Spectral splits in many-body simulations of three-flavor collective neutrino oscillations*

When the neutrinos are at high densities, the neutrino-neutrino coherent forward scattering may lead to collective flavor oscillations. This phenomenon is very crucial in understanding the dynamics of core-collapse supernova explosion and the nucleosynthesis in astrophysical environment. The evolution of these oscillations becomes a time-dependent quantum many-body problem. The collective neutrino oscillations have been extensively studied within two-flavor approximations both in mean-field and many-body picture. However, it has been proven by mean-field calculations that all three flavor of neutrinos are crucial to include. Multiple spectral splits have been observed and they significantly depend on the mass ordering of neutrinos. We aim to see if these conclusions from the mean-field approximations persist and how the width of spectral splits changes in the many-body picture. The preliminary results within the many-body picture exhibit some of these features.