用大时间步长模拟随机动力学
Simulating Stochastic Dynamics Using Large Time Steps
摘要：
我们提出了一种新的方法来研究与热浴接触的多维经典系统的长时间随机动力学。当势能地形崎岖时，动力学显示出短时间尺度和长时间尺度的解耦，并且分子动力学（MD）或蒙特卡罗（MC）模拟通常是低效的。使用场论的方法，我们进行分析的平均在短期的随机波动。这样，我们得到了一个有效的理论，它产生了与原始理论相同的长时间动力学，但具有较低的时间分辨率。这种方法是用来开发一个改进版本的MC算法，这是特别适合于调查罕见的构象转变的动力学。在室温下的分子系统的特定情况下，我们表明，用于模拟有效理论的基本积分时间步长可以选择比原始理论中使用的大100倍。我们的研究结果说明和测试一个简单的系统，其特点是一个崎岖的能源景观。
英文摘要：
We present a novel approach to investigate the long-time stochastic dynamics of multi-dimensional classical systems, in contact with a heat-bath. When the potential energy landscape is rugged, the kinetics displays a decoupling of short and long time scales and both Molecular Dynamics (MD) or Monte Carlo (MC) simulations are generally inefficient. Using a field theoretic approach, we perform analytically the average over the short-time stochastic fluctuations. This way, we obtain an effective theory, which generates the same long-time dynamics of the original theory, but has a lower time resolution power. Such an approach is used to develop an improved version of the MC algorithm, which is particularly suitable to investigate the dynamics of rare conformational transitions. In the specific case of molecular systems at room temperature, we show that elementary integration time steps used to simulate the effective theory can be chosen a factor ~100 larger than those used in the original theory. Our results are illustrated and tested on a simple system, characterized by a rugged energy landscape.
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