Fermi acceleration in time-dependent rectangular billiards due to   multiple passages through resonances
  We consider a slowly rotating rectangular billiard with moving boundaries and use the canonical perturbation theory to describe the dynamics of a billiard particle. In the process of slow evolution certain resonance conditions can be satisfied. Correspondingly, phenomena of scattering on a resonance and capture into a resonance happen in the system. These phenomena lead to destruction of adiabatic invariance and to unlimited acceleration of the particle. 
A. P. Itin and A. I. Neishtadt
nlin.CD cond-mat.stat-mech