Abstract
It has been recently shown that the flavor composition of a self-interacting neutrino gas can spontaneously acquire a time-dependent pulsating component during its flavor evolution. In this work, we perform a more detailed study of this effect in a model where neutrinos are assumed to be emitted in a two-dimensional plane from an infinite line that acts as a neutrino antenna. We consider several examples with varying matter and neutrino densities and find that temporal instabilities with various frequencies are excited in a cascade. We compare the numerical calculations of the flavor evolution with the predictions of linearized stability analysis of the equations of motion. The results obtained with these two approaches are in good agreement in the linear regime, while a dramatic speed-up of the flavor conversions occurs in the non-linear regime due to the interactions among the different pulsating modes. We show that large flavor conversions can take place if some of the temporal modes are unstable for long enough, and that this can happen even if the matter and neutrino densities are changing, as long as they vary slowly.
Highlights
It has been recently shown that the flavor composition of a self-interacting neutrino gas can spontaneously acquire a time-dependent pulsating component during its flavor evolution
The results obtained with these two approaches are in good agreement in the linear regime, while a dramatic speed-up of the flavor conversions occurs in the non-linear regime due to the interactions among the different pulsating modes
We find a good agreement between the results obtained with this two approaches in the linear regime, while a dramatic amplification of the flavor conversions occur in the non-linear case due to the interaction among the different pulsating modes, that get excited in a cascade
Summary
We consider the situation that neutrinos and antineutrinos are emitted from a surface and subsequently free-stream, but with forward scatterings with other neutrinos and antineutrinos as well as the background matter. The flavor evolution can be characterized in terms of the (anti)neutrino density matrix E,v, for each neutrino mode with energy E and velocity v. The problem boils down to calculating Pω,v(t, x), given their values at the source as a function of time This boundary condition is taken to be stationary in time and homogeneous over the source, which may naively suggest that the solution ought to respect these symmetries as well. Such a solution is often unstable to small spatial and temporal fluctuations, and it is important to ascertain the role of spontaneous breaking of these spatial and temporal symmetries. We will study this in both the linear and nonlinear regime, and we introduce the set-up and the notation
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