  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.
