Anomalous fluctuations of currents in Sinai-type random chains with strongly correlated disorder.
Anomalous fluctuations of currents in Sinai-type random chains with strongly correlated disorder.
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具有强相关无序性的西奈型随机链中电流的异常波动。
DOI：
10.1103/physrevlett.110.100602
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发表时间：
2012
影响因子：
8.6
通讯作者：
G. Schehr
中科院分区：
文献类型：
--
作者：
G. Oshanin;A. Rosso;G. Schehr
研究了广义Sinai模型中随机游动的性质，其中熄灭的随机势是具有任意Hurst参数H，0<；H<；1的分数布朗运动的轨迹，使得随机力场具有很强的空间相关性。在这种情况下，无序平均均方位移与log(2/H)(N)成正比增长，n是时间。我们证明了定态电流J(L)通过有限长L链的k阶矩衰减为L(-(1-H))，且与k无关，这表明在齐次系统中，尽管是对数限制，平均电流比它的Fickian对应的要高得多。我们的结果揭示了一个悖论行为：对于固定的n和L，当H从0到1变化时，均方位移减小，而平均电流增加。这种违反直觉的行为是通过分析典型的无序实现来解释的。
We study properties of a random walk in a generalized Sinai model, in which a quenched random potential is a trajectory of a fractional Brownian motion with arbitrary Hurst parameter H, 0<H<1, so that the random force field displays strong spatial correlations. In this case, the disorder-average mean-square displacement grows in proportion to log(2/H)(n), n being time. We prove that moments of arbitrary order k of the steady-state current J(L) through a finite segment of length L of such a chain decay as L(-(1-H)), independently of k, which suggests that despite a logarithmic confinement the average current is much higher than its Fickian counterpart in homogeneous systems. Our results reveal a paradoxical behavior such that, for fixed n and L, the mean-square displacement decreases when one varies H from 0 to 1, while the average current increases. This counterintuitive behavior is explained via an analysis of representative realizations of disorder.