Quantum resonances and ratchets in free-falling frames.
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/(2pi) , and the quasimomentum beta . Exact results are obtained concerning wave-packet evolution for arbitrary periodic kicking potentials in the case of integer tau/(2pi) (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 .
Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.
Itzhack
I
Dana
Vladislav
V
Roitberg