Decoherence in Quantum Many Body Neutrino Oscillations

Neutrinos experience a potential induced by coherent forward scattering with other neutrinos in a dense neutrino gas. This effect results in an all-to-all coupled Heisenberg-like contribution to the Hamiltonian in the quantum many body (MB) treatment, and results in a nonlinear system of flavor transport equations in a mean field (MF) approximation. When considering simple, but nonuniform, two body couplings and generic product state initial conditions, we observe a substantial loss of coherence in trace reduced partitions of the many body system. We further observe that these partitions are well approximated by a few parameter statistical mixture. Such decoherence cannot be captured in a MF approximation and our observations warrant further investigation using methods which can retain the relevant quantum many body correlations.