The Liouville equation for flavour evolution of neutrinos and neutrino wave packets

Abstract

We consider several aspects related to the form, derivation and applications of the Liouville equation (LE) for flavour evolution of neutrinos. To take into account the quantum nature of neutrinos we derive the evolution equation for the matrix of densities using wave packets instead of Wigner functions. The obtained equation differs from the standard LE by an additional term which is proportional to the difference of group velocities. We show that this term describes loss of the propagation coherence in the system. In absence of inelastic collisions, the LE can be reduced to a single derivative equation over a trajectory coordinate. Additional time and spacial dependence may steam from initial (production) conditions. The transition from single neutrino evolution to the evolution of a neutrino gas is considered.

arXiv comment17 pages

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• Fast Neutrino Flavor Conversion: Collective Motion vs. Decoherence
• Liouville term for neutrinos: Flavor structure and wave interpretation
• Astrophysical neutrino oscillations after pulsar timing array analyses
• Insights into neutrino decoupling gleaned from considerations of the role of electron mass
• Microscopic and Macroscopic Effects in the Decoherence of Neutrino Oscillations
• Relating quantum mechanics and kinetics of neutrino oscillations
• Spin-Flavor Precession Phase Effects in Supernova
• Accounting for the Heisenberg and Pauli principles in the kinetic approach to neutrino oscillations