Controlled kinetic theory beyond the linear regime
Develop a controlled kinetic description of dense neutrino plasmas beyond the linear regime that determines the validity of quasi-linear theory, treats interacting or degenerate flavomon modes, and incorporates propagation in inhomogeneous media.
References
What is the controlled kinetic description beyond the linear regime? The quasi-linear approximation has met some success, and has especially provided an intuitive understanding of saturation. However, its quantitative validity needs to be tested systematically. When may the waves be treated as weakly interacting quasiparticles? When is their evolution slow compared with their oscillation period? How should broad, overlapping, or nearly degenerate modes be treated? In an inhomogeneous medium, this description must moreover be joined to a WKB theory of flavor-wave propagation.
What is the nature of seeding? Mass-induced mixing triggers flavor instabilities, but the amount of power that goes into inhomogeneous modes at the scale of the flavomon wavelength depends on the classical, hydrodynamical turbulence at these scales, well below the neutrino mean free path. It may also be that the increase in wavenumber caused by matter inhomogeneity in Eq.~\ref{eq:WKB_equations} allows large-scale fluctuations to develop into small-scale unstable modes. Thermal fluctuations may of course also provide a seeding mechanism. Finally, seeding by quantum fluctuations, i.e. from higher-order correlators in the BBGKY hierarchy is an additional, often forgotten contribution. This effect is not included in the standard kinetic equations, but present in the neutrino-flavomon kinetic equations, corresponding to the spontaneous flavomon emission. Which contribution is the most important remains an open question;
However, how generic such a prediction would be in a space and time-dependent environment is not at all clear, see the examples in Ref..
A direct solution of these equations remains to be achieved, and may offer additional challenges, e.g. the passage through exceptional points where multiple branches of modes cross together, a difficulty emphasized by Johns and Kost.