AstroNu Data Archive

Supplemental material for "Collisional dilemma: Enhancement or damping of fast flavor conversion of neutrinos" (arXiv:2204.11873)

Authors: Rasmus S. L. Hansen, Shashank Shalgar, and Irene Tamborra

The density matrix $\rho$ and self-interaction Hamiltonian $H_{\nu\nu}$ in the two flavor approximation can be expressed as polarization vectors, $\mathbf{P}$, and potential vectors, $\mathbf{V}_{\nu\nu}$ using a vector of Pauli matrices, $\boldsymbol{\sigma}$: $$ \rho = \frac{1}{2}(P_0+\mathbf{P} \cdot \boldsymbol{\sigma}) , \qquad H_{\nu\nu} = \frac{1}{2} (V_{\nu\nu,0}+\mathbf{V}_{\nu\nu} \cdot \boldsymbol{\sigma}) . $$ Below we show results for our neutrino model with three angular bins. The evolution of $\mathbf{P}$ and $\mathbf{V}_{\nu\nu}$ is shown in the eigenframe (EF) for each angular bin. The right most column shows the total polarization vector mulitplied by $\frac{1}{2}$ to fit on the same scale.

The first row shows the $x$-$y$ plane (top view) while the second row shows the $x$-$z$ plane (side view).

Polarization vectors $\mathbf{P}^{\rm EF}$ and potential vectors $\mathbf{V}_{\nu\nu}^{\rm EF}$ for case A (almost isotropic angular distribution), with collision rate $C=3$ km$^{-1}$.

Polarization vectors $\mathbf{P}^{\rm EF}$ and potential vectors $\mathbf{V}_{\nu\nu}^{\rm EF}$ for case B (forward peaked angular distribution) with collision rate $C=3$ km$^{-1}$.

Note that the first $ct=0.02$ km are slowed down to show the details of the initial evolution. After a brief pause, the rest is played faster to cover the entire evolution.