发表机构
Tata Institute of Fundamental Research（塔塔基础研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究采用基于Kuramoto同步统计力学的分布方法，推导中微子味极化矢量系综的非线性Fokker-Planck方程，分析其定态解的稳定性，所得本征值条件可推广至任意初始分布，还重现了双束模型的同步阈值并给出稳定性相图。
AI 中文摘要
我们利用基于Kuramoto同步统计力学的分布方法研究集体中微子振荡的稳定性。在热力学极限N→∞下处理中微子味极化矢量系综，我们推导了味球上单体分布F(𝐒⃗,ω,t)的精确非线性Fokker-Planck（连续性）方程。该方程容许双参数族的轴对称定态解，我们通过对其线性化分析这些解的稳定性。所得本征值条件决定了来自任意初始分布（不仅是接近完全味相干的态）的小扰动的增长或衰减率，从而显著超越了集体模式的常规线性稳定性分析。在特殊极限下，该条件重现了双束模型中已知的同步阈值，为该框架提供了非平凡验证。我们给出本征值方程的解析结果，并探究了与物理相关的频率分布的稳定性相图。
英文摘要
We study the stability of collective neutrino oscillations using a distributional approach motivated by the statistical mechanics of Kuramoto synchronization. Treating the ensemble of neutrino flavor polarization vectors in the thermodynamic limit $N\to\infty$, we derive an exact nonlinear Fokker--Planck (continuity) equation for the one-body distribution $F(\vec{\mathbf{S}},ω,t)$ on the flavor sphere. This equation admits a two-parameter family of azimuthally symmetric stationary solutions, whose stability we analyze by linearizing around them. The resulting eigenvalue condition determines the growth or decay rate of small perturbations from \emph{any} initial distribution -- not merely from a state close to full flavor coherence -- thereby going significantly beyond the conventional linear stability analysis of collective modes. In special limits the condition reproduces known synchronization thresholds in the two-beam model, providing a non-trivial check of the framework. We present analytical results for the eigenvalue equation and explore stability phase diagrams for physically relevant frequency distributions.
Comments17 pages, 5 figures
