Ratchetlike pulse controlling the Fermi deceleration and hyperacceleration

TL;DR

This paper demonstrates how asymmetric, ratchetlike pulses can control Fermi acceleration and deceleration, showing that pulse shape manipulation influences particle dynamics, including chaos and ergodicity, in the Fermi-Ulam model.

Contribution

It introduces a method to control particle acceleration using deformed sawtooth pulses, linking pulse integral sign to acceleration regimes, and analyzes the resulting chaotic and ergodic behaviors.

Findings

Deceleration is chaotic, hyperacceleration is ergodic.

Pulse integral sign determines acceleration direction.

Control of acceleration achieved by switching pulse deformation.

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.