Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the Stäckel Transform
The Stäckel transform is applied to the geodesic motion on Euclidean space, through the harmonic oscillator and Kepler-Coloumb potentials, in order to obtain maximally superintegrable classical systems on N-dimensional Riemannian spaces of nonconstant curvature. By one hand, the harmonic oscillator...
Збережено в:
| Дата: | 2011 |
|---|---|
| Автори: | , , , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2011
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147172 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the Stäckel Transform / A. Ballesteros, A. Enciso, F.J. Herranz, O. Ragnisco, D. Riglioni // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 48 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147172 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1471722019-02-14T01:25:11Z Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the Stäckel Transform Ballesteros, A. Enciso, A. Herranz, F.J. Ragnisco, O. Riglioni, D. The Stäckel transform is applied to the geodesic motion on Euclidean space, through the harmonic oscillator and Kepler-Coloumb potentials, in order to obtain maximally superintegrable classical systems on N-dimensional Riemannian spaces of nonconstant curvature. By one hand, the harmonic oscillator potential leads to two families of superintegrable systems which are interpreted as an intrinsic Kepler-Coloumb system on a hyperbolic curved space and as the so-called Darboux III oscillator. On the other, the Kepler-Coloumb potential gives rise to an oscillator system on a spherical curved space as well as to the Taub-NUT oscillator. Their integrals of motion are explicitly given. The role of the (flat/curved) Fradkin tensor and Laplace-Runge-Lenz N-vector for all of these Hamiltonians is highlighted throughout the paper. The corresponding quantum maximally superintegrable systems are also presented. 2011 Article Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the Stäckel Transform / A. Ballesteros, A. Enciso, F.J. Herranz, O. Ragnisco, D. Riglioni // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 48 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37J35; 70H06; 81R12 DOI:10.3842/SIGMA.2011.048 http://dspace.nbuv.gov.ua/handle/123456789/147172 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The Stäckel transform is applied to the geodesic motion on Euclidean space, through the harmonic oscillator and Kepler-Coloumb potentials, in order to obtain maximally superintegrable classical systems on N-dimensional Riemannian spaces of nonconstant curvature. By one hand, the harmonic oscillator potential leads to two families of superintegrable systems which are interpreted as an intrinsic Kepler-Coloumb system on a hyperbolic curved space and as the so-called Darboux III oscillator. On the other, the Kepler-Coloumb potential gives rise to an oscillator system on a spherical curved space as well as to the Taub-NUT oscillator. Their integrals of motion are explicitly given. The role of the (flat/curved) Fradkin tensor and Laplace-Runge-Lenz N-vector for all of these Hamiltonians is highlighted throughout the paper. The corresponding quantum maximally superintegrable systems are also presented. |
| format |
Article |
| author |
Ballesteros, A. Enciso, A. Herranz, F.J. Ragnisco, O. Riglioni, D. |
| spellingShingle |
Ballesteros, A. Enciso, A. Herranz, F.J. Ragnisco, O. Riglioni, D. Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the Stäckel Transform Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Ballesteros, A. Enciso, A. Herranz, F.J. Ragnisco, O. Riglioni, D. |
| author_sort |
Ballesteros, A. |
| title |
Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the Stäckel Transform |
| title_short |
Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the Stäckel Transform |
| title_full |
Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the Stäckel Transform |
| title_fullStr |
Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the Stäckel Transform |
| title_full_unstemmed |
Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the Stäckel Transform |
| title_sort |
superintegrable oscillator and kepler systems on spaces of nonconstant curvature via the stäckel transform |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147172 |
| citation_txt |
Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the Stäckel Transform / A. Ballesteros, A. Enciso, F.J. Herranz, O. Ragnisco, D. Riglioni // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 48 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT ballesterosa superintegrableoscillatorandkeplersystemsonspacesofnonconstantcurvatureviathestackeltransform AT encisoa superintegrableoscillatorandkeplersystemsonspacesofnonconstantcurvatureviathestackeltransform AT herranzfj superintegrableoscillatorandkeplersystemsonspacesofnonconstantcurvatureviathestackeltransform AT ragniscoo superintegrableoscillatorandkeplersystemsonspacesofnonconstantcurvatureviathestackeltransform AT riglionid superintegrableoscillatorandkeplersystemsonspacesofnonconstantcurvatureviathestackeltransform |
| first_indexed |
2023-05-20T17:26:47Z |
| last_indexed |
2023-05-20T17:26:47Z |
| _version_ |
1796153300667596800 |