Neutrino Flavor Development in Multidimensional Models

In extreme events involving the formation of compact objects such as core collapse supernovae (CCSNe) and binary neutron star mergers, neutrinos are emitted in such large quantities that the neutrino gas can experience a self-induced, flavor dependent index of refraction. This nonlinear self-coupling subsequently results in correlation forming between neutrinos on different trajectories. In stationary one dimensional models this can lead to large scale coherent and collective behavior, but was it later shown to cause loss of large scale correlation in the flavor field in two dimensional models. In this talk I will focus on two stationary 2D models and one dynamic 1D model that are relevant to CCSNe explosions. I will demonstrate that this loss of correlation, while ubiquitous in the stationary models, should not be universally expected to occur. I will describe some general features of systems which undergo this correlation loss, and I will demonstrate that for some regimes coherence is maintained and, most surprisingly, that spontaneously broken symmetries may be restored.