The subject of this dissertation is the evolution of neutrino distributions in hot, dense astrophysical environments, such as the early Universe, core collapse supernovae or compact object mergers. This is an important problem in astrophysics because the dynamics and the composition of these systems can be strongly influenced by neutrinos, leading to potential modification of nucleosynthesis and of astrophysical observables. In these environments, neutrinos can undergo both coherent forward scattering and direction-changing or inelastic collisions. The transport equations for flavored neutrinos, or quantum kinetic equations (QKEs), are derived from first principles, beginning with quantum field theory and Standard Model neutrino interactions. The QKEs can reduce to the standard Schrödinger-like equations for neutrino flavor evolution in the limit of low matter density, and to a Boltzmann-like equation describing neutrino scattering at high density. In addition, in high-density, anisotropic environments we find a novel process that can mediate coherent exchange of particle number and flavor information between neutrino and antineutrino states (spin coherence). We discuss the prospects for modification of the standard picture of neutrino flavor evolution in supernovae and other astrophysical environments by non- forward scattering and spin coherence

Recent studies have demonstrated that in anisotropic environments a coherent spin-flip term arises in the Quantum Kinetic Equations (QKEs) which govern the evolution of neutrino flavor and spin in hot and dense media. This term can mediate neutrino-antineutrino transformation for Majorana neutrinos and active-sterile transformation for Dirac neutrinos. We discuss the physical origin of the coherent spin-flip term and provide explicit expressions for the QKEs in a two-flavor model with spherical geometry. In this context, we demonstrate that coherent neutrino spin transformation depends on the absolute neutrino mass and Majorana phases.

We present a formulation of the quantum kinetic equations (QKEs), which govern the evolution of neutrino flavor at high density and temperature. Here, the structure of the QKEs is derived from the ground up, using fundamental neutrino interactions and quantum field theory. We show that the resulting QKEs describe coherent flavor evolution with an effective mass when inelastic scattering is negligible. The QKEs also contain a collision term. This term can reduce to the collision term in the Boltzmann equation when scattering is dominant and the neutrino effective masses and density matrices become diagonal in the interaction basis. We also find that the QKEs include equations of motion for a new dynamical quantity related to neutrino spin. This quantity decouples from the equations of motion for the density matrices at low densities or in isotropic conditions. However, the spin equations of motion allow for the possibility of coherent transformation between neutrinos and antineutrinos at high densities and in the presence of anisotropy. Although the requisite conditions for this exist in the core collapse supernova and compact object merger environments, it is likely that only a self-consistent incorporation of the QKEs in a sufficiently realistic model could establish whether or not significant neutrino-antineutrino conversion occurs. © 2014 American Physical Society.

We examine whether the newly derived neutrino spin coherence could lead to large-scale coherent neutrino-antineutrino conversion. In a linear analysis we find that such transformation is largely suppressed, but demonstrate that nonlinear feedback can enhance it. We point out that conditions which favor this feedback may exist in core collapse supernovae and in binary neutron star mergers.

We argue that the small fraction of neutrinos that undergo direction-changing scattering outside of the neutrinosphere could have significant influence on neutrino flavor transformation in core-collapse supernova environments. We show that the standard treatment for collective neutrino flavor transformation is adequate at late times but could be inadequate in early epochs of core-collapse supernovae, where the potentials that govern neutrino flavor evolution are affected by the scattered neutrinos. Taking account of this effect, and the way it couples to entropy and composition, will require a new approach in neutrino flavor transformation modeling.

We give the first self-consistent calculation of the effect of the scattered neutrino halo on flavor evolution in supernovae. Our example case is an O-Ne-Mg core collapse supernova neutronization neutrino burst. We find that the addition of the halo neutrinos produces qualitative and quantitative changes in the final flavor states of neutrinos. We also find that the halo neutrinos produce a novel distortion of the neutrino flavor swap. Our results provide strong motivation for tackling the full multidimensional and composition-dependent aspects of this problem in the future. © 2013 American Physical Society.