Dynamical equilibria of fast neutrino flavor conversion

Abstract

Dense neutrino systems, which display collectivity mediated by the weak interaction, have deep parallels with mean-field kinetic systems governed by other fundamental forces. We identify analogues in fast flavor conversion (FFC) of some time-honored nonlinear phenomena in plasmas and self-gravitating systems. We focus in particular on nonlinear Landau damping and collisionless equilibria, which are likely important pieces of the unsolved puzzle of neutrino oscillations in core-collapse supernovae and neutron star mergers. Our analysis additionally reveals the previously unexplored phenomenon of flavor-wave synchronization.

Figures (4)

• Figure 1: Illustration of phase-aligned, circularly polarized flavor-wave synchronization with a single inhomogeneous Fourier mode ($n = 1$). All $\bm{P}_I(r)$ co-precess around $\bm{z}$. This configuration is consistent with equilibrium spatial averages $\bm{P}_{I,0}$. By contrast, sustained phase misalignment causes secular change in $\bm{P}_{I,0}$.
• Figure 2: Comparison between the full QKE simulation and the reduced model for mode $n=1$ in a box of size $L=4$. Left: Periodic fast flavor oscillations using identical initial conditions with single-mode transverse seed perturbations. Middle: Phase portrait showing completely regular dynamics. Right: Eigenmode decomposition of the QKE solution, with projection coefficients normalized to unit total power.
• Figure 3: Time evolution of $D^z$ for box sizes $L = 4$, 25, and 1000, corresponding to 1, 11, and 450 unstable Fourier modes, respectively. As the number of unstable modes increases, the system transitions from coherent recurrences to chaotic evolution and effectively irreversible relaxation.
• Figure 4: Probability density of the flavor-wave phase difference $\delta^x_n$ for each mode $n$ in the $L = 1000$ simulation. Upper panel: nonequilibrium regime ($t \in [0, 40]$) showing phase misalignment. Lower panel: equilibrium regime ($t \in [40, 80]$) showing phase alignment. Color indicates mode index $n$. The total probability for each mode $n$ is normalized to unity.