Speaker
Description
A dense neutrino gas can exhibit collective flavor oscillations, driven by neutrino–neutrino forward scattering, which profoundly affect flavor evolution in core-collapse supernovae and the early Universe. While numerous studies have shown that a zero crossing in the difference of flavor distributions ($g_{\Gamma}$) of neutrinos determines the existence and character of instabilities, a rigorous criterion applicable to a general distribution function has not yet been established. In our work (arXiv:2505.03886), we propose a set of sufficient (and necessary) conditions on the local and global properties of phase-space distribution that, when satisfied, guarantee the existence of unstable collective modes. By mapping the dispersion relation onto a complex contour and invoking the Nyquist theorem, we generalize the Penrose criteria in plasma physics to this context. We illustrate the conditions with analytical examples in some special cases and a general case that demonstrates how crossings in $g_{\Gamma}$ correspond directly to encirclements of the origin and hence to flavor-instability growth. Our study provides a framework for predicting fast, slow, and mixed collective oscillations for certain initial distribution functions.
