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Rocking Subdiffusive Ratchets: Origin, Optimization andEfficiency

Published online by Cambridge University Press:  24 April 2013

I. Goychuk  and
V. O. Kharchenko
I. Goychuk*
Affiliation:
Institute of Physics, University of Augsburg, Universitätstr. 1, D-86135 Augsburg, Germany & Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, D-14476 Potsdam-Golm, Germany
V. O. Kharchenko
Affiliation:
Institute of Applied Physics, NAS of Ukraine, 58 Petropavlovskaya str., 40030 Sumy, Ukraine
*
⋆ Corresponding author. E-mail:goychuk@physik.uni-augsburg.de
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Abstract

We study origin, parameter optimization, and thermodynamic efficiency of isothermalrocking ratchets based on fractional subdiffusion within a generalized non-MarkovianLangevin equation approach. A corresponding multi-dimensional Markovian embedding dynamicsis realized using a set of auxiliary Brownian particles elastically coupled to the centralBrownian particle (see video on the journal web site). We show that anomalous subdiffusivetransport emerges due to an interplay of nonlinear response and viscoelastic effects forfractional Brownian motion in periodic potentials with broken space-inversion symmetry anddriven by a time-periodic field. The anomalous transport becomes optimal for asubthreshold driving when the driving period matches a characteristic time scale ofinterwell transitions. It can also be optimized by varying temperature, amplitude ofperiodic potential and driving strength. The useful work done against a load shows aparabolic dependence on the load strength. It grows sublinearly with time and thecorresponding thermodynamic efficiency decays algebraically in time because the energysupplied by the driving field scales with time linearly. However, it compares well withthe efficiency of normal diffusion rocking ratchets on an appreciably long time scale.

Keywords

anomalous Brownian motiongeneralized Langevin equationmemory effectsviscoelasticityratchet transportstochastic thermodynamics

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Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 2: Anomalous diffusion , 2013 , pp. 144 - 158
Copyright
© EDP Sciences, 2013

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