Chaos in neutrino fast flavor instability

Neutrinos play a crucial role in explosive stellar events. In core collapse supernovae (CCSN), neutrinos produced thermally in the proto-neutron star drive the CCSN dynamics reviving the shock wave that causes the explosion. In neutron star mergers (NSM), neutrinos can significantly affect the ratio of neutrons to protons in the ejected mass via charged-current reactions, having a big impact on the production of heavy elements. Simulations have revealed that neutrinos undergo substantial flavor instabilities that make it challenging to fully understand the neutrino non-linear many-body dynamics. In simplified neutrino models, the presence of chaos in flavor evolution has been proposed. Since chaotic systems are very sensitive to initial conditions, i.e. trajectories of slightly different initial conditions diverge exponentially, our ability to predict the neutrino flavor behavior in CCSN and NSM could be limited. To clarify this problem, we approximate the behavior of neutrinos inside NSM by simulating neutrino flavor instabilities in a domain a few centimeters wide. Our goal is to analyze the dynamics of nearby flavor states in the presence of neutrino instabilities. We solve the neutrino quantum kinetic equation numerically including the neutrino self-interaction term in the flavor Hamiltonian, using the particle-in-cell code EMU under the mean field approximation. We conclude that nearby initial states diverge in the non-linear regime of flavor instabilities suggesting the presence of chaos.