Robustness of Solutions of the Quantum Kinetic Equations in the Presence of Matter Density Fluctuations

TL;DR

This study examines how matter density fluctuations impact neutrino flavor evolution using quantum kinetic equations, finding that such perturbations have negligible effects and solutions are numerically stable across resolutions.

Contribution

The paper demonstrates that matter density fluctuations do not significantly alter neutrino flavor evolution in spherical symmetry, confirming numerical convergence and robustness of solutions.

Findings

Solutions are numerically converged at coarse resolution.

Matter fluctuations do not induce instabilities in flavor evolution.

Angular distributions and spectra are minimally affected by perturbations.

Abstract

We investigate the role of fluctuations in the matter density on neutrino flavor evolution by studying their effects on the collision terms in the spherically symmetric quantum kinetics equations (QKEs). We solve the QKEs with varying radial resolution ($r_{\mathrm{bins}} = 150 \, , 1500 \, , 15000$) to assess numerical convergence in angular distributions, number densities, and energy spectra for four neutrino flavors ($\nu_e$, $\bar{\nu}_e$, $\nu_x$, $\bar{\nu}_x$). Our results demonstrate that the solutions are numerically converged already at the coarsest resolution, with higher resolutions yielding almost identical outcomes. We introduce random perturbations to each radial bin, thus adding perturbations with a length scale that is related to the radial resolution. We study both time-independent and time-dependent perturbations to the matter density that affect the collision term and analyze their effects on neutrino flavor evolution. We find that such fluctuations do not induce any significant instabilities or qualitative changes in flavor evolution. Angular structure remains robust, and flavor-dependent number densities and energy spectra show only minor deviations compared to the unperturbed case. These findings suggest that matter perturbations have a negligible effect on neutrino flavor evolution in spherically symmetric settings.