AI 中文总结
该研究在无碰撞磁化等离子体中，通过轴向根与极化混合公式预测外尔奇异环的离轴半径，经五次扫描验证其与非线性二重根半径偏差小于0.12%，揭示了延迟响应束的拓扑特性。
AI 中文摘要
消除连续自由度会将保守动力学转化为色散性的非厄米响应，其拓扑结构无需表征因果选择的动力学。在无碰撞磁化等离子体中，延迟朗道共振和回旋共振以不同方式阻尼两个外尔模，并将冷外尔点替换为奇异环。轴向根和根归一化极化混合可预测其离轴半径，公式为$R_{\rm EP}^{\rm pred}=|\triangle\boldsymbol{\rm \u0393}|/(2|v_{\rm mix}|)$，且无需计算任何二重根。在覆盖310倍差阻尼范围的五次非相对论扫描中，$R_{\rm EP}^{\rm pred}$与非线性二重根半径$R_{\rm EP}^{\rm full}$的偏差在0.12%以内。所选延迟动力学响应束是电根线丛上的连续图，在给定条件下具有相同的第一陈类。冷界面模延续为局域化的Keldysh极点，在测试的线隙窗口中有一个定向交叉，与继承的电荷一致。
英文摘要
Eliminating continuum degrees of freedom converts conservative dynamics into a dispersive, non-Hermitian response whose topology need not represent the causally selected kinetic dynamics. In collisionless magnetized plasma, retarded Landau and cyclotron resonances damp two Weyl modes differently and replace a cold Weyl point by an exceptional ring. Axial roots and root-normalized polarization mixing predict its off-axis radius, $R_{\rm EP}^{\rm pred}=|ΔΓ|/(2|v_{\rm mix}|)$, before any double root is computed. Across five nonrelativistic scans spanning a 310-fold range of differential damping, $R_{\rm EP}^{\rm pred}$ agrees with the nonlinear double-root radius $R_{\rm EP}^{\rm full}$ within $0.12\%$. The selected retarded kinetic-response bundle is a continuous graph over the electric root line bundle and has the same first Chern class under stated conditions. The cold interface mode continues to a localized Keldysh pole with one oriented crossing in the tested line-gap window, consistent with the inherited charge.
Comments6 pages, 2 figures; Supplemental Material appended. Data and code are available at https://doi.org/10.5281/zenodo.22020911
