Proof Of The Invalidity Of The Boltzmann Property In The FMO Many-Body Neutrino Model

Abstract

There has been recent debate over the use of the Boltzmann property in the kinetic equations describing dense neutrino systems such as early Universe and Supernova core. A technique developed by Bell, Rawlinson, and Sawyer utilises the flavour evolution timescales of the neutrino systems to test the validity of this assumption. The Friedland-McKellar-Okuniewicz (FMO) many-body neutrino model was developed to conduct this test. It was concluded by its authors, using the Bell-Rawlinson-Sawyer timescale test, that the model lent support to the Boltzmann property assumption. We developed kinetic equations for the FMO model. By direct analysis of the kinetic equations we find, in stark contrast to Friedland et al., that in fact the Boltzmann property assumption does breakdown in the FMO model. We have shown that the Bell-Rawlinson-Sawyer timescale technique can only be used to invalidate the Boltzmann property but not validate it.