Stability of incoherence in an isotropic gas of oscillating neutrinos

In the early universe and in supernovae, the flavor evolution of massive neutrinos is nonlinear. Previously, numerical simulations have explored these conditions and have sometimes found collective, synchronized neutrino oscillations. Here these coherent phenomena are studied in the simplest possible system, an isotropic gas of two-flavor neutrinos. An analytical method is used to study the stability of the incoherent state. It is found that the incoherent state has neutral stability. That is, a steady state synchronization can exist for all nonzero neutrino densities, but the amount depends on the initial conditions. This result is verified by numerical simulation, but it is shown that numerical simulations are accurate for only a limited time. In more complicated neutrino systems, the incoherent state could be stable or unstable.