Once-in-a-lifetime encounter models for neutrino media: From coherent oscillations to flavor equilibration

Collective neutrino oscillations are typically studied using the lowest-order quantum kinetic equation, also known as the mean-field approximation. However, some recent quantum many-body simulations suggest that quantum entanglement among neutrinos may be important and may result in flavor equilibration of the neutrino gas. In this work, we develop new quantum models for neutrino gases in which any pair of neutrinos can interact at most once in their lifetimes. A key parameter of our models is $\gamma=\mu \Delta z$, where $\mu$ is the neutrino coupling strength, which is proportional to the neutrino density, and $\Delta z$ is the duration over which a pair of neutrinos can interact each time. Our models reduce to the mean-field approach in the limit $\gamma\to0$ and achieve flavor equilibration in time $t \gg (\gamma\mu)^{-1}$. These models demonstrate the emergence of coherent flavor oscillations from the particle perspective and may help elucidate the role of quantum entanglement in collective neutrino oscillations.