Non-Boltzmann behaviour in models of interacting neutrinos

Abstract

We reconsider the question of the relative importance of single particle effects and correlations in the solvable interacting neutrino models introduced by Friedland and Lunardini and by Bell, Rawlinson and Sawyer. We show, by an exact calculation, that the two particle correlations are not "small", and that they dominate the time evolution in these models, in spite of indications to the contrary from the rate of equilibration. This result holds even after the model in generalized from the original 2 flavor case to $N$ flavors. The failure of the Boltzmann single particle approximation in this model is tentatively attributed to the simplicity of the model, in particular to the assumption that all neutrinos in the initial state are in flavor eigenstates.