Chaos in Neutrino Fast Flavor Instability

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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 in those systems neutrinos undergo substantial fast flavor instabilities that make it challenging to fully understand the neutrino non-linear many-body dynamics, mainly because of the large number of neutrinos involved and the small spatial scale of the neutrino flavor oscillation in comparison with the CCSN and NSM spatial scale. In simplified neutrino models (bipolar oscillations), the presence of chaos in the 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 fast 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 fast flavor 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 solutions with nearby initial states diverge exponentially in the non-linear regime of the neutrino flavor evolution, demonstrating the presence of chaos. This produces a huge uncertainty in both the spatial flavor neutrino distributions and the density matrix of the individual computational particles. However, the domain-averaged neutrino density matrix component is not highly affected by chaos (1% maximum uncertainty) and could be used as a key variable in global neutrino simulations of CCSN and NSM.