论文标题
Herman-Kluk传播器的抽样策略
Sampling strategies for the Herman-Kluk propagator of the wavefunction
论文作者
论文摘要
当使用半经典的Herman-kluk繁殖器来评估量子力学可观察物或时间相关函数时，通常从HUSIMI密度中对引导轨迹的初始条件进行采样。在这里，我们采用这个繁殖器来发展波功能本身。我们研究了两种无网格的策略，用于针对波函数的Herman-kluk繁殖器的初始采样，并验证所得的时间依赖性波函数在谐波和非谐波电位中演变而成。特别是，我们考虑基于最初的husimi密度或其平方根和最自然的采样密度的蒙特卡洛二次。我们证明了分析收敛误差估计，并通过对谐波振荡器的数值实验和一系列摩尔斯电势进行验证，并随着过度的过度性而进行验证。在所有情况下，从Husimi密度的平方根进行采样都会导致波功能的收敛速度更快。
When the semiclassical Herman-Kluk propagator is used for evaluating quantum-mechanical observables or time-correlation functions, the initial conditions for the guiding trajectories are typically sampled from the Husimi density. Here, we employ this propagator to evolve the wavefunction itself. We investigate two grid-free strategies for the initial sampling of the Herman-Kluk propagator applied to the wavefunction and validate the resulting time-dependent wavefunctions evolved in harmonic and anharmonic potentials. In particular, we consider Monte Carlo quadratures based either on the initial Husimi density or on its square root as possible and most natural sampling densities. We prove analytical convergence error estimates and validate them with numerical experiments on the harmonic oscillator and on a series of Morse potentials with increasing anharmonicity. In all cases, sampling from the square root of Husimi density leads to faster convergence of the wavefunction.
