A kinetic description of neutrino-antineutrino interactions

The collective behaviour of neutrinos and anti neutrinos is analysed within the framework of a semi-classical model. Neutrinos close to thermal equilibrium are described by a coupled system of Schrodinger equations with nonlinear asymmetric selfinteraction potentials. The nonlinearity allows for dark soliton formation. It is shown that the interaction of incoherent neutrinos can be modelled by a coupled system of nonlinear Vlasov equations. The latter is analysed perturbatively, and a dispersion relation is derived.