Estimating the Euclidean Quantum Propagator with Deep Generative Modelling of Feynman paths

• URL: http://arxiv.org/abs/2202.02750v1
• Date: Sun, 6 Feb 2022 10:27:15 GMT
• Title: Estimating the Euclidean Quantum Propagator with Deep Generative Modelling of Feynman paths
• Authors: Yanming Che, Clemens Gneiting, Franco Nori
• Abstract summary: We propose the concept of Feynman path generator, which efficiently generates Feynman paths with fixed endpoints from a (low-dimensional) latent space. Our work leads to a fresh approach for calculating the quantum propagator, paves the way toward generative modelling of Feynman paths, and may also provide a future new perspective to understand the quantum-classical correspondence through deep learning.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: 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 concept of Feynman path generator, which efficiently generates Feynman paths with fixed endpoints from a (low-dimensional) latent space, 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 leads to a fresh approach for calculating the quantum propagator, paves the way toward generative modelling of Feynman paths, and may also provide a future new perspective to understand the quantum-classical correspondence through deep learning.

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