一维随机游动中的对数周期调制
Log-periodic modulation in one-dimensional random walks
摘要：
我们研究了一维晶格上单个粒子的扩散。结果表明，对于自相似分布的跳跃率，均方位移的时间依赖性遵循对数周期振荡调制的反常幂律。这种调制的起源追溯到扩散系数的长度的依赖性。随机游走指数和调制周期的解析计算和蒙特卡罗模拟证实。
英文摘要：
We have studied the diffusion of a single particle on a one-dimensional lattice. It is shown that, for a self-similar distribution of hopping rates, the time dependence of the mean-square displacement follows an anomalous power law modulated by logarithmic periodic oscillations. The origin of this modulation is traced to the dependence on the length of the diffusion coefficient. Both the random walk exponent and the period of the modulation are analytically calculated and confirmed by Monte Carlo simulations.
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