Ratchetlike pulse controlling the Fermi deceleration and hyperacceleration

Abstract

Using an ac driven asymmetric pulse we show how the Fermi acceleration (deceleration) can be controlled. A {\it deformed} sawtooth (Ratchetlike) pulse representing the moving wall in the static Fermi-Ulam model is considered. The time integral from the pulse over one period of oscillation must be negative to obtain deceleration and positive to obtain hyperacceleration. We show that while the decelerated case is chaotic, for the hyperaccelerated case the Lyapunov exponents converge to zero. Numerical simulations indicate that the hyperaccelerated case is ergodic in velocity space. Switching between different pulse deformations we are able to control the particle acceleration. Results should be valid for any pulse for which the time integral can be manipulated between positive and negative values.