Further studies on relic neutrino asymmetry generation I: the adiabatic Boltzmann limit, non-adiabatic 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 (QKEs) reduces to the Boltzmann limit that is dependent only on the instantaneous neutrino number densities, 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 to understanding the sharply contrasting resonance behaviours exhibited by the neutrino ensemble in opposing collision regimes. We also present a classical analogue for the evolution of the difference in ${\nu }_{\alpha }$ and ${\nu }_s$ number densities which, in the Boltzmann limit, is akin to the behaviour of the generic reaction $A\rightleftharpoons B$ with equal forward and reverse reaction rate constants. A new characteristic quantity, the matter and collision-affected mixing angle of the neutrino ensemble, is identified here for the first time. The role of collisions is revealed to be twofold: (i) to wipe out the inherent oscillations, and (ii) to equilibrate the ${\nu }_{\alpha }$ and ${\nu }_s$ number densities in the long run. Studies on non-adiabatic evolution and its possible relation to rapid oscillations in lepton number generation also feature, with the introduction of an adiabaticity parameter for collision-affected oscillations.

RevTeX, 38 pages including 8 embedded figures

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• Light Element Signatures of Sterile Neutrinos and Cosmological Lepton Numbers
• Probing secret interactions of eV-scale sterile neutrinos with the diffuse supernova neutrino background
• Sterile neutrino production via active-sterile oscillations: the quantum Zeno effect
• Further studies on relic neutrino asymmetry generation II: a rigorous treatment of repopulation in the adiabatic limit
• Production of a sterile species via active-sterile mixing: an exactly solvable model
• Production of heavy sterile neutrinos from vector boson decay at electroweak temperatures
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• Comment on ``Neutrino oscillations in the early universe: how can large lepton asymmetry be generated?"
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• Chaos, Determinacy and Fractals in Active-Sterile Neutrino Oscillations in the Early Universe
• Relic neutrino asymmetry generation from ${\nu }_{\alpha }-{\nu }_s$ oscillations
• Phenomenological and Cosmological Implications of Neutrino Oscillations
• Neutrino oscillations and Big Bang Nucleosynthesis
• Production of a sterile species: quantum kinetics