求解狄拉克方程的深度神经网络方法

IF 2.8 3区物理与天体物理 Q2 PHYSICS, NUCLEAR

The European Physical Journal A Pub Date : 2025-07-15 DOI:10.1140/epja/s10050-025-01630-5

Chuanxin Wang, Tomoya Naito, Jian Li, Haozhao Liang

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引用次数: 0

摘要

我们扩展了[Naito， Naito, and Hashimoto， Phys]的方法。Rev. Research, 5, 033189(2023)]利用深度神经网络和无监督机器学习技术，不仅求解基态的狄拉克方程，还求解低空激发态的狄拉克方程。变分法由于狄拉克海的存在而失效，通过引入逆哈密顿法避免了这一问题。对于低洼激发态，提出了两种方法，它们具有不同的性能和优点。通过库仑势和伍兹-撒克逊势的计算，验证了该方法的有效性。

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A deep neural network approach to solve the Dirac equation

We extend the method from [Naito, Naito, and Hashimoto, Phys. Rev. Research 5, 033189 (2023)] to solve the Dirac equation not only for the ground state but also for low-lying excited states using a deep neural network and the unsupervised machine learning technique. The variational method fails because of the Dirac sea, which is avoided by introducing the inverse Hamiltonian method. For low-lying excited states, two methods are proposed, which have different performances and advantages. The validity of this method is verified by the calculations with the Coulomb and Woods-Saxon potentials.

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来源期刊

The European Physical Journal A 物理-物理：核物理

CiteScore

5.00

自引率

18.50%

发文量

216

审稿时长

3-8 weeks

期刊介绍： Hadron Physics Hadron Structure Hadron Spectroscopy Hadronic and Electroweak Interactions of Hadrons Nonperturbative Approaches to QCD Phenomenological Approaches to Hadron Physics Nuclear and Quark Matter Heavy-Ion Collisions Phase Diagram of the Strong Interaction Hard Probes Quark-Gluon Plasma and Hadronic Matter Relativistic Transport and Hydrodynamics Compact Stars Nuclear Physics Nuclear Structure and Reactions Few-Body Systems Radioactive Beams Electroweak Interactions Nuclear Astrophysics Article Categories Letters (Open Access) Regular Articles New Tools and Techniques Reviews.