Anomalous dimensionality dependence of diffusion in a rugged energy landscape: How pathological is one dimension?
Anomalous dimensionality dependence of diffusion in a rugged energy landscape: How pathological is one dimension?
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DOI：
10.1063/1.4948936
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发表时间：
2016-01
期刊：
影响因子：
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通讯作者：
K. Seki;Kaushik Bagchi;B. Bagchi
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文献类型：
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作者：
K. Seki;Kaushik Bagchi;B. Bagchi
在一维崎岖的能量景观（REL）中的扩散被预测为病理上不同的（从任何更高的维度），有更大的机会遇到破碎的遍历性[D。L. Stein和C. M.纽曼，AIP Conf.Proc.1479，620（2012）]。然而，尽管文献中普遍存在多维物理模型（如指导蛋白质折叠/展开的高维漏斗），但尚未报道这种差异的定量研究。奇怪的是，这些现象的一些理论研究仍然采用一维扩散描述的分析处理。我们探讨了维数依赖的扩散REL进行有效的介质近似为基础的分析计算，并与现有的计算机模拟结果进行比较。我们发现，在一个中等水平的坚固性（假设有一个高斯分布），扩散是明确定义的，有效扩散系数的值取决于维数和变化（增加）的几个因素（105 -10），从1d到2d。相比之下，后续过渡（如2d到3d和3d到4d等）的变化要温和得多，只有10-20%的数量级。当粗糙度是由随机陷阱与指数分布的障碍高度，均方位移（MSD）是次扩散（一个众所周知的结果），但MSD的增长是由不同的指数在一个和更高的维度。讨论了在一维REL情况下，这种强烈的粗糙度引起的延迟的原因。我们还讨论了无限维（d = ∞）的特殊极限情况，在这种情况下，有效介质近似变得精确，理论结果变得简单。我们讨论，第一次，在景观中的空间相关性的随机步行者扩散的作用。
Diffusion in one dimensional rugged energy landscape (REL) is predicted to be pathologically different (from any higher dimension) with a much larger chance of encountering broken ergodicity [D. L. Stein and C. M. Newman, AIP Conf. Proc. 1479, 620 (2012)]. However, no quantitative study of this difference has been reported, despite the prevalence of multidimensional physical models in the literature (like a high dimensional funnel guiding protein folding/unfolding). Paradoxically, some theoretical studies of these phenomena still employ a one dimensional diffusion description for analytical tractability. We explore the dimensionality dependent diffusion on REL by carrying out an effective medium approximation based analytical calculations and compare them with the available computer simulation results. We find that at an intermediate level of ruggedness (assumed to have a Gaussian distribution), where diffusion is well-defined, the value of the effective diffusion coefficient depends on dimensionality and changes (increases) by several factors (∼5-10) in going from 1d to 2d. In contrast, the changes in subsequent transitions (like 2d to 3d and 3d to 4d and so on) are far more modest, of the order of 10-20% only. When ruggedness is given by random traps with an exponential distribution of barrier heights, the mean square displacement (MSD) is sub-diffusive (a well-known result), but the growth of MSD is described by different exponents in one and higher dimensions. The reason for such strong ruggedness induced retardation in the case of one dimensional REL is discussed. We also discuss the special limiting case of infinite dimension (d = ∞) where the effective medium approximation becomes exact and where theoretical results become simple. We discuss, for the first time, the role of spatial correlation in the landscape on diffusion of a random walker.