Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 26 min ago
PreprintCC BY 4.0arXiv

First-Order Transition to Chaos with Critical Slowing Down

  • Anne Ketri P. da Fonseca
  • Marcelo de Almeida Presotto
  • Diego F. M. Oliveira
  • Edson D. Leonel
Open at sourcePDFDOICite

Abstract

Can the transition from integrability to chaos be discontinuous? We show that it can, and that the resulting first-order dynamical transition coexists with critical slowing down. Using an analytically tractable confined random walk and a deterministic stadium-like billiard, we find a finite jump of the stationary diffusive observable at the transition while the relaxation time diverges. Both systems display normal diffusion and the same exponent set (α,β,z)=(0,1/2,−2). We trace this agreement to a common coarse-grained mechanism: diffusion in a finite accessible domain with a diffusion coefficient that vanishes quadratically with the perturbation. The results identify a discontinuous route from integrability to chaos and provide evidence for a broader universality class of first-order dynamical transitions.

Related

  1. Stochastic model of elongation-shortening-switching kinetics of a polymeric filament: Critical slowing down of first-passage and finite-size regularization
    Manvendra Singh, Ashok Garai, Debashish Chowdhury
    arXivPreprintarXiv licenceFull textBiological & medical physicsCondensed matterarXiv
  2. Manipulating the stability of crystallographic and magnetic sub-lattices: A first-order magnetoelastic transformation in transition metal based Laves phase
    H. Yibole, A.K. Pathak, Y. Mudryk +5
    Acta MaterialiaPeer-reviewedLicence not stated49 citedMaterials & polymersGeneral physicsHAL
  3. "Ultra-weak" First-Order Phase Transition in Biaxial Liquid Crystals
    Soumyajit Pramanick, Mrinal Kanti Debnath, Nababrata Ghoshal +2
    arXivPreprintCC BY 4.0Full textCondensed matterarXiv
  4. Parameter dependence of the mapping of the mean-field Ising model onto QCD in the first-order phase transition regime
    Xue Pan, Yuepeng Li
    arXivPreprintCC BY 4.0Full textHigh-energy & particle physicsNuclear physicsarXiv
  5. Enhancing Gravitational Waves from Global Strings via a First-Order Phase Transition
    Yongtao Jia, Ligong Bian, Huai-Ke Guo
    arXivPreprintCC BY 4.0Full textCosmologyHigh-energy & particle physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{fonseca2026firstorder,
  title = {{First-Order Transition to Chaos with Critical Slowing Down}},
  author = {Anne Ketri P. da Fonseca and Marcelo de Almeida Presotto and Diego F. M. Oliveira and Edson D. Leonel},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13614},
  eprint = {2609.13614},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13614},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - First-Order Transition to Chaos with Critical Slowing Down
AU  - Anne Ketri P. da Fonseca
AU  - Marcelo de Almeida Presotto
AU  - Diego F. M. Oliveira
AU  - Edson D. Leonel
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2609.13614
UR  - https://arxiv.org/abs/2609.13614
AB  - Can the transition from integrability to chaos be discontinuous? We show that it can, and that the resulting first-order dynamical transition coexists with critical slowing down. Using an analytically tractable confined random walk and a deterministic stadium-like billiard, we find a finite jump of the stationary diffusive observable at the transition while the relaxation time diverges. Both systems display normal diffusion and the same exponent set (α,β,z)=(0,1/2,−2). We trace this agreement to a common coarse-grained mechanism: diffusion in a finite accessible domain with a diffusion coefficient that vanishes quadratically with the perturbation. The results identify a discontinuous route from integrability to chaos and provide evidence for a broader universality class of first-order dynamical transitions.
ER  -