Nudged Elastic Bands and Lightly Bound Skyrmions
It has become clear in recent years that the configuration space of the nuclear Skyrme model has, in each topological class, many almost degenerate local energy minima and that the number of such minima grows with the degree (or baryon number) . Rigid body quantization, in which one quantizes motion...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2023 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2023
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212011 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Nudged Elastic Bands and Lightly Bound Skyrmions. James Martin Speight and Thomas Winyard. SIGMA 19 (2023), 073, 26 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862735896703401984 |
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| author | Speight, James Martin Winyard, Thomas |
| author_facet | Speight, James Martin Winyard, Thomas |
| citation_txt | Nudged Elastic Bands and Lightly Bound Skyrmions. James Martin Speight and Thomas Winyard. SIGMA 19 (2023), 073, 26 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | It has become clear in recent years that the configuration space of the nuclear Skyrme model has, in each topological class, many almost degenerate local energy minima and that the number of such minima grows with the degree (or baryon number) . Rigid body quantization, in which one quantizes motion on the spin-isospin orbit of just one minimum, is thus an ill-justified approximation. Instead, one should identify a (finite-dimensional) moduli space of configurations containing all local minima (for a given ) as well as fields interpolating smoothly between them. This paper proposes a systematic computational scheme for generating such a moduli space: one constructs an energy-minimizing path between each pair of local minima, then defines the moduli space to be the union of spin-isospin orbits of points on the union of these curves, a principal bundle over a graph. The energy-minimizing curves may be constructed in practice using the nudged elastic band method, a standard tool in mathematical chemistry for analyzing reaction paths and computing activation energies. To illustrate, we apply this scheme to the lightly bound Skyrme model in the point particle approximation, constructing the graphs for 5 ≤ ≤ 10. We go on to complete the quantization for = 7, in which the graph has two vertices and a single edge. The low-lying quantum states with isospin 1/2 do not strongly localize around either of the local energy minima (the vertices). Their energies rise monotonically with spin, conflicting with experimental data for Lithium-7.
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| first_indexed | 2026-04-17T16:29:42Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-212011 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T16:29:42Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
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| spelling | Speight, James Martin Winyard, Thomas 2026-01-22T09:17:36Z 2023 Nudged Elastic Bands and Lightly Bound Skyrmions. James Martin Speight and Thomas Winyard. SIGMA 19 (2023), 073, 26 pages 1815-0659 2020 Mathematics Subject Classification: 81T12; 70G45 arXiv:2305.18126 https://nasplib.isofts.kiev.ua/handle/123456789/212011 https://doi.org/10.3842/SIGMA.2023.073 It has become clear in recent years that the configuration space of the nuclear Skyrme model has, in each topological class, many almost degenerate local energy minima and that the number of such minima grows with the degree (or baryon number) . Rigid body quantization, in which one quantizes motion on the spin-isospin orbit of just one minimum, is thus an ill-justified approximation. Instead, one should identify a (finite-dimensional) moduli space of configurations containing all local minima (for a given ) as well as fields interpolating smoothly between them. This paper proposes a systematic computational scheme for generating such a moduli space: one constructs an energy-minimizing path between each pair of local minima, then defines the moduli space to be the union of spin-isospin orbits of points on the union of these curves, a principal bundle over a graph. The energy-minimizing curves may be constructed in practice using the nudged elastic band method, a standard tool in mathematical chemistry for analyzing reaction paths and computing activation energies. To illustrate, we apply this scheme to the lightly bound Skyrme model in the point particle approximation, constructing the graphs for 5 ≤ ≤ 10. We go on to complete the quantization for = 7, in which the graph has two vertices and a single edge. The low-lying quantum states with isospin 1/2 do not strongly localize around either of the local energy minima (the vertices). Their energies rise monotonically with spin, conflicting with experimental data for Lithium-7. We would like to thank Chris Halcrow and Derek Harland for useful conversations. This work was partially funded by the UK Engineering and Physical Sciences Research Council, through grant EP/P024688/1. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Nudged Elastic Bands and Lightly Bound Skyrmions Article published earlier |
| spellingShingle | Nudged Elastic Bands and Lightly Bound Skyrmions Speight, James Martin Winyard, Thomas |
| title | Nudged Elastic Bands and Lightly Bound Skyrmions |
| title_full | Nudged Elastic Bands and Lightly Bound Skyrmions |
| title_fullStr | Nudged Elastic Bands and Lightly Bound Skyrmions |
| title_full_unstemmed | Nudged Elastic Bands and Lightly Bound Skyrmions |
| title_short | Nudged Elastic Bands and Lightly Bound Skyrmions |
| title_sort | nudged elastic bands and lightly bound skyrmions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212011 |
| work_keys_str_mv | AT speightjamesmartin nudgedelasticbandsandlightlyboundskyrmions AT winyardthomas nudgedelasticbandsandlightlyboundskyrmions |