Single-wave solutions of the neutrino fast flavor system. Part I. Mechanical properties

TL;DR

This paper investigates single-wave solutions in the fast neutrino flavor system, revealing their properties, differences from other solutions, and their non-integrability, contributing to understanding collective neutrino flavor evolution.

Contribution

It introduces a comprehensive taxonomy of nonlinear collective flavor solutions, highlighting the unique properties and limitations of single-wave solutions in the fast flavor system.

Findings

Single-wave solutions have homogeneous occupation numbers but spatially varying flavor coherence.

The fast flavor system is not integrable and lacks Gaudin invariants.

Two-beam pendulum solutions are inevitable but do not extend to multi-angle systems.

Abstract

A dense neutrino plasma can exhibit collective flavor evolution caused by neutrino--neutrino refraction. Recently, a new class of exact nonlinear inhomogeneous solutions was discovered: single-wave (SW) solutions of the fast flavor system. The key property is that the flavor occupation numbers remain homogeneous, whereas the field of flavor coherence varies spatially with a single wave vector. The equations of motion for this structure resemble those of a collection of classical spins, in analogy with the homogeneous slow and fast flavor cases. In contrast, the SW system is not integrable (it does not possess Gaudin invariants) so that, while two-beam pendulum solutions are inevitable, they do not extend to a multi-angle system. We develop a taxonomy of all known nonlinear collective flavor solutions, explaining the overlap between categories and their differences.