Classical and Quantum Coherent Neutrino Oscillations

Neutrinos are emitted in enormously large fluxes in extreme astrophysical environments such as core collapse supernovae, binary neutron star mergers and the early universe. Through coherent forward scattering, neutrinos traveling along different trajectories may exchange flavor information resulting in macroscopically large scale flavor oscillations. The Hamiltonian which governs the flavor content evolution in these dense neutrino gases in the two-flavor approximation can be written as a quantum spin-spin Hamiltonian similar to the Heisenberg model, but with all-to-all couplings in the two-body interaction. Solving the full quantum evolution in this system even for very simple initial conditions can be prohibitively difficult, and as such much of the investigation into the flavor dynamics present in such dense neutrino gases has been performed in the mean-field approximation. We examined the fully quantum evolution of a dense neutrino gas in a simple "two-beam" model under a product state prototypical initial condition. By exploiting the symmetries of this model, we are able to track the full coherent evolution of thousands of neutrino flavor spins, and make direct comparisons with two well understood flavor oscillation modes in the mean-field limit. In all cases we find that the mean-field well describes the evolution of simple one-body observables despite the presence and development of entanglement among the neutrinos in the two beams.