3D Stochastic Helix Dynamics 三维随机螺旋动力学

摘要本文建立三维数空间 𝕋 上的随机螺旋动力学理论。将光子、引力波等三维数螺旋运动推广到随机涨落环境,给出三维布朗螺旋随机过程的定义及其随机微分方程(SDE)。理论证明:在黄金比例耗散驱动下,δ 分量的稳态概率密度严格满足 ρ(δ)=C·e-δ/φ(φ 为黄金分割常数),自相关函数精确为 AC(τ)=e-|τ|/φ。提出中道随机均值作为处理多路径随机演化的工具,并证明中道偏差守恒律。全部结论通过大样本数值实验验证。关键词:三维数;随机螺旋动力学;黄金分割;Ornstein-Uhlenbeck 过程;自相关;中道均值 AbstractThis paper establishes the theory of stochastic helix dynamics on the 3D number space 𝕋, extending the deterministic helical motion of photons/gravitational waves to fluctuating environments. We define a 3D Brownian helix SDE and prove that under golden-ratio dissipation, the δ-component steady-state density is ρ(δ)=C·e-δ/φ and the autocorrelation is AC(τ)=e-|τ|/φ (φ the golden ratio). We introduce the middle-path ensemble mean to handle multi-trajectory stochastic evolution and prove the middle-deviation conservation law. All results are verified by large-sample numerical experiments.