One-parameter discrete-time Calogero-Moser system

Umpon Jairuk; Sikarin Yoo-Kong

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arXiv · 2305.18168

One-parameter discrete-time Calogero-Moser system

Umpon Jairuk·Sikarin Yoo-Kong

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Abstract

We present a new type of integrable one-dimensional many-body systems called a one-parameter Calogero-Moser (CM) system. In the discrete level, the Lax pairs with a parameter are introduced and, of course, the discrete-time equations of motion are obtained as well as their corresponding discrete-time Lagrangian. The integrability feature of this new system can be captured through the discrete Lagrangian closure relation by employing a connection with the temporal Lax matrices of the discrete-time Ruijsenaars-Schneider (RS) system, exact solution, and the existence of the classical r-matrix. Under the appropriate limit on the parameter, which in this case is approaching zero, the standard CM system is retrieved both discrete-time and continuous-time.

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BibTeX RIS

Umpon Jairuk, Sikarin Yoo-Kong. 2023-05-29. One-parameter discrete-time Calogero-Moser system. https://arxiv.org/abs/2305.18168

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