Note on the Retarded van der Waals Potential within the Dipole Approximation
We examine the dipole approximated Pauli-Fierz Hamiltonians of the nonrelativistic QED. We assume that the Coulomb potential of the nuclei, together with the Coulomb interaction between the electrons, can be approximated by harmonic potentials. By an exact diagonalization method, we prove that the b...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210714 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Note on the Retarded van der Waals Potential within the Dipole Approximation. Tadahiro Miyao. SIGMA 16 (2020), 036, 34 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862710887130857472 |
|---|---|
| author | Miyao, Tadahiro |
| author_facet | Miyao, Tadahiro |
| citation_txt | Note on the Retarded van der Waals Potential within the Dipole Approximation. Tadahiro Miyao. SIGMA 16 (2020), 036, 34 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We examine the dipole approximated Pauli-Fierz Hamiltonians of the nonrelativistic QED. We assume that the Coulomb potential of the nuclei, together with the Coulomb interaction between the electrons, can be approximated by harmonic potentials. By an exact diagonalization method, we prove that the binding energy of the two hydrogen atoms behaves as R⁻⁷, provided that the distance between the atoms R is sufficiently large. We employ Feynman's representation of the quantized radiation fields, which enables us to diagonalize Hamiltonians rigorously. Our result supports the famous conjecture by Casimir and Polder.
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| first_indexed | 2025-12-17T12:04:33Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210714 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-17T12:04:33Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Miyao, Tadahiro 2025-12-15T15:29:32Z 2020 Note on the Retarded van der Waals Potential within the Dipole Approximation. Tadahiro Miyao. SIGMA 16 (2020), 036, 34 pages 1815-0659 2020 Mathematics Subject Classification: 81V10;81V55;47A75 arXiv:1902.05207 https://nasplib.isofts.kiev.ua/handle/123456789/210714 https://doi.org/10.3842/SIGMA.2020.036 We examine the dipole approximated Pauli-Fierz Hamiltonians of the nonrelativistic QED. We assume that the Coulomb potential of the nuclei, together with the Coulomb interaction between the electrons, can be approximated by harmonic potentials. By an exact diagonalization method, we prove that the binding energy of the two hydrogen atoms behaves as R⁻⁷, provided that the distance between the atoms R is sufficiently large. We employ Feynman's representation of the quantized radiation fields, which enables us to diagonalize Hamiltonians rigorously. Our result supports the famous conjecture by Casimir and Polder. The original idea of the present paper comes from an unpublished sketch by Herbert Spohn. I would like to thank the kind referees for their very helpful comments. The discussions in Section 9 heavily rely on their comments. This work was partially supported by KAKENHI 18K03315. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Note on the Retarded van der Waals Potential within the Dipole Approximation Article published earlier |
| spellingShingle | Note on the Retarded van der Waals Potential within the Dipole Approximation Miyao, Tadahiro |
| title | Note on the Retarded van der Waals Potential within the Dipole Approximation |
| title_full | Note on the Retarded van der Waals Potential within the Dipole Approximation |
| title_fullStr | Note on the Retarded van der Waals Potential within the Dipole Approximation |
| title_full_unstemmed | Note on the Retarded van der Waals Potential within the Dipole Approximation |
| title_short | Note on the Retarded van der Waals Potential within the Dipole Approximation |
| title_sort | note on the retarded van der waals potential within the dipole approximation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210714 |
| work_keys_str_mv | AT miyaotadahiro noteontheretardedvanderwaalspotentialwithinthedipoleapproximation |