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We calculate fast conversions of two flavor neutrinos by consideringBoltzmann collisions of neutrino scatterings. In an idealized angulardistribution of neutrinos with electron-lepton number crossing, we find thatthe collision terms of the neutrino scattering enhance the transitionprobability of fast flavor conversions as in the previous study. We analyze thedynamics of fast flavor conversions with collisions in detail based on themotion of polarization vectors in cylindrical coordinate analogous to apendulum motion. The phase of the all polarization vector synchronizes in thelinear evolution, and the phase deviation from the Hamiltonian governs theconversion of neutrino flavor. In the non-linear evolution, a closed orbit inthe phase space is observed. The collision terms break the closed orbit andgradually make the phase space smaller. The flavor conversions are enhancedduring this limit cycle. After the significant flavor conversion, all of theneutrino polarization vectors start to align with the z-axis owing to thecollision effect within the time scale of the collision term irrespective ofneutrino scattering angles. We also show the enhancement or suppression of theflavor conversions in various setups of the collision terms and verifyconsistency with previous studies. Though our analysis does not fullyunderstand the dynamics of fast flavor conversion, the framework gives a newinsight into this complicated phenomenon in further study.

Dynamics of fast neutrino flavor conversions with scattering effects: a detailed analysis