Spontaneous symmetry breaking in collective neutrino oscillations

We explore the phenomenon of spontaneous symmetry breaking in the
context of collective neutrino flavor oscillations. Namely, we
investigate the spontaneous breaking of isotropy in a homogeneous
gas of neutrinos and of azimuthal isotropy in the context of
core-collapse supernovae. For the homo- geneous gas, a simple
one-dimensional model is analysed in order to demonstrate the
phenomenon and understand the connection to the linearized
stability analysis. The effect is then investigated in the context
of isotropic emission from a supernova core. We show that an
azimuthally isotropic flavor configuration is unstable under the
differential equations of motion. We analyse the linear stability
of propagation in the flavor state and the important consequences
to the general prediction of collective flavor conversion. This
symmetry-breaking instability is sensitive to the ordering of the
neutrino masses.