Integrability-breaking phase transitions in stadium-like billiards
Abstract
We investigate integrability-breaking transitions in two classes of stadium-like billiards with parabolic boundaries. While focusing boundaries generate a mixed phase space in which regular islands coexist with a chaotic sea, dispersing boundaries produce a fully chaotic phase space for any finite boundary deformation. By analyzing the scaling behavior of the roughness ω, we identify two qualitatively distinct transitions: a continuous transition for the focusing geometry and a first-order transition for the dispersing one. We determine the corresponding critical exponents and establish the associated scaling laws. For the continuous transition, we further provide a complete characterization within the framework of critical phenomena by identifying the broken symmetry, the order parameter and its diverging susceptibility, the elementary excitations responsible for chaotic diffusion, and the topological defects governing transport. These results establish a statistical-mechanics framework for describing integrability-breaking transitions in Hamiltonian billiards and suggest that the concepts of critical phenomena naturally extend to deterministic nonlinear dynamical systems.
Versions
Related
- First-order integrability-breaking phase transitions in dynamical systems
- Breaking of integrability in elliptic deformations of AdS3 strings with mixed flux
- Optimal limits on weak integrability breaking and protected thermal memory near qutrit exchange
- Fractionalization-Induced Time-Reversal Symmetry Breaking at Continuous Superconducting Transitions in Low-Symmetry Kondo Lattices
- Ginzburg-Landau Theory for Non-Invertible Symmetry-Breaking Transitions
BibTeX
@misc{fonseca2026integrabilitybreaking,
title = {{Integrability-breaking phase transitions in stadium-like billiards}},
author = {Anne Kétri P. da Fonseca and Edson D. Leonel},
howpublished = {arXiv},
year = {2026},
month = jul,
doi = {10.48550/arxiv.2607.16482},
eprint = {2607.16482},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.16482},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Integrability-breaking phase transitions in stadium-like billiards
AU - Anne Kétri P. da Fonseca
AU - Edson D. Leonel
PY - 2026
DA - 2026/07/17
PB - arXiv
DO - 10.48550/arxiv.2607.16482
UR - https://arxiv.org/abs/2607.16482
AB - We investigate integrability-breaking transitions in two classes of stadium-like billiards with parabolic boundaries. While focusing boundaries generate a mixed phase space in which regular islands coexist with a chaotic sea, dispersing boundaries produce a fully chaotic phase space for any finite boundary deformation. By analyzing the scaling behavior of the roughness ω, we identify two qualitatively distinct transitions: a continuous transition for the focusing geometry and a first-order transition for the dispersing one. We determine the corresponding critical exponents and establish the associated scaling laws. For the continuous transition, we further provide a complete characterization within the framework of critical phenomena by identifying the broken symmetry, the order parameter and its diverging susceptibility, the elementary excitations responsible for chaotic diffusion, and the topological defects governing transport. These results establish a statistical-mechanics framework for describing integrability-breaking transitions in Hamiltonian billiards and suggest that the concepts of critical phenomena naturally extend to deterministic nonlinear dynamical systems.
ER -