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首页> 外文期刊>Physica, A. Statistical mechanics and its applications >Relaxation time distributions for an anomalously diffusing particle
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Relaxation time distributions for an anomalously diffusing particle

机译：异常扩散粒子的弛豫时间分布

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摘要

As well known, the generalized Langevin equation with a memory kernel decreasing at large times as an inverse power law of time describes the motion of an anomalously diffusing particle. Here, we focus attention on some new aspects of the dynamics, successively considering the memory kernel, the particle's mean velocity, and the scattering function. All these quantities are studied from a unique angle, namely, the discussion of the possible existence of a distribution of relaxation times characterizing their time decay. Although a very popular concept, a relaxation time distribution cannot be associated with any time-decreasing quantity (from a mathematical point of view, the decay has to be described by a completely monotonic function). Technically, we use a memory kernel decaying as a Mittag-Leffler function (the Mittag-Leffler functions interpolate between stretched or compressed exponential behaviour at short times and inverse power law behaviour at large times). We show that, in the case of a subdiffusive motion, relaxation time distributions can be defined for the memory kernel and for the scattering function, but not for the particle's mean velocity. The situation is opposite in the superdiffusive case.
机译：众所周知，随着时间的逆幂定律，具有大幅度减小的记忆核的广义Langevin方程描述了异常扩散粒子的运动。在这里，我们将注意力集中在动力学的一些新方面，依次考虑内存核，粒子的平均速度和散射函数。从一个独特的角度研究所有这些量，即讨论表征其时间衰减的弛豫时间分布的可能存在。尽管这是一个非常流行的概念，但弛豫时间分布不能与任何随时间减少的量相关联（从数学角度来看，衰减必须由完全单调的函数来描述）。从技术上讲，我们使用衰减的内存内核作为Mittag-Leffler函数（Mittag-Leffler函数在短时间内插值在拉伸或压缩的指数行为和在大比例上反幂律的行为之间插值）。我们表明，在亚扩散运动的情况下，可以为记忆核和散射函数定义弛豫时间分布，但不能为粒子的平均速度定义弛豫时间分布。在超扩散情况下情况则相反。

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