Quantum Resonances and Ratchets in Free-Falling Frames

TL;DR

This paper explores quantum resonances and ratchet effects in a free-falling frame, deriving conditions for resonance, analyzing wave-packet evolution, and showing how gravity and initial conditions influence ratchet behavior.

Contribution

It introduces general quantum resonance conditions in free-falling frames and analyzes how gravity and initial states affect quantum ratchet phenomena.

Findings

Quantum resonance conditions require rational parameters.

Quantum ratchets emerge under resonant conditions for certain initial states.

Gravity modifies the effective kicking potential influencing ratchet behavior.

Abstract

Quantum resonance (QR) is defined in the free-falling frame of the quantum kicked particle subjected to gravity. The general QR conditions are derived. They imply the rationality of the gravity parameter $\eta$, the kicking-period parameter $\tau /(2\pi)$, and the quasimomentum $\beta$. Exact results are obtained concerning wave-packet evolution for arbitrary periodic kicking potentials in the case of integer $\tau /(2\pi)$ (the main QRs). It is shown that a quantum ratchet generally arises in this case for resonant $\beta$. The noninertial nature of the free-falling frame affects the ratchet by effectively changing the kicking potential to one depending on $(\beta ,\eta)$. For a simple class of initial wave packets, it is explicitly shown that the ratchet characteristics are determined to a large extent by symmetry properties and by number-theoretical features of $\eta$.