Influence of Quantum Decoherence on Collective Neutrino Oscillations in the Model of Homogeneous Neutrino Gas

Collective oscillations and quantum decoherence in neutrino physics are two rapidly developing lines of research that act as gateways to a potentially new physics. Moreover, they promise to shed light on still unresolved problems, particularly the neutrino mass hierarchy. In this paper we study the interplay of these two effects, namely we consider the possible suppression effect on the collective oscillations when neutrinos are viewed in the formalism of open quantum systems, i.e., when quantum decoherence is taken into account. We consider a model of a homogeneous neutrino gas to take into account angular asymmetries, which play a special role in the formation of collective unstable modes. Using numerical analyses of the emerging slow modes, we find that in the case of neutrino fluxes from supernovae there is a potential to differentiate between two hierarchies of neutrino masses by taking into account the dissipative effect of quantum decoherence on collective oscillations.