Subdiffusive rocking ratchets in viscoelastic media: Transport optimization and thermodynamic efficiency in overdamped regime
Subdiffusive rocking ratchets in viscoelastic media: Transport optimization and thermodynamic efficiency in overdamped regime
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DOI：
10.1103/physreve.87.052119
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发表时间：
2013-05-15
影响因子：
2.4
通讯作者：
Goychuk, Igor
中科院分区：
文献类型：
--
作者：
Kharchenko, Vasyl O.;Goychuk, Igor
我们在非马尔可夫广义朗之万方程方法和相关的多维马尔可夫嵌入动力学框架内研究粘弹性介质中外部零均值力周期性摇动的次扩散过阻尼布朗棘轮。由传输粒子引起的介质粘弹性变形由一组弹性耦合到传输粒子的辅助布朗准粒子建模，并以服从分形尺度的弛豫时间层次为特征。最缓慢的松弛变形不能立即跟随移动粒子，留下关于其先前位置的长程记忆，并在足够长的时间尺度上引起次扩散和异常传输。这种异常行为与过阻尼运动初始时间尺度上的正常扩散和传输相结合。由于零均值周期性驱动违反了热详细平衡，出现了具有破坏空间反演对称性的周期性棘轮势中异常缓慢的定向输运，并且通过驱动频率、其幅度和温度进行了优化。这种优化的反常输运可以是低色散的并且以大的广义佩克莱特数为特征。此外，我们表明过阻尼次扩散棘轮可以承受大量负载并做有用的工作。相应的热力学效率随时间以代数方式衰减，因为在传输粒子位置之后，针对负载所做的有用功随时间呈次线性缩放，但外力泵送的能量随时间呈线性缩放。然而，它可以短暂地相当高，并且在足够长的时间和空间尺度上与正常扩散过阻尼棘轮的热力学效率相当。
We study subdiffusive overdamped Brownian ratchets periodically rocked by an external zero-mean force in viscoelastic media within the framework of a non-Markovian generalized Langevin equation approach and associated multidimensional Markovian embedding dynamics. Viscoelastic deformations of the medium caused by the transport particle are modeled by a set of auxiliary Brownian quasiparticles elastically coupled to the transport particle and characterized by a hierarchy of relaxation times which obey a fractal scaling. The most slowly relaxing deformations which cannot immediately follow to the moving particle imprint long-range memory about its previous positions and cause subdiffusion and anomalous transport on a sufficiently long time scale. This anomalous behavior is combined with normal diffusion and transport on an initial time scale of overdamped motion. Anomalously slow directed transport in a periodic ratchet potential with broken space inversion symmetry emerges due to a violation of the thermal detailed balance by a zero-mean periodic driving and is optimized with frequency of driving, its amplitude, and temperature. Such optimized anomalous transport can be low dispersive and characterized by a large generalized Peclet number. Moreover, we show that overdamped subdiffusive ratchets can sustain a substantial load and do useful work. The corresponding thermodynamic efficiency decays algebraically in time since the useful work done against a load scales sublinearly with time following to the transport particle position, but the energy pumped by an external force scales with time linearly. Nevertheless, it can be transiently appreciably high and compare well with the thermodynamical efficiency of the normal diffusion overdamped ratchets on sufficiently long temporal and spatial scales.