  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.
