论文标题
关于谐波系统中兰格文方程的数值固定分布
On the Numerical Stationary Distribution of Overdamped Langevin Equation in Harmonic System
论文作者
论文摘要
长期以来，用于随机微分方程的有效数值算法一直是统计物理和数学研究的重要对象。在本文中，我们研究了过度阻尼Langevin方程的高度准确的数值算法。特别是，我们的兴趣是数值方案的行为，用于解决谐波系统中抑制过度抑制的langevin方程。从阻尼不足的Langevin动力学的方案的较大摩擦极限中，获得了三种算法，用于过度阻尼的Langevin方程。我们通过分析离散时间轨迹的一维情况和多维情况来得出每种算法的固定分布的显式表达。通过比较确切的玻尔兹曼分布来说明每种算法的固定分布的准确性。我们的结果表明，“ Baoa-limit”算法在时间间隔的稳定制度内生成了规范集合中谐波系统的确切分布。其他算法不会产生谐波系统的确切分布。
Efficient numerical algorithm for stochastic differential equation has been an important object in the research of statistical physics and mathematics for a long time. In this paper we study the highly accurate numerical algorithm of the overdamped Langevin equation. In particular, our interest is the behaviour of the numerical schemes for solving the overdamped Langevin equation in the harmonic system. Three algorithms are obtained for overdamped Langevin equation, from the large friction limit of the schemes for underdamped Langevin dynamics. We derive the explicit expression of the stationary distribution of each algorithm by analysing the discrete time trajectory, for both one-dimensional and multi-dimensional cases. The accuracy of the stationary distribution of each algorithm is illustrated by comparing to the exact Boltzmann distribution. Our results demonstrate that, the "BAOA-limit" algorithm generates the exact distribution for the harmonic system in the canonical ensemble, within the stable regime of the time interval. The other algorithms do not produce the exact distribution of the harmonic system.
