تقرير
Jacobi last multiplier and two-dimensional superintegrable oscillators
| العنوان: | Jacobi last multiplier and two-dimensional superintegrable oscillators |
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| المؤلفون: | Sinha, Akash, Ghosh, Aritra |
| المصدر: | Pramana 98, 101 (2024) |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics Mathematical Physics Nonlinear Sciences Physics (Other) |
| مصطلحات موضوعية: | Nonlinear Sciences - Exactly Solvable and Integrable Systems, Mathematical Physics, Physics - Classical Physics |
| الوصف: | In this paper, we examine the role of the Jacobi last multiplier in the context of two-dimensional oscillators. We first consider two-dimensional unit-mass oscillators admitting a separable Hamiltonian description, i.e., $H = H_1 + H_2$, where $H_1$ and $H_2$ are the Hamiltonians of two one-dimensional unit-mass oscillators; it is shown that there exists a third functionally-independent first integral $\Theta$, thereby ensuring superintegrablility. Various examples are explicitly worked out. We then consider position-dependent-mass oscillators and the Bateman pair, where the latter consists of a pair of dissipative linear oscillators. Quite remarkably, the Bateman pair is found to be superintegrable, despite admitting a Hamiltonian which cannot be separated into those of two isolated (non-interacting) one-dimensional oscillators. Comment: v1: Preliminary version, comments are welcome; v2: Revised version with some new examples and few errors corrected; V3: To appear in Pramana |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s12043-024-02786-3 |
| URL الوصول: | http://arxiv.org/abs/2306.08837 |
| رقم الأكسشن: | edsarx.2306.08837 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/s12043-024-02786-3 |
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