  In an interacting neutrino gas, flavor coherence becomes dynamical and can
propagate as a collective mode. In particular, tachyonic instabilities can
appear, leading to "fast flavor conversion" that is independent of neutrino
masses and mixing angles. On the other hand, without neutrino-neutrino
interaction, a prepared wave packet of flavor coherence simply dissipates by
kinematical decoherence of infinitely many non-collective modes. We reexamine
the dispersion relation for fast flavor modes and show that for any
wavenumber,there exists a continuum of non-collective modes besides a few
discrete collective ones. So for any initial wave packet, both decoherence and
collective motion occurs, although the latter typically dominates for a
sufficiently dense gas. We derive explicit eigenfunctions for both collective
and non-collective modes. If the angular mode distribution of electron-lepton
number crosses between positive and negative values, two non-collective modes
can merge to become a tachyonic collective mode. We explicitly calculate the
interaction strength for this critical point. As a corollary we find that a
single crossing always leads to a tachyonic instability. For an even number of
crossings, no instability needs to occur.
