Synchronization versus decoherence of neutrino oscillations at intermediate densities

We study collective oscillations of a two-flavor neutrino system with arbitrary but fixed density. In the vacuum limit, modes with different energies quickly dephase (kinematical decoherence), whereas in the limit of infinite density they lock to each other (synchronization). For intermediate densities, we find different classes of solutions. There is always a phase transition in the sense of partial synchronization occurring only above a density threshold. For small mixing angles, partial or complete decoherence can be induced by a parametric resonance, introducing a new time scale to the problem, the final outcome depending on the spectrum and mixing angle. We derive an analytic relation that allows us to calculate the late-time degree of coherence based on the spectrum alone.