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arXiv · 2609.04441

Stability of Collective Neutrino Oscillations -- A Distributional Approach

Rupak Majumder·Dwaipayan Mukherjee·Shamik Gupta·Basudeb Dasgupta
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Abstract

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 $F(\vec{\mathbf{S}},\omega,t)$ 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.

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Rupak Majumder, Dwaipayan Mukherjee, Shamik Gupta, Basudeb Dasgupta. 2026-09-03. Stability of Collective Neutrino Oscillations -- A Distributional Approach. https://arxiv.org/abs/2609.04441

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