Neutrino-antineutrino superfluidity

Despite their feeble interactions, dense astrophysical neutrinos can behave collectively, exchanging flavor through waves of the neutrino plasma. Can collective interactions also induce pairing instabilities and reorganize the neutrino momentum distribution, in analogy to the superfluid instability of fermions? We show that, for standard weak interactions, pairing instabilities can arise only in the presence of discontinuities in the occupation number, such as the sharp Fermi surface responsible for superconductivity in metals. However, discretized energy spectra can mimic such discontinuities and artificially generate superfluid instabilities. These spurious instabilities disappear in the continuum limit.