Energy transfer of a chaotic particle in a classical oscillating potential barrier

We study the classical dynamics of a particle inside a rigid box with an internal, arbitrarily located, square-potential barrier that oscillates periodically in time. We derive an area-preserving map that describes the dynamics of the particle, and show that it presents periodic, quasiperiodic and chaotic behavior, and generally mixed phase-space structure. We analyze the properties of the particle’s classical “dwell time” to traverse the oscillating potential barrier. We also discuss in some detail the orbits and the time dependence of the energy transfer.