Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Straße 24/25, 14476 Potsdam-Golm, Germany.
Phys Rev Lett. 2019 Nov 1;123(18):180603. doi: 10.1103/PhysRevLett.123.180603.
Diffusion in tilted washboard potentials can paradoxically exceed free normal diffusion. The effect becomes much stronger in the underdamped case due to inertial effects. What happens upon inclusion of usually neglected fractional hydrodynamics memory effects (Basset-Boussinesq frictional force), which result in a heavy algebraic tail of the velocity autocorrelation function of the potential-free diffusion making it transiently superdiffusive? Will a giant enhancement of diffusion become even stronger, and the transient superdiffusion last even longer? These are the questions that we answer in this Letter based on an accurate numerical investigation. We show that a resonancelike enhancement of normal diffusion becomes indeed much stronger and sharper. Moreover, a long-lasting transient regime of superdiffusion, including Richardson-like diffusion, ⟨δx^{2}(t)⟩∝t^{3} and ballistic supertransport, ⟨δx(t)⟩∝t^{2}, is revealed.
倾斜洗衣板势中的扩散可以反常地超过自由正态扩散。由于惯性效应，在欠阻尼情况下，这种效应会变得更强。当包括通常被忽略的分数流体动力学记忆效应（巴斯-博素内斯克摩擦力）时会发生什么情况，这会导致无势扩散的速度自相关函数的沉重代数尾部使其暂时超扩散？扩散的巨大增强是否会变得更强，瞬态超扩散是否会持续更长时间？这是我们基于准确的数值研究在这封信中回答的问题。我们表明，正常扩散的共振增强确实变得更强更尖锐。此外，揭示了包括理查德森扩散在内的长时间瞬态超扩散，〈δx^{2}(t)〉∝t^{3}和弹道超输运，〈δx(t)〉∝t^{2}。
