Nonequilibrium dynamics of mixing, oscillations, and equilibration : A model study

The nonequilibrium 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 nonequilibrium 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 ${\ensuremath{\Gamma}}_{1}(k)={\ensuremath{\Gamma}}_{ee}(k){cos }^{2}{\ensuremath{\theta}}_{m}(k)+{\ensuremath{\Gamma}}_{\ensuremath{\mu}\ensuremath{\mu}}(k){sin }^{2}{\ensuremath{\theta}}_{m}(k)$; ${\ensuremath{\Gamma}}_{2}(k)={\ensuremath{\Gamma}}_{\ensuremath{\mu}\ensuremath{\mu}}(k){cos }^{2}{\ensuremath{\theta}}_{m}(k)+{\ensuremath{\Gamma}}_{ee}(k){sin }^{2}{\ensuremath{\theta}}_{m}(k)$ where ${\ensuremath{\Gamma}}_{\ensuremath{\alpha}\ensuremath{\alpha}}(k)$ are the relaxation rates of the flavor fields in absence of mixing, and ${\ensuremath{\theta}}_{m}(k)$ 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 $\ensuremath{\gg}{\ensuremath{\Gamma}}_{1,2}^{\ensuremath{-}1}$ neutrinos equilibrate with the bath. The equilibrium density matrix is nearly diagonal in the basis of eigenstates of an effective Hamiltonian that includes self-energy corrections in the medium. The equilibration of ``sterile neutrinos'' via active-sterile mixing is discussed.