Particle Motion in Rapidly Oscillating Potentials: The Role of the Potential's Initial Phase

TL;DR

This paper reveals that the initial phase of rapidly oscillating potentials critically influences particle motion and trapping, challenging the traditional view that it is irrelevant at high frequencies, supported by theory and numerical simulations.

Contribution

It demonstrates that the initial phase affects particle dynamics in high-frequency oscillating potentials, introducing a phase-dependent transformation of initial conditions and proposing experimental verification.

Findings

Particle motion depends on initial phase at high frequencies.

The effective potential approach requires phase-dependent initial condition transformation.

Numerical simulations confirm the phase influence on trapping and dynamics.

Abstract

Rapidly oscillating potentials with a vanishing time average have been used for a long time to trap charged particles in source-free regions. It has been argued that the motion of a particle in such a potential can be approximately described by a time independent effective potential, which does not depend upon the initial phase of the oscillating potential. However, here we show that the motion of a particle and its trapping condition significantly depend upon this initial phase for arbitrarily high frequencies of the potential's oscillation. We explain this novel phenomenon by showing that the motion of a particle is determined by the effective potential stated in the literature only if its initial conditions are transformed according to a transformation which we show to significantly depend on the potential's initial phase for arbitrarily high frequencies. We confirm our theoretical findings by numerical simulations. Further, we demonstrate that the found phenomenon offers new ways to manipulate the dynamics of particles which are trapped by rapidly oscillating potentials. Finally, we propose a simple experiment to verify the theoretical findings of this work.