Supermetallic and Trapped States in Periodically Kicked Lattices

A periodically driven lattice with two commensurate spatial periodicities is found to exhibit super metallic states characterized by enhancements in wave packet spreading and entropy. These resonances occur at critical values of parameters where multi-band dispersion curves reduce to a universal function that is topologically a circle and the effective quantum dynamics describes free propagation. Sandwiching every resonant state are a pair of anti-resonant trapped states distinguished by dips in entropy where the transport, as seen in the spreading rate, is only somewhat inhibited. Existing in gapless phases fo the spectrum, a sequence of these peaks and dips are interspersed by gapped phases assocated with flat band states where both the wave packet spreading as well as the entropy exhibit local minima.