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The dispersion relation of the fast neutrino oscillation wave
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A dense neutrino medium can support flavor oscillation waves which are coherent among different momentum modes of the neutrinos. The dispersion relation (DR) branches of such a wave with complex frequencies and/or wave numbers can lead to the exponential growth of the wave amplitude which in turn will engender a collective flavor transformation in the neutrino medium. In this work we propose that the complex DR branches of the neutrino oscillation wave should be bound by the critical points of the DR. We demonstrate how this theory can be applied to the neutrino medium with an (approximate) axial symmetry about the propagation direction of the neutrino oscillation wave. We also show how the flavor instabilities in this medium can be identified by tracing the critical points of the DR as the electron lepton number distribution of the neutrino medium is changed continuously.
Forward citations
Cited by 5 Pith papers
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Flavomons in Matter Gradients: Ray Tracing and Amplitude Evolution
Matter gradients slow but do not suppress neutrino-mass-induced flavor instabilities, so flavomon ray tracing is required instead of local stability analysis alone.
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Fast flavor conversion in a time-varying supernova background proceeds through three episodes and broadly agrees with static two-step model results.
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Single-wave solutions of the neutrino fast flavor system. Part II. Weak instabilities and their resonant behavior
For shallow angular crossings, the nonlinear evolution of a single-wave fast flavor instability is a flavor pendulum whose amplitude and period are set by the linear growth rate.
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Theory of neutrino slow flavor evolution. Part II. Space-time evolution of linear instabilities
All weak fast and slow neutrino flavor instabilities are convective, so they grow spatially along neutrino directions rather than locally in time.
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Fast Flavor Pendulum: Instability Condition
The Nyquist criterion for homogeneous fast flavor instability is corrected to N = W - Ns/2, where W is the subluminal winding number and Ns counts real superluminal solutions.
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