Slow and fast collective neutrino oscillations: Invariants and reciprocity

Abstract

The flavor evolution of a neutrino gas can show ''slow'' or ''fast'' collective motion. In terms of the usual Bloch vectors to describe the mean-field density matrices of a homogeneous neutrino gas, the slow two-flavor equations of motion (EOMs) are ${\dot{\mathbf{P}}}_{\omega }=(\omega \mathbf{B}+\mu \mathbf{P})\times {\mathbf{P}}_{\omega }$, where $\omega =\Delta m^2/2E$, $\mu =\sqrt{2}{G}_{\mathrm{F}}(n_{\nu }+n_{\bar{\nu }})$, $\mathbf{B}$ is a unit vector in the mass direction in flavor space, and $\mathbf{P}=\int d\omega {\mathbf{P}}_{\omega }$. For an axisymmetric angle distribution, the fast EOMs are ${\dot{\mathbf{D}}}_v=\mu ({\mathbf{D}}_0-v{\mathbf{D}}_1)\times {\mathbf{D}}_v$, where ${\mathbf{D}}_v$ is the Bloch vector for lepton number, $v=\cos \theta$ is the velocity along the symmetry axis, ${\mathbf{D}}_0=\int dv{\mathbf{D}}_v$, and ${\mathbf{D}}_1=\int dvv{\mathbf{D}}_v$. We discuss similarities and differences between these generic cases. Both systems can have pendulum-like instabilities (soliton solutions), both have similar Gaudin invariants, and both are integrable in the classical and quantum case. Describing fast oscillations in a frame comoving with ${\mathbf{D}}_1$ (which itself may execute pendulum-like motions) leads to transformed EOMs that are equivalent to an abstract slow system. These conclusions carry over to three flavors.

16 pages; post-publication corrected treatment of Lax vectors and Gaudin invariants, especially for three-flavor case. Matching the corrections in the Erratum accepted on PRD

References in corpus (8)

• Multiple Spectral Splits of Supernova Neutrinos
• Fast Pairwise Conversion of Supernova Neutrinos: A Dispersion-Relation Approach
• Analysis of Collective Neutrino Flavor Transformation in Supernovae
• Neutrino oscillations in supernovae: angular moments and fast instabilities
• Fast neutrino flavor instability and neutrino flavor lepton number crossings
• Neutrino Flavor Pendulum Reloaded: The Case of Fast Pairwise Conversion
• Collective Neutrino Flavor Instability Requires a Crossing
• Normal and anomalous solitons in the theory of dynamical Cooper pairing

Cited by in corpus (22)

• Flavor solitons in dense neutrino gases
• Collisional and Fast Neutrino Flavor Instabilities in Two-dimensional Core-collapse Supernova Simulation with Boltzmann Neutrino Transport
• Neutrino Oscillations in Core-Collapse Supernovae and Neutron Star Mergers
• Universality of the Neutrino Collisional Flavor Instability in Core Collapse Supernovae
• Neutrino fast flavor oscillations with moments: linear stability analysis and application to neutron star mergers
• Fast flavor conversions at the edge of instability in a two-beam model
• Qutrit and Qubit Circuits for Three-Flavor Collective Neutrino Oscillations
• Theory of neutrino slow flavor evolution. Part I. Homogeneous medium
• Neutrino many-body correlations
• Symmetry and bipolar motion in collective neutrino flavor oscillations
• Fast Flavor Pendulum: Instability Condition
• Collective flavor conversions are interactions of neutrinos with quantized flavor waves
• Subgrid modeling of neutrino oscillations in astrophysics
• Muon-induced collisional flavor instability in core-collapse supernova
• Supernova Neutrinos: flavour conversion mechanisms and new physics scenarios
• Thermodynamics of oscillating neutrinos
• Neutrino quantum kinetics in two spatial dimensions
• Steady state of fast-oscillating neutrinos in an inhomogeneous medium
• Sufficient and Necessary Conditions for Collective Neutrino Instability: Fast, Slow, and Mixed
• Single-wave solutions of the neutrino fast flavor system. Part I. Mechanical properties
• Neutrino quantum kinetics in three flavors
• Single-wave solutions of the neutrino fast flavor system. Part II. Weak instabilities and their resonant behavior