Fermi acceleration in time-dependent billiards
Dimitry Turaev, Lecturer, Imperial College London
We discuss the evolution of energy in billiards with slowly moving boundaries, based on the Anosov-Kasuga theory of adiabatic invariants. We propose a stochastic description for the energy change, and demonstrate that the ergodicity of the billiard impedes the energy transfer from the moving boundary to the particle inside the billiard. We describe recent examples of time-dependent billiards for which a controlled violation of ergodicity leads to an exponential energy growth, i.e. to the effective energy transfer which is much more effective than in the ergodic case. We argue that the effect is of a fairly general nature: the periodic violation of ergodicity must be the key mechanism behind the energy flow from slow to fast degrees of freedom in slow-fast Hamiltonian systems with chaotic behaviour in the fast variables. This is a joint work with V. Gelfreich, T. Pereira and V. Rom-Kedar.