Physics of synchronized neutrino oscillations caused by self-interactions

In the early universe or in some regions of supernovas, the neutrino refractive index is dominated by the neutrinos themselves. Several previous studies have found numerically that these self-interactiuns have the effect of coupling different neutrino modes in such a way as to synchronize the flavor oscillations which otherwise would depend on the energy of a given mode. We provide a simple explanation for this baffling phenomenon in analogy to a system of magnetic dipoles which are coupled by their self-interactions to form one large magnetic dipole which then precesses coherently in a weak external magnetic field. In this picture the synchronized neutrino oscillations are perfectly analogous to the weak-field Zeeman effect in atoms.