The three-body problem, as a century-old challenge in classical mechanics, has been constrained since Poincaré's discovery of its chaotic nature to traditional research focused on high-precision numerical simulations and enumeration of periodic solutions, without yielding a global universal criterion describing the system's transition from regular motion to chaos.
This paper introduces a dimensionless global bound order parameter S∈[0,1]. Through coarse-graining methods derived from Newtonian dynamical equations, we obtain a phenomenological effective field equation describing the evolution of three-body systems. We discover that the regular-to-chaotic transition in three-body systems is fundamentally a second-order topological phase transition, with the critical point precisely located at S≈0.5, where chaotic behavior manifests as critical slowing down and fluctuation amplification effects near the critical point. Through high-precision numerical simulations of classical systems such as the Pythagorean three-body problem and the planar restricted three-body problem, we verify that the order parameter evolution aligns with theoretical predictions at an accuracy ≥95%. We derive the critical scaling law relating the system's Lyapunov exponent to the order parameter: λ∼∣S−0.5∣^(−ν) , with critical exponent ν≈0.88, which is entirely consistent with the three-dimensional percolation universality class.
Finally, we propose a tabletop experimental scheme based on coupled Josephson junctions, presenting verifiable predictions of critical behavior. This work provides a novel universal framework for the global analysis of many-body chaotic systems.
关键词
三体问题/混沌动力学/临界现象/序参量/粗粒化方法/有效场论
Key words
Three-Body Problem/ Chaotic Dynamics/ Critical Phenomena/ Order Parameter/ Coarse-Graining Method/ Effective Field Theory
国家预印本平台
评论