The q-deformed Calogero's Goldfish Systems

2025/04/20 by Umpon Jairuk, Jairuk, Umpon, Thanadon Kongkoom +3 · 1 voice
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons #nlin.SI

paper · pdf · doi:10.48550/arxiv.2504.14644

14 pages

openalex publication_date 2025/04/20 · arxiv published 2025/04/20 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28 · arxiv created 2026/08/03 · arxiv updated 2026/08/03

Abstract

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.

Citations

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• Lagrangian multiforms and multidimensional consistency
• Tsallis' deformation parameter q quantifies the classical-quantum transition
• A new extended q-deformed KP hierarchy
• A q-deformed nonlinear map
• Solution of the One-Dimensional N-Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials

Discussions

• Umpon Jairuk, Thanadon Kongkoom, Sikarin Yoo-Kong: The $q$-deformed Calogero's Goldfish Systems https://arxiv.org/abs/2504.14644 https://arxiv.org/pdf/2504.14644 https://arxiv.org/html/2504.14644 [bsky, 0 points, 1 comments]

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