Inertial effects in adiabatically driven flashing ratchets

Viktor M Rozenbaum, Makhnovskii Yurii A, Irina V Shapochkina, Sheh-Yi Sheu, Dah-Yen Yang, Sheng Hsien Lin

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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.
Original languageEnglish
Article number052131
JournalPhysical Review E
Issue number5
StatePublished - 19 May 2014



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    Rozenbaum, V. M., Yurii A, M., Shapochkina, I. V., Sheu, S-Y., Yang, D-Y., & Lin, S. H. (2014). Inertial effects in adiabatically driven flashing ratchets. Physical Review E, 89(5), [052131].