Quantum versus Classical Dynamics in a driven barrier: the role of kinematic effects

TL;DR

This paper compares classical and quantum scattering of wave packets from an oscillating barrier, highlighting how kinematic effects influence transmission and the conditions under which classical mechanics approximates quantum results.

Contribution

It demonstrates that in certain frequency regimes, classical mechanics accurately predicts quantum transmission, and reveals the behavior of wave packets under different oscillation frequencies.

Findings

Classical mechanics approximates quantum results well at intermediate frequencies.

The transmission threshold exhibits a minimum at optimal classical-quantum agreement.

Wave packets split into coherent pulses at low frequencies, explained by classical kinematics.

Abstract

We study the dynamics of the classical and quantum mechanical scattering of a wave packet from an oscillating barrier. Our main focus is on the dependence of the transmission coefficient on the initial energy of the wave packet for a wide range of oscillation frequencies. The behavior of the quantum transmission coefficient is affected by tunneling phenomena, resonances and kinematic effects emanating from the time dependence of the potential. We show that when kinematic effects dominate (mainly in intermediate frequencies), classical mechanics provides very good approximation of quantum results. Moreover, in the frequency region of optimal agreement between classical and quantum transmission coefficient, the transmission threshold, i.e. the energy above which the transmission coefficient becomes larger than a specific small threshold value, is found to exhibit a minimum. We also consider the form of the transmitted wave packet and we find that for low values of the frequency the incoming classical and quantum wave packet can be split into a train of well separated coherent pulses, a phenomenon which can admit purely classical kinematic interpretation.