Directed chaotic transport in Hamiltonian ratchets

We present a comprehensive account of directed transport in one-dimensionalHamiltonian systems with spatial and temporal periodicity. They can beconsidered as Hamiltonian ratchets in the sense that ensembles of particles canshow directed ballistic transport in the absence of an average force. Wediscuss general conditions for such directed transport, like a mixed classicalphase space, and elucidate a sum rule that relates the contributions ofdifferent phase-space components to transport with each other. We show thatregular ratchet transport can be directed against an external potentialgradient while chaotic ballistic transport is restricted to unbiased systems.For quantized Hamiltonian ratchets we study transport in terms of the evolutionof wave packets and derive a semiclassical expression for the distribution oflevel velocities which encode the quantum transport in the Floquet bandspectra. We discuss the role of dynamical tunneling between transportingislands and the chaotic sea and the breakdown of transport in quantum ratchetswith broken spatial periodicity.Comment: 22 page