Slow and fast collective neutrino oscillations:Invariants and reciprocity
| Autor: | Damiano F. G. Fiorillo, Georg Raffelt |
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| Jazyk: | dánština |
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Fiorillo, D F G & Raffelt, G 2023, ' Slow and fast collective neutrino oscillations : Invariants and reciprocity ', Physical Review D, bind 107, 043024 . https://doi.org/10.1103/PhysRevD.107.043024 Physical Review |
| DOI: | 10.1103/PhysRevD.107.043024 |
| Popis: | 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 $\mathbf{D}_1=\int dv\,v\mathbf{D}_v$. 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. Comment: 16 pages; typo below Eq. (5) and in Eq. (47) corrected |
| Databáze: | OpenAIRE |
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