Implications of conservation laws and ergodicity for neutrino flavor instability

Collective neutrino flavor instabilities are believed to be prevalent in core-collapse supernovae and neutron star mergers. This work establishes two points related to instability, both in the spirit of developing a more fundamental understanding of collective flavor dynamics. First, a conservation law related to lepton number implies that spectral crossings are necessary for instability. Second, the most permissive application of the ergodic hypothesis to neutrino flavor evolution implies that spectral crossings are in fact sufficient for instability. We also discuss flavor thermalization and energy conservation in relation to ergodicity.