Characterizing quasi-steady states of fast neutrino-flavor conversion by stability and conservation laws

The question of what ingredients characterize the quasi-steady state of fast neutrino-flavor conversion (FFC) is one of the long-standing riddles in neutrino oscillation. Addressing this issue is necessary for accurate modeling of neutrino transport in core-collapse supernova and binary neutron star merger. Recent numerical simulations of FFC have shown, however, that the quasi-steady state is sensitively dependent on boundary conditions in space, and the physical reason for the dependence is not clear at present. In this study, we provide a physical interpretation of this issue based on arguments with stability and conservation laws. The stability can be determined by the disappearance of ELN(electron neutrino-lepton number)-XLN(heavy-leptonic one) angular crossings, and we also highlight two conserved quantities characterizing the quasi-steady state of FFC: (1) lepton number conservation along each neutrino trajectory and (2) conservation law associated with angular moments, depending on boundary conditions, for each flavor of neutrinos. We present an analytic prescription that matches the results of the nonlinear simulations presented in this work. This study represents a major step forward a unified picture determining asymptotic states of FFCs.