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We investigate toy models for spatial and temporal instabilities in collective neutrino oscillations induced by neutrino self-interactions, with special emphasis on inhomogeneous systems with densities following a profile. Simulations are based on a Mathematica program that solves the Liouville equation with or without vacuum terms, refractive terms from a background medium, and neutrino-neutrino forward scattering, in one space dimension and in time. A discrete number of momentum modes are characterized by the neutrino velocity projection on the spatial direction. We also consider the effects of charged current interaction source terms and neutral current scattering contributions. We find that refractive effects from the medium, in particular for density distributions with a profile, and neutral current nonforward scattering off the background medium can strongly influence fast collective flavor transformations. Specifically we find that if both are present, fast flavor conversions can be strongly suppressed or at least delayed.
G. Sigl (Thu,) studied this question.
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