Institute of Physics, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, Taiwan.
Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan.
Phys Rev E. 2019 Jan;99(1-1):012103. doi: 10.1103/PhysRevE.99.012103.
We consider the overdamped dynamics of a Brownian particle in an arbitrary spatial periodic and time-dependent potential on the basis of an exact solution for the probability density in the form of a power series in the inverse friction coefficient. The expression for the average velocity of a Brownian ratchet is simplified in the high-temperature consideration when only the first terms of the series can be used. For the potential of an additive-multiplicative form (a sum of a time-independent contribution and a time-dependent multiplicative perturbation), general explicit expressions are obtained which allow comparative analysis of frequency dependencies of the average velocity, implying deterministic and stochastic potential energy fluctuations. For qualitative and quantitative analysis of these dependences, we choose illustrative examples for spatial harmonic fluctuations: with deterministic time dependences of a relaxation type and stochastic time dependences describing Markovian dichotomous and harmonic noise processes. We explore the influence of fluctuation types on the ratchet effect and demonstrate its enhancement in the case of harmonic noise.
我们基于概率密度的幂级数形式的精确解，研究了在任意空间周期性和时变势中布朗粒子的过阻尼动力学。在高温考虑下，当只能使用级数的前几项时，布朗棘轮的平均速度表达式得到简化。对于加性乘性形式的势（时间独立贡献和时间相关乘性微扰的和），我们得到了一般的显式表达式，允许对平均速度的频率依赖性进行比较分析，这些依赖性包含了确定性和随机的势能波动。为了对这些依赖性进行定性和定量分析，我们选择了空间谐波波动的示例：具有松弛型的确定性时间依赖性和描述马尔可夫二项式和谐波噪声过程的随机时间依赖性。我们研究了波动类型对棘轮效应的影响，并在谐波噪声的情况下证明了其增强。
