Jacobi last multiplier and two-dimensional superintegrable oscillators

Author:

Akash Sinha, Aritra Ghosh

Keyword:

Nonlinear Sciences, Exactly Solvable and Integrable Systems, Exactly Solvable and Integrable Systems (nlin.SI), Mathematical Physics (math-ph), Classical Physics (physics.class-ph)

journal:

date:

2023-06-14 16:00:00

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, and subsequently show 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.

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