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

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 $t\lesssim (\mu\gamma)^{-1}$, where $\mu$ measures the strength of the mean-field neutrino self-interaction potential and is proportional to the neutrino density, and the dimensionless "impact parameter" $\gamma$ 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 $\gamma\ll1$, 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.