标题： 采样权重在评估经典时间自相关函数中的作用 显示英文标题

标题： Role of the sampling weight in evaluating classical time autocorrelation functions

摘要： 我们分析了采样权重的选择如何影响经典时间自相关函数蒙特卡罗评估的效率。 假设无关联采样或具有恒定相关长度的采样，我们提出了一种采样权重，使得达到收敛所需的轨迹数量与相关量、维度、动力学和相空间密度无关。 相反，结果表明，直接从相空间密度采样的“标准”直观算法的计算成本可能随着自由度数量呈指数增长。 然而，对于谐波系统的平稳高斯分布以及相空间坐标线性函数的自相关函数，该标准算法的计算成本也与维度无关。 显示英文摘要

摘要： We analyze how the choice of the sampling weight affects the efficiency of the Monte Carlo evaluation of classical time autocorrelation functions. Assuming uncorrelated sampling or sampling with constant correlation length, we propose a sampling weight for which the number of trajectories needed for convergence is independent of the correlated quantity, dimensionality, dynamics, and phase-space density. In contrast, it is shown that the computational cost of the "standard" intuitive algorithm which samples directly from the phase-space density may scale exponentially with the number of degrees of freedom. Yet, for the stationary Gaussian distribution of harmonic systems and for the autocorrelation function of a linear function of phase-space coordinates, the computational cost of this standard algorithm is also independent of dimensionality.