Rozenbaum Viktor M, Makhnovskii Yurii A, Shapochkina Irina V, Sheu Sheh-Yi, Yang Dah-Yen, Lin Sheng Hsien
Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan.
Department of Applied Chemistry, National Chiao Tung University, 1001 Ta Hsuen Road, Hsinchu, Taiwan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Dec;92(6):062132. doi: 10.1103/PhysRevE.92.062132. Epub 2015 Dec 18.
We generalize a theory of diffusion of a massive particle by the way in which transport characteristics are described by analytical expressions that formally coincide with those for the overdamped massless case but contain a factor comprising the particle mass which can be calculated in terms of Risken's matrix continued fraction method (MCFM). Using this generalization, we aim to elucidate how large gradients of a periodic potential affect the current in a tilted periodic potential and the average current of adiabatically driven on-off flashing ratchets. For this reason, we perform calculations for a sawtooth potential of the period L with an arbitrary sawtooth length (l<L) instead of the smooth potentials typically considered in MCFM-solvable problems. We find nonanalytic behavior of the transport characteristics calculated for the sharp extremely asymmetric sawtooth potential at l→0 which appears due to the inertial effect. Analysis of the temperature dependences of the quantities under study reveals the dominant role of inertia in the high-temperature region. In particular, we show, by the analytical strong-inertia approach developed for this region, that the temperature-dependent contribution to the mobility at zero force and to the related effective diffusion coefficient are proportional to T(-3/2) and T(-1/2), respectively, and have a logarithmic singularity at l→0.
我们通过一种方式推广了大质量粒子的扩散理论，即传输特性由解析表达式描述，这些表达式在形式上与过阻尼无质量情况的表达式一致，但包含一个由粒子质量组成的因子，该因子可根据里斯肯矩阵连分数法（MCFM）计算得出。利用这种推广，我们旨在阐明周期性势的大梯度如何影响倾斜周期性势中的电流以及绝热驱动的开关闪烁棘轮的平均电流。因此，我们针对周期为(L)且锯齿长度任意（(l < L)）的锯齿势进行计算，而不是像MCFM可解问题中通常考虑的光滑势。我们发现，在(l→0)时，针对尖锐的极不对称锯齿势计算出的传输特性呈现非解析行为，这是由惯性效应导致的。对所研究量的温度依赖性分析揭示了惯性在高温区域的主导作用。特别是，我们通过为该区域开发的解析强惯性方法表明，零力下迁移率的温度相关贡献以及相关的有效扩散系数分别与(T^{(-3/2)})和(T^{(-1/2)})成正比，并且在(l→0)时具有对数奇点。
