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.
