Pseudo-classical theory for directed transport at quantum resonance

Recent studies have demonstrated that a directed current arises in kicked atom systems at quantum resonance (so-called 'resonance ratchets'). Here, we demonstrate that this effect can be explained using a pseudo-classical model by taking classical initial conditions analogous to the initial quantum state. A corollary of our result is that a current is also expected to arise in the actual standard classical limit of the kicked atoms, demonstrating that the phenomenon can arise even in the absence of quantum interference. We show that in the standard classical limit, the momentum current undergoes far less saturation due to quasi-momentum spread than for the quantum resonance case. Additionally, we demonstrate that a phase-independent analytical scaling law exists for the mean momentum as a function of a single combined parameter and show that it predicts an unexpected current inversion regime.