Overdamped Brownian dynamics in piecewise-defined energy landscapes.
Overdamped Brownian dynamics in piecewise-defined energy landscapes.
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DOI：
10.1103/physreve.101.052123
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发表时间：
2020-05
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通讯作者：
Thomas H Gray;Ee Hou Yong
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文献类型：
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作者：
Thomas H Gray;Ee Hou Yong
研究了粒子在分段定义的势能景观U（x）中运动的过阻尼布朗动力学，其中每个截面的高度Q由指数分布p（Q）= a β exp（-a β Q）得到，其中β是热能的倒数，a> 0.引入平均有效扩散系数<$D_{eff}<$来表征扩散运动：<$x ^{2}<$= 2 <$D_{eff}<$t。导出了用U（x）和p（Q）表示的平均能量密度的一般表达式，并将其应用于三种类型的能量景观：平坦截面、光滑极大值和尖锐极大值。所有这三种情况都显示出在a = 1时亚扩散和扩散行为之间的转变，以及在a → ∞时还原为自由扩散。研究了相变附近的能量分布，发现极大值的形状对能量分布有很大的影响：由平坦截面或光滑极大值组成的能量分布呈现幂律分布，而对于具有尖锐极大值的能量分布，则表现出强烈的发散行为.亚扩散制度的两个方面进行了研究：增长的均方位移随时间和平均首次通过时间的分布。对于前者，布朗动力学模拟和粗粒度等效之间的协议进行了观察，但结果偏离随机势垒模型的预测。这种差异可能是有限时间效应。对于后者，在大振幅极限下观察到数值计算的特征指数与随机势垒模型预测的特征指数之间的一致性。
We study the overdamped Brownian dynamics of particles moving in piecewise-defined potential energy landscapes U(x), where the height Q of each section is obtained from the exponential distribution p(Q)=aβexp(-aβQ), where β is the reciprocal thermal energy, and a>0. The averaged effective diffusion coefficient 〈D_{eff}〉 is introduced to characterize the diffusive motion: 〈x^{2}〉=2〈D_{eff}〉t. A general expression for 〈D_{eff}〉 in terms of U(x) and p(Q) is derived and then applied to three types of energy landscape: flat sections, smooth maxima, and sharp maxima. All three cases display a transition between subdiffusive and diffusive behavior at a=1, and a reduction to free diffusion as a→∞. The behavior of 〈D_{eff}〉 around the transition is investigated and found to depend heavily upon the shape of the maxima: Energy landscapes made up of flat sections or smooth maxima display power-law behavior, while for landscapes with sharp maxima, strongly divergent behavior is observed. Two aspects of the subdiffusive regime are studied: the growth of the mean squared displacement with time and the distribution of mean first-passage times. For the former, agreement between Brownian dynamics simulations and a coarse-grained equivalent was observed, but the results deviated from the random barrier model's predictions. The discrepancy could be a finite-time effect. For the latter, agreement between the characteristic exponent calculated numerically and that predicted by the random barrier model is observed in the large-amplitude limit.