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SIGMA, 2011, том 7, 048, 15 стр. (Mi sigma606)  

Эта публикация цитируется в 20 научных статьях (всего в 20 статьях)

Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the Stäckel Transform

Ángel Ballesterosa, Alberto Encisob, Francisco J. Herranza, Orlando Ragniscocd, Danilo Riglionicd

a Departamento de Física, Universidad de Burgos, E-09001 Burgos, Spain
b Instituto de Ciencias Matemáticas (CSIC-UAM-UCM-UC3M), Consejo Superior de Investigaciones Cientícas, C/ Nicolás Cabrera 14-16, E-28049 Madrid, Spain
c Università degli Studi Roma Tre, Dipartimento di Fisica E. Amaldi
d Dipartimento di Fisica, Università di Roma Tre and Istituto Nazionale di Fisica Nucleare sezione di Roma Tre, Via Vasca Navale 84, I-00146 Roma, Italy

Аннотация: 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.

Ключевые слова: coupling constant metamorphosis; integrable systems; curvature; harmonic oscillator; Kepler–Coulomb; Fradkin tensor; Laplace–Runge–Lenz vector; Taub-NUT; Darboux surfaces

DOI: https://doi.org/10.3842/SIGMA.2011.048

Полный текст: PDF файл (424 kB)
Полный текст: http://emis.mi.ras.ru/journals/SIGMA/2011/048/
Список литературы: PDF файл   HTML файл

Реферативные базы данных:

ArXiv: 1103.4554
Тип публикации: Статья
MSC: 37J35; 70H06; 81R12
Поступила: 18 марта 2011 г.; в окончательном варианте 12 мая 2011 г.; опубликована 14 мая 2011 г.
Язык публикации: английский

Образец цитирования: Ángel Ballesteros, Alberto Enciso, Francisco J. Herranz, Orlando Ragnisco, Danilo Riglioni, “Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the Stäckel Transform”, SIGMA, 7 (2011), 048, 15 pp.

