Anomalous Diffusion in Random Dynamical Systems
Anomalous Diffusion in Random Dynamical Systems
复制标题
随机动力系统中的反常扩散
DOI：
10.1103/physrevlett.122.174101
复制
发表时间：
2019
影响因子：
8.6
通讯作者：
Klages Rainer
中科院分区：
文献类型：
--
作者：
Sato Yuzuru;Klages Rainer
考虑一个产生类扩散布朗运动的混沌动力系统。考虑第二个非混沌系统，其中所有粒子都定域。让一个粒子经历两个系统的随机组合，通过在时间上在它们之间采样。这个随机动力系统表现出什么样的扩散？我们表明，由此产生的动态可以产生异常扩散，在相反的布朗正常扩散的粒子的合奏的均方位移随时间非线性增加。随机混合简单的确定性行走的线上，我们发现异常动力学的特点是老化，弱遍历性打破，打破自平均，和无限不变的密度。这一结果适用于一般类型的噪声和扰动的非线性动力学在分叉的情况下。
Consider a chaotic dynamical system generating diffusionlike Brownian motion. Consider a second, nonchaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in time. What type of diffusion is exhibited by this random dynamical system? We show that the resulting dynamics can generate anomalous diffusion, where in contrast to Brownian normal diffusion the mean square displacement of an ensemble of particles increases nonlinearly in time. Randomly mixing simple deterministic walks on the line, we find anomalous dynamics characterized by aging, weak ergodicity breaking, breaking of self-averaging, and infinite invariant densities. This result holds for general types of noise and for perturbing nonlinear dynamics in bifurcation scenarios.