Dodin and Fisch show how a classical charged particle assumes quantum mechanical properties when driven by a rapidly oscillating external field.

Abstract. The average dynamics of a classical particle under the action of a high-frequency radiation resembles quantum particle motion in a conservative field with an effective de Broglie wavelength λ equal to the particle average displacement on the oscillation period. In a quasiclassical field, with a spatial scale large compared to λ, the guiding-center motion is adiabatic. Otherwise, a particle exhibits quantized eigenstates in ponderomotive potential wells, tunnels through “classically forbidden” regions, and experiences stochastic reflection from attractive potentials.