2134/15545
Xavier Leoncini
Xavier
Leoncini
Anatoly Neishtadt
Anatoly
Neishtadt
Alexei Vasiliev
Alexei
Vasiliev
Directed transport in a spatially periodic harmonic potential under periodic nonbiased forcing
Loughborough University
2014
untagged
Mathematical Sciences not elsewhere classified
2014-08-14 12:36:27
Journal contribution
https://repository.lboro.ac.uk/articles/journal_contribution/Directed_transport_in_a_spatially_periodic_harmonic_potential_under_periodic_nonbiased_forcing/9385247
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.