Цитирование в формате AMSBIB
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\by \'Angel~Ballesteros, Alberto Enciso, Francisco J.~Herranz, Orlando Ragnisco, Danilo Riglioni
\paper Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the St\"ackel Transform
\jour SIGMA
\yr 2011
\vol 7
\papernumber 048
\totalpages 15
\mathnet{http://mi.mathnet.ru/sigma606}
\crossref{https://doi.org/10.3842/SIGMA.2011.048}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    Эта публикация цитируется в следующих статьяx:
    1. Visinescu M., “Hidden Symmetries in a Gauge-Covariant Approach, Hamiltonian Reduction and Oxidation”, Modern Phys Lett A, 26:36 (2011), 2719–2730  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Rubin de Celis E., Santillan O.P., “Massless Geodesics in AdS(5) X Y(P, Q) as a Superintegrable System”, J. High Energy Phys., 2012, no. 9, 032  crossref  mathscinet  isi  elib  scopus
    3. Visinescu M., “Higher Order First Integrals, Killing Tensors and Killing-Maxwell System”, 7th International Conference on Quantum Theory and Symmetries (Qts7), Journal of Physics Conference Series, 343, IOP Publishing Ltd, 2012, 012126  crossref  isi  scopus
    4. Miller Jr. Willard, Post S., Winternitz P., “Classical and Quantum Superintegrability with Applications”, J. Phys. A-Math. Theor., 46:42 (2013), 423001  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. Riglioni D., “Classical and Quantum Higher Order Superintegrable Systems From Coalgebra Symmetry”, J. Phys. A-Math. Theor., 46:26 (2013), 265207  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. Panahi H., Alizadeh Z., “Deformed Oscillator Algebra for Quantum Superintegrable Systems in Two-Dimensional Euclidean Space and on a Complex Two-Sphere”, Chin. Phys. B, 22:6 (2013), 060304  crossref  adsnasa  isi  elib  scopus
    7. Ballesteros A., Enciso A., Herranz F.J., Ragnisco O., Riglioni D., “A Maximally Superintegrable Deformation of the N-Dimensional Quantum Kepler-Coulomb System”, Xxist International Conference on Integrable Systems and Quantum Symmetries (Isqs21), Journal of Physics Conference Series, 474, eds. Burdik C., Navratil O., Posta S., IOP Publishing Ltd, 2013  crossref  mathscinet  isi  scopus
    8. Ballesteros A., Enciso A., Herranz F.J., Ragnisco O., Riglioni D., “An Exactly Solvable Deformation of the Coulomb Problem Associated With the Taub-NUT Metric”, Ann. Phys., 351 (2014), 540–557  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    9. Latini D., Ragnisco O., “the Classical Taub-NUT System: Factorization, Spectrum Generating Algebra and Solution To the Equations of Motion”, J. Phys. A-Math. Theor., 48:17 (2015), 175201  crossref  mathscinet  zmath  adsnasa  isi  scopus
    10. Ranada M.F., “Superintegrable Deformations of Superintegrable Systems: Quadratic Superintegrability and Higher-Order Superintegrability”, J. Math. Phys., 56:4 (2015), 042703  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    11. Yuxuan Chen, Ernie G. Kalnins, Qiushi Li, Willard Miller Jr., “Examples of Complete Solvability of 2D Classical Superintegrable Systems”, SIGMA, 11 (2015), 088, 51 pp.  mathnet  crossref
    12. Post S., Winternitz P., “General Nth Order Integrals of Motion in the Euclidean Plane”, J. Phys. A-Math. Theor., 48:40 (2015), 405201  crossref  mathscinet  zmath  isi  elib  scopus
    13. Nikitin A.G., “Superintegrable and Shape Invariant Systems With Position Dependent Mass”, J. Phys. A-Math. Theor., 48:33, SI (2015), 335201  crossref  mathscinet  zmath  isi  elib  scopus
    14. Ballesteros A., Enciso A., Herranz F.J., Ragnisco O., Riglioni D., “Exactly Solvable Deformations of the Oscillator and Coulomb Systems and Their Generalization”, Xxxth International Colloquium on Group Theoretical Methods in Physics (Icgtmp) (Group30), Journal of Physics Conference Series, 597, IOP Publishing Ltd, 2015, 012014  crossref  isi  scopus
    15. Latini, D.; Ragnisco, O., “Superintegrable deformations of the KC and HO potentials on curved spaces”, NUOVO CIMENTO C-COLLOQUIA AND COMMUNICATIONS IN PHYSICS, 38:5 (2015), 168  crossref  scopus
    16. Ranada M.F., “Superintegrable systems with a position dependent mass: Kepler-related and oscillator-related systems”, Phys. Lett. A, 380:27-28 (2016), 2204–2210  crossref  mathscinet  zmath  isi  elib  scopus
    17. Carinena J.F., Herranz F.J., Ranada M.F., “Superintegrable systems on 3-dimensional curved spaces: Eisenhart formalism and separability”, J. Math. Phys., 58:2 (2017), 022701  crossref  mathscinet  zmath  isi  scopus
    18. Gubbiotti G., Nucci M.C., “Are all classical superintegrable systems in two-dimensional space linearizable?”, J. Math. Phys., 58:1 (2017), 012902  crossref  mathscinet  zmath  isi  scopus
    19. Ngoc-Hung Phan, Dai-Nam Le, Thoi T.-Q.N., Van-Hoang Le, “Variables Separation and Superintegrability of the Nine-Dimensional Micz-Kepler Problem”, J. Math. Phys., 59:3 (2018), 032102  crossref  mathscinet  zmath  isi  scopus
    20. Ragnisco O., Kuru S., Negro J., Xxv International Conference on Integrable Systems and Quantum Symmetries (Isqs-25), Journal of Physics Conference Series, 965, IOP Publishing Ltd, 2018  crossref  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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