The $q$-deformed Calogero's Goldfish Systems
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913806422114304 |
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| author | Jairuk, Umpon Kongkoom, Thanadon Yoo-Kong, Sikarin |
| author_facet | Jairuk, Umpon Kongkoom, Thanadon Yoo-Kong, Sikarin |
| contents | Searching for integrable models is a central theme in theoretical and mathematical physics, as such systems offer valuable insights into the underlying structure and symmetries of complex physical phenomena. In this work, we contribute to this pursuit by proposing a new class of one-dimensional many-body integrable systems, which we refer to as the $q$-deformed Calogero's Goldfish system. Our construction employs $q$-deformation of logarithmic and exponential functions inspired by Tsallis' formalism in non-extensive statistical mechanics. Notably, the model satisfies the double-zero condition on its solutions, underscoring its integrable nature and offering a novel perspective on deformation techniques within exactly solvable systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14644 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $q$-deformed Calogero's Goldfish Systems Jairuk, Umpon Kongkoom, Thanadon Yoo-Kong, Sikarin Exactly Solvable and Integrable Systems Searching for integrable models is a central theme in theoretical and mathematical physics, as such systems offer valuable insights into the underlying structure and symmetries of complex physical phenomena. In this work, we contribute to this pursuit by proposing a new class of one-dimensional many-body integrable systems, which we refer to as the $q$-deformed Calogero's Goldfish system. Our construction employs $q$-deformation of logarithmic and exponential functions inspired by Tsallis' formalism in non-extensive statistical mechanics. Notably, the model satisfies the double-zero condition on its solutions, underscoring its integrable nature and offering a novel perspective on deformation techniques within exactly solvable systems. |
| title | The $q$-deformed Calogero's Goldfish Systems |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2504.14644 |