Dynamical phase transitions in models of collective neutrino oscillations

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