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Dynamical Phase Transitions in models of Collective Neutrino Oscillations

Collective neutrino oscillations can potentially play an important role in transporting lepton flavor in astrophysical scenarios where the neutrino density is large, typical examples are the early universe and supernova explosions. It has been argued in the past that simple models of the neutrino Hamiltonian designed to describe forward scattering can support substantial flavor evolution on very short time scales $t\approx\log(N)/(G_Fρ_ν)$, with $N$ the number of neutrinos, $G_F$ the Fermi constant and $ρ_ν$ the neutrino density. This finding is in tension with results for similar but exactly solvable models for which $t\approx\sqrt{N}/(G_Fρ_ν)$ instead. In this work we provide a coherent explanation of this tension in terms of Dynamical Phase Transitions (DPT) and study the possible impact that a DPT could have in more realistic models of neutrino oscillations and their mean-field approximation.