Jacobi last multiplier and two-dimensional superintegrable oscillators

IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pramana Pub Date : 2024-07-16 DOI:10.1007/s12043-024-02786-3
Akash Sinha, Aritra Ghosh
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Abstract

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 \(\Theta \), ensuring superintegrability. 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 two isolated (non-interacting) one-dimensional oscillators.

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雅可比最后乘法器和二维超可整定振荡器
在本文中,我们研究了雅可比末乘法器在二维振荡器中的作用。我们首先考虑允许可分离哈密顿描述的二维单位质量振荡器,即 \(H = H_1 + H_2\),其中 \(H_1\) 和 \(H_2\) 是两个一维单位质量振荡器的哈密顿。研究表明,存在第三个与函数无关的第一积分 \(\Theta\),确保了超稳定性。我们明确地计算了各种实例。然后,我们考虑了与位置相关的质量振荡器和贝特曼振荡器对,后者由一对耗散线性振荡器组成。值得注意的是,尽管贝特曼振荡器对的哈密尔顿无法分离成两个孤立的(非相互作用的)一维振荡器,但我们发现贝特曼振荡器对是超可integrable 的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Pramana
Pramana 物理-物理:综合
CiteScore
3.60
自引率
7.10%
发文量
206
审稿时长
3 months
期刊介绍: Pramana - Journal of Physics is a monthly research journal in English published by the Indian Academy of Sciences in collaboration with Indian National Science Academy and Indian Physics Association. The journal publishes refereed papers covering current research in Physics, both original contributions - research papers, brief reports or rapid communications - and invited reviews. Pramana also publishes special issues devoted to advances in specific areas of Physics and proceedings of select high quality conferences.
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