Spontaneous symmetry breaking in collective neutrino oscillations
b'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.'