Supplemental material for "A change of direction in pairwise neutrino conversion physics: The effect of collisions" (arXiv:2011.00004)

Authors: Shashank Shalgar and Irene Tamborra

The density matrices of neutrinos and antineutrinos, $\rho$ and $\bar{\rho}$, can be written in terms of polarization vectors in the two-flavor approximation ($P$ and $\bar{P}$): $$\rho = \frac{1}{2}\left(1+\vec{P}\cdot\vec{\sigma}\right),$$ where $\vec{\sigma}$ are the Pauli matrices. We plot the angle-integrated polarization vectors, which are convenient tools for visualization and convey the same information as the density matrices. In the movies below, we show the evolution of the angular distributions of neutrinos and antineutrinos (on the left) and the evolution of the polarization vectors (on the right) for three different scenarios. We have fixed the initial length of the neutrino polarization vector to $1$ and the initial length of the antineutrino polarization vector to $1/2$ for the ease of viewing.