论文标题
通过自适应粒子歼灭来克服Wigner动力学中的数值标志问题
Overcoming the numerical sign problem in the Wigner dynamics via adaptive particle annihilation
论文作者
论文摘要
臭名昭著的数值符号问题为高维相空间中的基于粒子的随机Wigner模拟带来了基本障碍。尽管现有的粒子通过统一网格歼灭会大大减轻尺寸d $ \ le $ 4时的标志问题，但是当由于维度的诅咒而导致d $ \ ge $ 6时，网状尺寸会显着增长，因此使an灭会非常低效。在本文中，我们提出了一种自适应颗粒歼灭算法，称为顺序簇粒子通过差异估计（Spade）克服符号问题。 Spade遵循了分裂和拼接策略：通过控制每组的数量理论差异和独立的随机匹配，可以自适应粒子的自适应聚类，并且可以学习可以准确捕获Wigner函数的非古典性的粒子的最小粒子。我们基于固定相近似结合了铲子与方差降低技术，我们试图模拟6-D和12-D相空间中的质子电子耦合。在$ 73^3 \ times 80^3 $均匀的网格下，由特征性 - 光谱混合方案产生的6-D相空间中的参考解决方案提供了详尽的性能基准，该参考解决方案完全探索了基于网格的确定性Wigner求解器的极限。
The infamous numerical sign problem poses a fundamental obstacle to particle-based stochastic Wigner simulations in high dimensional phase space. Although the existing particle annihilation via uniform mesh significantly alleviates the sign problem when dimensionality D $\le$ 4, the mesh size grows dramatically when D $\ge$ 6 due to the curse of dimensionality and consequently makes the annihilation very inefficient. In this paper, we propose an adaptive particle annihilation algorithm, termed Sequential-clustering Particle Annihilation via Discrepancy Estimation (SPADE), to overcome the sign problem. SPADE follows a divide-and-conquer strategy: Adaptive clustering of particles via controlling their number-theoretic discrepancies and independent random matching in each group, and it may learn the minimal amount of particles that can accurately capture the non-classicality of the Wigner function. Combining SPADE with the variance reduction technique based on the stationary phase approximation, we attempt to simulate the proton-electron couplings in 6-D and 12-D phase space. A thorough performance benchmark of SPADE is provided with the reference solutions in 6-D phase space produced by a characteristic-spectral-mixed scheme under a $73^3 \times 80^3$ uniform grid, which fully explores the limit of grid-based deterministic Wigner solvers.
