Adiabatic & non-adiabatic perturbation theory for coherence vector description of neutrino oscillations

TL;DR

This paper introduces a unified quantum kinetic approach to neutrino oscillations at finite temperature, addressing limitations of the wave function method and providing a basis for including decoherence effects.

Contribution

It develops a novel framework using Magnus expansion for adiabatic and non-adiabatic neutrino oscillations in thermal ensembles, extending the theoretical tools available.

Findings

Formal solution of Quantum Kinetic Equations using Magnus expansion

Identification of parameters like effective oscillation length

Potential for incorporating decoherence effects

Abstract

The standard wave function approach for the treatment of neutrino oscillations fails in situations where quantum ensembles at a finite temperature with or without an interacting background plasma are encountered. As a first step to treat such phenomena in a novel way, we propose a unified approach to both adiabatic and non-adiabatic two-flavor oscillations in neutrino ensembles with finite temperature and generic (e.g. matter) potentials. Neglecting effects of ensemble decoherence for now we study the evolution of a neutrino ensemble governed by the associated Quantum Kinetic Equations, which apply to systems with finite temperature. The Quantum Kinetic Equations are solved formally using the Magnus expansion and it is shown that a convenient choice of the quantum mechanical picture (e.g. the interaction picture) reveals suitable parameters to characterize the physics of the underlying system (e.g. an effective oscillation length). It is understood that this method also provides a promising starting point for the treatment of the more general case in which decoherence is taken into account.