具有随机批次的相互作用量子粒子系统热辐射的有效采样
Efficient Sampling of Thermal Averages of Interacting Quantum Particle Systems with Random Batches
摘要：
提出了一种有效的采样方法pmmLang+RBM，用于计算相互作用量子粒子系统中的量子热平均。受益于随机批处理方法（RBM），pmmLang+RBM降低了由于从$O(NP^2)$到$O(NP)$的每个时间步的相互作用力而导致的复杂性，其中$N$是珠的数量，$P$是颗粒的数量。尽管RBM在每个时间步引入了相互作用力的随机扰动，但沿着采样过程的随机扰动的长期影响只会导致pmmLang+RBM的经验测量值与目标分布的小偏差，这也意味着热平均计算中的小误差。我们数值研究的pmmLang+RBM的收敛性，并定量研究的依赖性的误差计算的热平均值的参数，包括批量大小，时间步长等，我们还提出了一个扩展的pmmLang+RBM，这是基于分裂蒙特卡罗方法，适用于当相互作用的潜力包含一个奇异的部分。
英文摘要：
An efficient sampling method, the pmmLang+RBM, is proposed to compute the quantum thermal average in the interacting quantum particle system. Benefiting from the random batch method (RBM), the pmmLang+RBM reduces the complexity due to the interaction forces per timestep from $O(NP^2)$ to $O(NP)$, where $N$ is the number of beads and $P$ is the number of particles. Although the RBM introduces a random perturbation of the interaction forces at each timestep, the long time effects of the random perturbations along the sampling process only result in a small bias in the empirical measure of the pmmLang+RBM from the target distribution, which also implies a small error in the thermal average calculation. We numerically study the convergence of the pmmLang+RBM, and quantitatively investigate the dependence of the error in computing the thermal average on the parameters including the batch size, the timestep, etc. We also propose an extension of the pmmLang+RBM, which is based on the splitting Monte Carlo method and is applicable when the interacting potential contains a singular part.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
