Non equilibrium dynamics of mixing, oscillations and equilibration: a model study

The non-equilibrium dynamics of mixing, oscillations and equilibration is studied in a field theory of flavored neutral mesons that effectively models two flavors of mixed neutrinos, in interaction with other mesons that represent a thermal bath of hadrons or quarks and charged leptons. This model describes the general features of neutrino mixing and relaxation via charged currents in a medium. The reduced density matrix and the non-equilibrium effective action that describes the propagation of neutrinos is obtained by integrating out the bath degrees of freedom. We obtain the dispersion relations, mixing angles and relaxation rates of ``neutrino'' quasiparticles. The dispersion relations and mixing angles are of the same form as those of neutrinos in the medium, and the relaxation rates are given by $\Gamma_1(k) = \Gamma_{ee}(k) cos^2\theta_m(k)+\Gamma_{\mu\mu}(k)\sin^2\theta_m(k) ; \Gamma_2(k)=\Gamma_{\mu\mu}(k) \cos^2\theta_m(k)+\Gamma_{ee}(k)\sin^2\theta_m(k)$ where $\Gamma_{\alpha\alpha}(k)$ are the relaxation rates of the flavor fields in \emph{absence} of mixing, and $\theta_m(k)$ is the mixing angle in the medium. A Weisskopf-Wigner approximation that describes the asymptotic time evolution in terms of a non-hermitian Hamiltonian is derived. At long time $>>\Gamma^{-1}_{1,2}$ ``neutrinos'' equilibrate with the bath. The equilibrium density matrix is nearly diagonal in the basis of the \emph{mass eigenstates in the medium} with perturbatively small off diagonal elements in this basis. The diagonal elements are determined by the distribution function of the mass eigenstates in the medium. The equilibration of ``sterile neutrinos'' via active-sterile mixing is discussed