We present the first calculations with three flavors of collective and shock wave effects for neutrino propagation in core-collapse supernovae using hydrodynamical density profiles and the S matrix formalism. We explore the interplay between the neutrino-neutrino interaction and the effects of multiple resonances upon the time signal of positrons in supernova observatories. A specific signature is found for the inverted hierarchy and a large third neutrino mixing angle and we predict, in this case, a dearth of lower energy positrons in Cherenkov detectors midway through the neutrino signal and the simultaneous revelation of valuable information about the original fluxes. We show that this feature is also observable with current generation neutrino detectors at the level of several sigmas.

We explore CP violation effects on the neutrino propagation in dense environments, such as in core-collapse supernovae, where the neutrino self-interaction induces non-linear evolution equations. We demonstrate that the electron (anti)neutrino fluxes are not sensitive to the CP violating phase if the muon and tau neutrinos interact similarly with matter. On the other hand, we numerically show that new features arise, because of the non-linearity and the flux dependence of the evolution equations, when the muon and tau neutrinos have different fluxes at the neutrinosphere (due to loop corrections or of physics beyond the Standard Model). In particular, the electron (anti)neutrino probabilities and fluxes depend upon the CP violating phase. We also discuss the CP effects induced by radiative corrections to the neutrino refractive index.