TY - JOUR

T1 - Inertial effects in adiabatically driven flashing ratchets

AU - Rozenbaum, Viktor M

AU - Yurii A, Makhnovskii

AU - Shapochkina, Irina V

AU - Sheu, Sheh-Yi

AU - Yang, Dah-Yen

AU - Lin, Sheng Hsien

PY - 2014/5/19

Y1 - 2014/5/19

N2 - 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.

AB - 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.

KW - BROWNIAN MOTORS; PERIODIC POTENTIALS; CHAOTIC TRANSPORT; MOTION; FLUCTUATIONS; FORCE

U2 - 10.1103/PhysRevE.89.052131

DO - 10.1103/PhysRevE.89.052131

M3 - Article

C2 - 25353763

VL - 89

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 5

M1 - 052131

ER -