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Chaotic Hamiltonian ratchets for pulsed periodic double-well potentials: classical correlations and the ratchet current.

We present analytical derivations of the diffusion rates, ratchet currents, and time scales of a new ratchet in a fully chaotic Hamiltonian system, introduced in Phys. Rev. Lett. 89, 194102 (2002)] with a proposed implementation using atoms in pulsed standing waves of light. The origin of this type of ratchet current is in asymmetric momentum diffusion rates which result when a "double-well" lattice is pulsed with unequal "kick" periods. The form of the new short-time correlations which modify the diffusion rates are derived. The resulting formulas for the classical energy diffusion rates are shown to give good agreement with numerical simulations. A closed analytical formula for the ratchet current is also obtained, which predicts correctly the current magnitudes and current reversals. The characteristic "ratchet time," a classical time scale associated with the momentum-diffusion ratchet is derived analytically. The competition between the ratchet time t(r) , and the quantum break time t(*) is investigated further.