论文标题
用Feynman路径的深层产生建模估算欧几里得量子传播器
Estimating the Euclidean quantum propagator with deep generative modeling of Feynman paths
论文作者
论文摘要
Feynman路径积分通过概括所有可能的路径的巨大多种流形，为量子传播器和量子动力学提供了优雅的，经典的启发代表。从计算和模拟的角度来看，整个路径歧管的千古跟踪是一个困难的问题。机器学习可以有效地帮助您确定相关的子空间和位于巨大路径歧管一小部分的内在结构。在这项工作中，我们提出了用于量子机械系统的Feynman路径发生器，该系统从（低维）潜在空间以及通过靶向欧几里得时空的所需路径密度来有效地生成具有固定端点的Feynman路径。对于此类路径发生器，可以有效地估计欧几里得传播器以及地面波函数，以估计通用势能。我们的工作提供了一种用于计算量子传播器和地面波函数的替代方法，它为量子机械Feynman路径的生成建模铺平了道路，并提供了不同的观点来通过深度学习来了解量子古典的对应关系。
Feynman path integrals provide an elegant, classically inspired representation for the quantum propagator and the quantum dynamics, through summing over a huge manifold of all possible paths. From computational and simulational perspectives, the ergodic tracking of the whole path manifold is a hard problem. Machine learning can help, in an efficient manner, to identify the relevant subspace and the intrinsic structure residing at a small fraction of the vast path manifold. In this work, we propose the Feynman path generator for quantum mechanical systems, which efficiently generates Feynman paths with fixed endpoints, from a (low-dimensional) latent space and by targeting a desired density of paths in the Euclidean space-time. With such path generators, the Euclidean propagator as well as the ground-state wave function can be estimated efficiently for a generic potential energy. Our work provides an alternative approach for calculating the quantum propagator and the ground-state wave function, paves the way toward generative modeling of quantum mechanical Feynman paths, and offers a different perspective to understand the quantum-classical correspondence through deep learning.
