Simulation of coherent nonlinear neutrino flavor transformation in the supernova environment: Correlated neutrino trajectories

We present results of large-scale numerical simulations of the evolution of neutrino and antineutrino flavors in the region above the late-time post-supernova-explosion proto-neutron star. Our calculations are the first to allow explicit flavor evolution histories on different neutrino trajectories and to self-consistently couple flavor development on these trajectories through forward scattering-induced quantum coupling. Employing the atmospheric-scale neutrino mass-squared difference ($|\ensuremath{\delta}{m}^{2}|\ensuremath{\simeq}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\text{ }\text{ }{\mathrm{eV}}^{2}$) and values of ${\ensuremath{\theta}}_{13}$ allowed by current bounds, we find transformation of neutrino and antineutrino flavors over broad ranges of energy and luminosity in roughly the ``bi-polar'' collective mode. We find that this large-scale flavor conversion, largely driven by the flavor off-diagonal neutrino-neutrino forward scattering potential, sets in much closer to the proto-neutron star than simple estimates based on flavor-diagonal potentials and Mikheyev-Smirnov-Wolfenstein evolution would indicate. In turn, this suggests that models of $r$-process nucleosynthesis sited in the neutrino-driven wind could be affected substantially by active-active neutrino flavor mixing, even with the small measured neutrino mass-squared differences.