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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2301.09650 |
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Table of Contents:
- 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 $\dot{\mathbf{P}}_ω=(ω\mathbf{B}+μ\mathbf{P})\times\mathbf{P}_ω$, where $ω=Δm^2/2E$, $μ=\sqrt{2} G_{\mathrm{F}} (n_ν+n_{\barν})$, $\mathbf{B}$ is a unit vector in the mass direction in flavor space, and $\mathbf{P}=\int dω\,\mathbf{P}_ω$. For an axisymmetric angle distribution, the fast EOMs are $\dot{\mathbf{D}}_v=μ(\mathbf{D}_0-v\mathbf{D}_1)\times\mathbf{D}_v$, where $\mathbf{D}_v$ is the Bloch vector for lepton number, $v=\cosθ$ is the velocity along the symmetry axis, $\mathbf{D}_0=\int dv\,\mathbf{D}_v$, and $\mathbf{D}_1=\int dv\,v\mathbf{D}_v$. 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.