The Abraham-Lorentz force and the time evolution of a chaotic system: The case of charged classical and quantum Duffing oscillators.

Abstract

This paper proves that the Abraham-Lorentz (AL) force can noticeably modify the trajectories of the charged Duffing oscillators over time. The influence of the reaction force on the oscillator evolution is strongly enhanced if the system is considered at the level of quantum mechanics. For example, the AL force examined within the scope of Newtonian description can change the trajectory of the Duffing oscillator only if it has the mass of an electron. However, we showed that when quantum corrections along with the nondeterministic contributions are taken into account, the reaction force of the electromagnetic field affects noticeably even the oscillator with a mass equal to the mass of the Pb ion. The charged Duffing oscillators belong to the class of systems characterized by the chaotic nondeterministic dynamics. In classical terms, the nondeterministic behavior of the discussed systems results from the breaking of the causality principle by the AL force.