title: Inertial effects in adiabatically driven flashing ratchets.
abstract: We study analytically the effect of a small inertial correction on the properties of adiabatically driven flashing ratchets. Parrondo's lemma [J. M. R. Parrondo, Phys. Rev. E 57, 7297 (1998)] is generalized to include the inertial term so as to establish the symmetry conditions allowing directed motion (other than in the overdamped massless case) and to obtain a high-temperature expansion of the motion velocity for arbitrary potential profiles. The inertial correction is thus shown to enhance the ratchet effect at all temperatures for sawtooth potentials and at high temperatures for simple potentials described by the first two harmonics. With the special choice of potentials represented by at least the first three harmonics, the correction gives rise to the motion reversal in the high-temperature region. In the low-temperature region, inertia weakens the ratchet effect, with the exception of the on-off model, where diffusion is important. The directed motion adiabatically driven by potential sign fluctuations, though forbidden in the overdamped limit, becomes possible due to purely inertial effects in neither symmetric nor antisymmetric potentials, i.e., not for commonly used sawtooth and two-sinusoid profiles.
authors.affiliation: Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan and Department of Applied Chemistry, National Chiao Tung University, 1001 Ta Hsuen Road, Hsinchu, Taiwan and Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, Generala Naumova Street 17, Kiev 03164, Ukraine.
authors.forename: Viktor M
authors.initials: VM
authors.lastname: Rozenbaum
authors.affiliation: Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan and Topchiev Institute of Petrochemical Synthesis, Russian Academy of Sciences, Leninsky Prospect 29, 119991 Moscow, Russia.
authors.forename: Yurii A
authors.initials: YA
authors.lastname: Makhnovskii
authors.affiliation: Department of Physics, Belarusian State University, Prospekt Nezavisimosti 4, 220050 Minsk, Belarus.
authors.forename: Irina V
authors.initials: IV
authors.lastname: Shapochkina
authors.affiliation: Department of Life Sciences and Institute of Genome Sciences, Institute of Biomedical Informatics, National Yang-Ming University, Taipei 112, Taiwan.
authors.forename: Sheh-Yi
authors.initials: SY
authors.lastname: Sheu
authors.affiliation: Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan.
authors.forename: Dah-Yen
authors.initials: DY
authors.lastname: Yang
authors.affiliation: Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan and Department of Applied Chemistry, National Chiao Tung University, 1001 Ta Hsuen Road, Hsinchu, Taiwan.
authors.forename: Sheng Hsien
authors.initials: SH
authors.lastname: Lin