{
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  "slug": "double-pendulum-as-a-topological-bridge",
  "title": "Double Pendulum as a Topological Bridge",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "The double pendulum serves as the paradigmatic model for the transition from integrability to chaos, yet its potential as a rigorous bridge between classical nonlinear dynamics and quantum open systems remains underutilized. By treating the system’s phase space as a topologically tiled manifold under 2π periodicity, we establish a structural isomorphism between classical Lyapunov instability and quantum decoherence rates. Leveraging recent advances in open quantum system dynamics (Hernández et al., 2025) and topological critical phases (Yu et al., 2026), we demonstrate that classical “flip” events correspond to topological winding number transitions that drive quantum state delocalization. Numerical simulations reveal that the fractal geometry of stability islands quantitatively predicts the resilience of quantum states to environmental coupling, suggesting a novel “decoherence-free” encoding scheme based on Kolmogorov-Arnold-Moser (KAM) tori. These findings unify the deterministic geometry of chaos with the probabilistic nature of quantum mechanics, resolving the Ehrenfest time paradox through a topological gauge argument.",
  "abstract_markdown": "The double pendulum serves as the paradigmatic model for the transition from integrability to chaos, yet its potential as a rigorous bridge between classical nonlinear dynamics and quantum open systems remains underutilized. By treating the system’s phase space as a topologically tiled manifold under \\(2\\pi\\) periodicity, we establish a structural isomorphism between classical Lyapunov instability and quantum decoherence rates. Leveraging recent advances in open quantum system dynamics (Hernández et al., 2025) and topological critical phases (Yu et al., 2026), we demonstrate that classical “flip” events correspond to topological winding number transitions that drive quantum state delocalization. Numerical simulations reveal that the fractal geometry of stability islands quantitatively predicts the resilience of quantum states to environmental coupling, suggesting a novel “decoherence-free” encoding scheme based on Kolmogorov-Arnold-Moser (KAM) tori. These findings unify the deterministic geometry of chaos with the probabilistic nature of quantum mechanics, resolving the Ehrenfest time paradox through a topological gauge argument.",
  "date": "2026-01-01",
  "first_published": "2026-01-01",
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