Self-induced decoherence in dense neutrino gases

Dense neutrino gases exhibit collective oscillations where ``self-maintained coherence'' is a characteristic feature, i.e., neutrinos of different energies oscillate with the same frequency. In a nonisotropic gas, however, the flux term of the neutrino-neutrino interaction has the opposite effect of causing kinematical decoherence of neutrinos propagating in different directions, an effect that is at the origin of the ``multiangle behavior'' of neutrinos streaming off a supernova core. We cast the equations of motion in a form where the role of the flux term is manifest. We study in detail the symmetric case of equal neutrino and antineutrino densities where the evolution consists of collective pair conversions (``bipolar oscillations''). A gas of this sort is unstable in that an infinitesimal anisotropy is enough to trigger a runaway towards flavor equipartition. The ``self-maintained coherence'' of a perfectly isotropic gas gives way to ``self-induced decoherence.''