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 bec...
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| Published in | The European physical journal. A, Hadrons and nuclei Vol. 61; no. 7 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Berlin/Heidelberg
Springer Berlin Heidelberg
15.07.2025
Springer Nature B.V |
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| Abstract | 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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| AbstractList | 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. 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. |
| ArticleNumber | 162 |
| Author | Liang, Haozhao Wang, Chuanxin Li, Jian Naito, Tomoya |
| Author_xml | – sequence: 1 givenname: Chuanxin surname: Wang fullname: Wang, Chuanxin organization: College of Physics, Jilin University, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) – sequence: 2 givenname: Tomoya orcidid: 0000-0002-0010-3558 surname: Naito fullname: Naito, Tomoya email: tnaito@ribf.riken.jp organization: RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), Department of Physics, Graduate School of Science, The University of Tokyo – sequence: 3 givenname: Jian surname: Li fullname: Li, Jian email: jianli@jlu.edu.cn organization: College of Physics, Jilin University – sequence: 4 givenname: Haozhao surname: Liang fullname: Liang, Haozhao email: haozhao.liang@phys.s.u-tokyo.ac.jp organization: RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), Department of Physics, Graduate School of Science, The University of Tokyo |
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| Snippet | 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... 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... |
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| SubjectTerms | Artificial neural networks Dirac equation Excitation Hadrons Heavy Ions Machine learning Nuclear Fusion Nuclear Physics Particle and Nuclear Physics Physics Physics and Astronomy Regular Article - Theoretical Physics Unsupervised learning |
| Title | A deep neural network approach to solve the Dirac equation |
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