# Collective Neutrino Oscillations

Neutrino oscillations in a matter background have well-defined linear dynamics as I have discussed in the preceding chapters. In this chapter, I will discuss neutrino oscillations in a dense neutrino medium where the equation of motion becomes nonlinear. One of such examples is the (core-collapse) supernova explosion which releases approximately $10^{58}$ neutrinos within seconds 1. The neutrino density inside a supernova can be so large that the neutrino self-interaction potential $H_{\nu\nu}$ to be comparable to or even larger than the matter potential in certain regions 2. It has been shown that the self-interaction between the neutrinos can cause the neutrino medium to oscillate collectively 3 4. The neutrino self-interaction also introduces a new characteristic energy scale which is proportional to the neutrino number density. As a result it is possible that neutrinos can oscillate on distance scales much shorter than the vacuum neutrino oscillation wavelength 5 6.

In this chapter, I will first review some of the general features of collective neutrino oscillations and introduce the method of linearized flavor stability analysis. I will then discuss the dispersion relations of the collective modes of neutrino oscillations and show that it may or may not be related to the flavor stability of a neutrino gas. Finally, I will demonstrate a preliminary study of a toy model which can be used to understand the neutrino oscillations in the presence of the neutrino halo 7 8.

1. J. N. Bahcall, "Neutrinos from the recent LMC supernova", Nature 326, 135-136 (1987) . ↩︎

2. Elliott G Flowers, "Neutrino-neutrino scattering and supernovae", The Astrophysical Journal 208, L19 (1976) . ↩︎

3. Huaiyu Duan, "Collective neutrino oscillations", Annual Review of Nuclear and Particle Science 60, 569-594 (2010) . ↩︎

4. Huaiyu Duan, "Simulation of coherent nonlinear neutrino flavor transformation in the supernova environment: Correlated neutrino trajectories", Physical Review D 74, 1-22 (2006) . ↩︎

5. R. F. Sawyer, "Neutrino cloud instabilities just above the neutrino sphere of a supernova", Physical Review Letters 116, 1-5 (2016) . ↩︎

6. Sovan Chakraborty, "Self-induced neutrino flavor conversion without flavor mixing", Journal of Cosmology and Astroparticle Physics 2016, 042-042 (2016) . ↩︎

7. Srdjan Sarikas, "Supernova neutrino halo and the suppression of self-induced flavor conversion", Physical Review D 85, 1-5 (2012) . ↩︎

8. John F. Cherry, "Neutrino scattering and flavor transformation in supernovae", Physical Review Letters 108, 1-5 (2012) . ↩︎