标题： 对细胞化的改进方法：从Heller的融化高斯近似到Herman--Kluk传播器 显示英文标题

标题： Refined approach to cellularization: going from Heller's thawed Gaussian approximation to the Herman--Kluk propagator

摘要： 我们提出了一种改进的细胞化（Filinov过滤）方案，用于半经典Herman--Kluk传播器，该方案使用了逆Weierstrass变换以及单元格大小与单元格数量的最优缩放，并且之前仅在去相位表示的背景下使用过。 在新的方法中，单元格中心的采样密度与单元格大小相关，从而能够有效地对系统初始状态所覆盖的相空间进行采样。 所提出方法的主要优势在于，与标准的细胞化不同，它在轨迹数量无限大的极限下收敛于原始的Herman--Kluk结果，并且在使用单个轨迹时收敛于展开的高斯近似。 我们通过计算可积和混沌模型系统的自相关函数和谱来展示改进的细胞化方案的性能。 显示英文摘要

摘要： We present a refined cellularization (Filinov filtering) scheme for the semiclassical Herman--Kluk propagator, which employs the inverse Weierstrass transform and optimal scaling of the cell's size with the number of cells, and was previously used only in the context of the dephasing representation. In the new methodology, the sampling density for the cell centers correlates with the cell size, allowing for an effective sampling of the phase space covered by the initial state of the system. The main advantage of the presented approach is that, unlike the standard cellularization, it converges to the original Herman--Kluk result in the limit of an infinite number of trajectories and to the thawed Gaussian approximation when a single trajectory is used. We illustrate the performance of the refined cellularization scheme by calculating autocorrelation functions and spectra of both integrable and chaotic model systems.