LEONCINI, X., NEISHTADT, A. and VASILIEV, A., 2009. Directed transport in a spatially periodic harmonic potential under periodic nonbiased forcing. Physical Review E, 79, 026213, 6pp.
Transport of a particle in a spatially periodic harmonic potential under the influence of a slowly timedependent
unbiased periodic external force is studied. The equations of motion are the same as in the problem
of a slowly forced nonlinear pendulum. Using methods of the adiabatic perturbation theory we show that for a
periodic external force of a general kind the system demonstrates directed ratchet transport in the chaotic
domain on very long time intervals and obtain a formula for the average velocity of this transport. Two cases
are studied: The case of the external force of small amplitude, and the case of the external force with amplitude
of order one. The obtained formulas can also be used in case of a nonharmonic periodic potential.
The work was partially supported by the RFBR Grants
No. 06-01-00117 and No. NSh 691.2008.1.