Bodrova Anna S, Chechkin Aleksei V, Cherstvy Andrey G, Safdari Hadiseh, Sokolov Igor M, Metzler Ralf
Institut für Physik, Humboldt-Universität zu Berlin, Newtonstrasse 15, 12489 Berlin, Germany.
Faculty of Physics, M.V.Lomonosov Moscow State University, Moscow, 119991, Russia.
Sci Rep. 2016 Jul 27;6:30520. doi: 10.1038/srep30520.
It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases.
人们普遍认为，过阻尼朗之万方程在长时间极限下为经典布朗粒子的动力学提供了定量描述。我们建立并研究了一个由欠阻尼朗之万方程支配的范式反常扩散过程，该方程中系统温度以及扩散和阻尼系数具有明确的时间依赖性。我们表明，对于这种欠阻尼标度布朗运动（UDSBM），过阻尼极限无法描述系统的长时间行为，并且在一定参数值范围内实际上甚至可能根本不存在。因此，即使在相当长的时间内，持续的惯性效应也起着不可忽略的作用。从这项研究中，出现了一个关于过阻尼极限用于描述反常扩散粒子长时间运动的适用性的一般性问题，这对过阻尼反常扩散模型的相关性产生了深远影响。我们根据自由冷却颗粒气体中粒子反常扩散的分析和模拟结果来阐明我们的结果。
