  We consider a simplifed model for self-induced flavor conversions of a dense
neutrino gas in two dimensions, showing new solutions that spontaneously break
the spatial symmetries of the initial conditions. As a result of the symmetry
breaking induced by the neutrino-neutrino interactions, the coherent behavior
of the neutrino gas becomes unstable. This instability produces large spatial
variations in the flavor content of the ensemble. Furthermore, it also leads to
the creation of domains of different net lepton number flux. The transition of
the neutrino gas from a coherent to incoherent behavior shows an intriguing
analogy with a streaming flow changing from laminar to turbulent regime. These
finding would be relevant for the self-induced conversions of neutrinos
streaming-off a supernova core.
