Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes
Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes
复制标题
DOI：
10.1088/1367-2630/15/8/083039
复制
发表时间：
2013-08-20
影响因子：
3.3
通讯作者：
Metzler, Ralf
中科院分区：
文献类型：
--
作者：
Cherstvy, Andrey G.;Chechkin, Aleksei V.;Metzler, Ralf
我们证明了具有空间相关扩散系数D(X)的简单马氏随机过程的非遍历性。对于类似或等于垂直条形x垂直条形(α)的幂定律形式D(X)，该过程产生类似或等于t(2/(2-α))的形式<；x(2)(T)>；的反常扩散。有趣的是，在亚扩散区和超扩散区，我们都观察到了弱遍历破坏：时间平均均方位移的标度在滞后时间增量中保持线性，因此不同于相应的系综平均值<；x(2)(T)>；。我们根据杆上的时间平均均方位移(2)及其随机特征，即杆上的统计分布和遍历破坏参数，分析了这一过程的非遍历行为。非均质扩散模型代表了非遍历、异常扩散的另一种方法，它可能与非均质介质中的扩散特别相关。
We demonstrate the non-ergodicity of a simple Markovian stochastic process with space-dependent diffusion coefficient D(x). For power-law forms D(x) similar or equal to vertical bar x vertical bar(alpha), this process yields anomalous diffusion of the form < x(2)(t)> similar or equal to t(2/(2-alpha)). Interestingly, in both the sub- and superdiffusive regimes we observe weak ergodicity breaking: the scaling of the time-averaged mean-squared displacement remains linear in the lag time Delta and thus differs from the corresponding ensemble average < x(2)(t)>. We analyse the non-ergodic behaviour of this process in terms of the time-averaged mean- squared displacement (delta(2)) over bar and its random features, i.e. the statistical distribution of (delta(2)) over bar and the ergodicity breaking parameters. The heterogeneous diffusion model represents an alternative approach to non- ergodic, anomalous diffusion that might be particularly relevant for diffusion in heterogeneous media.