Time-dependent and quasi-steady features of fast neutrino-flavor conversion

Despite the theoretical indication that fast neutrino-flavor conversion (FFC) ubiquitously occurs in core-collapse supernova and binary neutron star merger, the lack of global simulations has been the greatest obstacle to study their astrophysical consequences. In this {\it Letter}, we present large-scale ($50 {\rm km}$) simulations of FFC in spherical symmetry by using a novel approach. We effectively rescale the oscillation scale of FFC by reducing the number of injected neutrinos in the simulation box, and then extrapolate back to the case of the target density of neutrinos with a convergence study. We find that FFC in all models achieves quasi-steady state in the non-linear regime, and its saturation property of FFC is universal. We also find that temporal- and spatial variations of FFC are smeared out at large radii due to phase cancellation through neutrino self-interactions. Finally, we provide a new diagnostic quantity, ELN-XLN angular crossing, to assess the non-linear saturation of FFC.