论文标题
扩散在配置空间中使用域的蒙特卡洛
Diffusion Monte Carlo using domains in configuration space
论文作者
论文摘要
扩散蒙特卡洛（DMC）中配置空间的采样是使用随机移动的步行者进行的。在先前的有关Hubbard模型[\ href {https://doi.org/10.1103/physrevb.60.2299} {Assaraf等人。 Poisson Law，可以准确地集成了州的动力学，从而导致仅连接不同状态的有效动力学。在这里，我们将这个想法扩展到被困在任意形状和大小领域中的助行器的一般情况。得出了产生的有效随机动力学的方程。步行者在域内花费的平均时间越大，统计波动的减少越大。提出了对Hubbard模型的数值应用。尽管这项工作介绍了有限线性空间的方法，但可以将其推广而没有根本困难的连续配置空间。
The sampling of the configuration space in diffusion Monte Carlo (DMC) is done using walkers moving randomly. In a previous work on the Hubbard model [\href{https://doi.org/10.1103/PhysRevB.60.2299}{Assaraf et al.~Phys.~Rev.~B \textbf{60}, 2299 (1999)}], it was shown that the probability for a walker to stay a certain amount of time in the same state obeys a Poisson law and that the on-state dynamics can be integrated out exactly, leading to an effective dynamics connecting only different states. Here, we extend this idea to the general case of a walker trapped within domains of arbitrary shape and size. The equations of the resulting effective stochastic dynamics are derived. The larger the average (trapping) time spent by the walker within the domains, the greater the reduction in statistical fluctuations. A numerical application to the Hubbard model is presented. Although this work presents the method for finite linear spaces, it can be generalized without fundamental difficulties to continuous configuration spaces.
