Relating quantum mechanics and kinetics of neutrino oscillations

TL;DR

This paper clarifies the structure of quantum kinetic equations for neutrino oscillations, deriving their form from the Schrödinger equation and demonstrating their consistency with the uncertainty principle, relevant for astrophysical environments like supernovae.

Contribution

It provides a detailed derivation of neutrino kinetic equations from fundamental quantum mechanics and confirms their consistency with the uncertainty principle and wave packet effects.

Findings

Derived the evolution equation for neutrinos from the Schrödinger equation.

Showed the kinetic equation matches known forms in the relativistic limit.

Demonstrated solutions are consistent with the uncertainty principle and wave packet separation.

Abstract

Simultaneous treatment of neutrino oscillations and collisions in astrophysical environments requires the use of (quantum) kinetic equations. Despite major advances in the field of quantum kinetics, the structure of the kinetic equations and their consistency with the uncertainty principle are still debated. The goals of the present work are threefold. First, it clarifies the structure of the Liouville term in the presence of mixing. Second, we derive evolution equation for neutrinos propagating in vacuum or matter from the Schrodinger equation and show that in the relativistic limit its form matches the form of the (collisionless part of the) kinetic equation derived by Sigl and Raffelt. Third, by constructing solutions of the evolution equation from the known solutions of the Schrodinger equation, we show that the former also admits solutions consistent with the uncertainty principle and accounts for neutrino wave packet separation. The obtained results speak in favor of a (quantum) kinetic approach to the analysis of neutrino propagation in exploding supernovae where neutrino oscillations and collisions, as well as the effect of wave packet separation, might be equally important.