N-mode coherence in collective neutrino oscillations

TL;DR

This paper investigates collective neutrino oscillations in a homogeneous ensemble, revealing self-maintained coherence modes and providing an analytic solution for bimodal coherence relevant to supernova neutrino spectra.

Contribution

It introduces a classification of collective oscillation modes by the number of independent functions and derives an analytic solution for two-mode coherence.

Findings

Existence of self-maintained coherence modes in neutrino ensembles

Equivalence between continuous and discrete energy ensembles for analysis

Analytic solution for bimodal coherence in supernova neutrinos

Abstract

We study two-flavor neutrino oscillations in a homogeneous and isotropic ensemble under the influence of neutrino-neutrino interactions. For any density there exist forms of collective oscillations that show self-maintained coherence. They can be classified by a number N of linearly independent functions that describe all neutrino modes as linear superpositions. What is more, the dynamics is equivalent to another ensemble with the same effective density, consisting of N modes with discrete energies E_i with i=1, ..., N. We use this equivalence to derive the analytic solution for two-mode (bimodal) coherence, relevant for spectral-split formation in supernova neutrinos.