Further studies on relic neutrino asymmetry generation. I. The adiabatic Boltzmann limit, nonadiabatic evolution, and the classical harmonic oscillator analogue of the quantum kinetic equations

Abstract

We demonstrate that the relic neutrino asymmetry evolution equation derived from the quantum kinetic equations (QKE's) reduces to the Boltzmann limit that is dependent only on the instantaneous neutrino distribution functions, in the adiabatic limit in conjunction with sufficient damping. An original physical and/or geometrical interpretation of the adiabatic approximation is given, which serves as a convenient visual aid for understanding the sharply contrasting resonance behaviors exhibited by the neutrino ensemble in opposing collision regimes. We also present a classical analogue for the evolution of the difference in the vα and vs distribution functions which, in the Boltzmann limit, is..