Competition between suppression and production of Fermi acceleration

The behavior of the average velocity for a classical particle in the one-dimensional Fermi accelerator model under sawtooth external force is considered. For elastic collisions, it is known that the average velocity of the particle grows unlimitedly because of the discontinuities of the derivative of the moving wall's position with respect to time. However, and contrary to what was expected to be observed, the introduction of a friction force generated from a slip of a body against a rough surface leads to a boundary separating different regions of the phase space that yields the particle to either experience unlimited energy growth or suppression of Fermi acceleration. The Fermi acceleration is described by using scaling arguments. The formalism presented can be extended to two-dimensional time-dependent billiards as well as to higher-order mappings.