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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 Schrödinger 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.