Quantum Kinetic Equilibrium

We solved the Quantum Kinetic Equations (QKEs) for an active-sterile neutrino system in the early universe. While on the surface this may seem to be an overly simplistic system, other linear two-state systems can be mapped onto the active-sterile system. In the early universe, we find that solutions to the QKEs are well described by an adiabatic approximation where the off-diagonal terms of the density operator are constant on short (oscillation and/or scattering) timescales, but may slowly evolve on long (expansion) timescales. This "quantum kinetic equilibrium" attains as the quantum development of phase balances with the kinetic destruction of phase. In this work, we introduce and assess this equilibrium ansatz as the neutrino states evolve in the early universe with a non-zero lepton number, engendering level crossings that result in scattering-induced active-sterile neutrino transformation.