Fermi acceleration and suppression of Fermi acceleration in a time-dependent Lorentz Gas

TL;DR

This paper investigates the dynamical behavior of a Lorentz gas with static and time-dependent boundaries, demonstrating how dissipation suppresses unlimited energy growth and analyzing velocity behavior through a nonlinear map.

Contribution

It introduces a four-dimensional nonlinear map to model the time-dependent Lorentz gas and analyzes the effects of dissipation on energy growth suppression.

Findings

Unlimited energy growth occurs in the non-dissipative case.

Dissipation suppresses the unlimited energy growth.

Velocity behavior analyzed using a scaling approach.

Abstract

We study some dynamical properties of a Lorentz gas. We have considered both the static and time dependent boundary. For the static case we have shown that the system has a chaotic component characterized with a positive Lyapunov Exponent. For the time-dependent perturbation we describe the model using a four-dimensional nonlinear map. The behaviour of the average velocity is considered in two situations (i) non-dissipative and (ii) dissipative. Our results show that the unlimited energy growth is observed for the non-dissipative case. However, when dissipation, via damping coefficients, is introduced the senary changes and the unlimited engergy growth is suppressed. The behaviour of the average velocity is described using scaling approach.