Entropy in quantum ratchet for a delta-kicked model

We investigate the evolution of Shannon entropy in quantum ratchet effect for a delta-kicked model, where a particle with initial momentum zero is periodically kicked by an asymmetric potential. It is shown that the evolution of Shannon entropy of the particle can remarkably reflect whether quantum resonance emerges and gives rise to ratchet current or not. Furthermore, for different kinds of quantum resonances, low-order or high-order quantum resonances, the evolutions of the entropy are quite different.