  Neutrinos drive core-collapse supernovae, launch outflows from neutron star
merger accretion disks, and set the ratio of protons to neutrons in ejecta from
both systems that generate heavy elements in the universe. Neutrinos of
different flavors interact with matter differently, and much recent work has
suggested that fast flavor instabilities are likely ubiquitous in both systems,
but the final flavor content after the instability saturates has not been well
understood. In this work we present particle-in-cell calculations which follow
the evolution of all flavors of neutrinos and antineutrinos through saturation
and kinematic decoherence. We conduct one-dimensional three-flavor simulations
of neutrino quantum kinetics to demonstrate the outcome of this instability in
a few example cases. We demonstrate the growth of both axially symmetric and
asymmetric modes whose wavelength and growth rate match predictions from linear
stability analysis. Finally, we vary the number density, flux magnitude, and
flux direction of the neutrinos and antineutrinos and demonstrate that these
factors modify both the growth rate and post-saturation neutrino flavor
abundances. Weak electron lepton number (ELN) crossings in these simulations
produce both slow growth of the instability and little difference between the
flavor abundances in the initial and final states. In all of these calculations
the same number of neutrinos and antineutrinos change flavor, making the least
abundant between them the limiting factor for post-saturation flavor change.
Many more simulations and multi-dimensional simulations are needed to fully
probe the parameter space of the initial conditions.
