在空间相关的波纹势中扩散的反常特征：比正常的快，和其它的惊奇
Anomalous features of diffusion in corrugated potentials with spatial correlations: faster than normal, and other surprises
摘要：
具有空间不相关的高斯能量无序的波纹势中的正常扩散著名地解释了无序系统中非阿克里乌斯$\exp[-σ^2/(k_BT^2)]$温度依赖性的起源。在这里，我们表明，无偏扩散仍然是渐近正常的空间相关性衰减到零的存在。然而，由于缺乏时间的自平均瞬态亚扩散出现在中尺度上，它可以很容易地达到宏观尺度，即使是中等强度的无序波动的$σ\sim 4-5\, k_BT$。由于它的非遍历起源，这样的次扩散表现出一个大的分散在单轨迹平均。然而，与直觉不一致的是，它发生的速度比人们在没有相关性的情况下从正常扩散中预期的要快。我们将这些结果应用于DNA分子上的调节蛋白的扩散，并预测这种扩散应该是异常的，但比以前预期的几个房间$k_BT$，或仅仅是$0.05-0.075$ eV的现实能量紊乱的基因的典型长度快得多。
英文摘要：
Normal diffusion in corrugated potentials with spatially uncorrelated Gaussian energy disorder famously explains the origin of non-Arrhenius $\exp[-σ^2/(k_BT^2)]$ temperature-dependence in disordered systems. Here we show that unbiased diffusion remains asymptotically normal also in the presence of spatial correlations decaying to zero. However, due to a temporal lack of self-averaging transient subdiffusion emerges on mesoscale, and it can readily reach macroscale even for moderately strong disorder fluctuations of $σ\sim 4-5\, k_BT$. Due to its nonergodic origin such subdiffusion exhibits a large scatter in single trajectory averages. However, at odds with intuition, it occurs essentially faster than one expects from the normal diffusion in the absence of correlations. We apply these results to diffusion of regulatory proteins on DNA molecules and predict that such diffusion should be anomalous, but much faster than earlier expected on a typical length of genes for a realistic energy disorder of several room $k_BT$, or merely $0.05-0.075$ eV.
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