Once-in-a-lifetime encounter models for neutrino media II: Quasi-steady states and miscidynamic flavor evolution

TL;DR

This work extends the once-in-a-lifetime encounter (OILE) framework to incorporate stochastic, pairwise neutrino interactions, bridging mean-field flavor evolution with entanglement-induced decoherence. The authors derive a master equation for a foreground neutrino and, under a uniform, randomly oriented background, obtain a closed Bloch-vector dynamics that includes both coherent refraction and a collision term of order $\mu\gamma$. In the limit $\gamma \ll 1$, the system exhibits a miscidynamic, adiabatic precession through a sequence of quasi-steady states characterized by a common precession frequency $\Omega$, with self-consistency relations governing the macroscopic variables. These quasi-steady states slow the decoherence and, ultimately, lead to flavor equilibration, offering a tractable coarse-grained description of neutrino kinetics in dense astrophysical environments such as core-collapse supernovae and neutron-star mergers.

Abstract

We extended the once-in-a-lifetime encounter (OILE) model to stochastic interactions among neutrinos. As in the original OILE model, the new model reproduces the mean-field behavior of a dense neutrino gas for time $t\lesssim (μγ)^{-1}$, where $μ$ measures the strength of the mean-field neutrino self-interaction potential and is proportional to the neutrino density, and the dimensionless "impact parameter" $γ$ is a measure of the change in the flavor quantum state of a neutrino during interaction with another neutrino when the wave packets of the two neutrinos overlap. As in the mean-field case, the OILE model with random neutrino velocities experiences kinetic flavor decoherence as the flavor quantum states of the neutrinos diverge from each other. Unlike the mean-field case, however, the OILE model has a "collision term" due to the quantum entanglement among neutrinos. For $γ\ll1$, this incoherent effect can drive the neutrinos into a quasi-steady state that is similar to the collective precession mode in a homogeneous and isotropic neutrino gas in the mean-field approximation. Subsequently, the collision term drives the neutrino gas adiabatically through different quasi-steady states and eventually to flavor equilibration. This process is an example of miscidynamic flavor evolution, with the mixing equilibria being the quasi-steady precession states.

Figures (2)

• Figure 1: The evolution of an OILE model that consists of 60 $\nu_e$s (group 1) and 40 $\nu_\tau$s (group 2) initially and a small mixing angle $\theta=10^{-3}$. The top two panels show the $x$ and $z$ components of the average Bloch vectors, $\langle \bm{P}\rangle_g$ ($g=1,2$), of the two groups in the mass basis, respectively. The bottom panel shows the average magnitudes of the Bloch vectors. The thin solid curves represent the adiabatic precession / miscidynamic solutions for $|\langle \bm{P}_\perp\rangle_g|$ (top panel), $\langle P_z\rangle_g$ (middle panel), and $\langle |\bm{P}|\rangle_g$ (bottom panel), respectively. The dot dashed line in the middle panel shows the ensemble average $\langle P_z \rangle$ which approximately equals $0.2$ in this case.
• Figure 2: Similar to Fig. \ref{['fig:ex1']} but for two different OILE models with a large mixing angle $\theta=0.7$. The horizontal dotted lines in the lower panels are the approximate values of $P^g_z$ in the precession / miscidynamic solution according to Eq. \ref{['eq:stage2-approx']}. See the text for details.