Stability of Collective Neutrino Oscillations -- A Distributional Approach
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→∞, we derive an exact nonlinear Fokker--Planck (continuity) equation for the one-body distribution F(S⃗,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.
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BibTeX
@misc{majumder2026stability,
title = {{Stability of Collective Neutrino Oscillations -- A Distributional Approach}},
author = {Rupak Majumder and Dwaipayan Mukherjee and Shamik Gupta and Basudeb Dasgupta},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04441},
eprint = {2609.04441},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04441},
}
RIS
TY - UNPB
TI - Stability of Collective Neutrino Oscillations -- A Distributional Approach
AU - Rupak Majumder
AU - Dwaipayan Mukherjee
AU - Shamik Gupta
AU - Basudeb Dasgupta
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.04441
UR - https://arxiv.org/abs/2609.04441
AB - 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→∞, we derive an exact nonlinear Fokker--Planck (continuity) equation for the one-body distribution F(S⃗,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.
ER -