Construction and Analysis of a Many-Body Neutrino model

Abstract

In systems such as the early universe and supernova neutrinos comprise a large fraction of the total particle number density thus one needs to consider neutrino self-refraction. Coherent neutrino-neutrino scattering has been found to play a role in the flavour evolution of the system. Traditionally this problem has been analysed by assuming that the wavefunction of the system can be factorised into one-body states. However in 1992 Pantaleone showed that a neutrino ensemble is in general a many-body problem due to the off-diagonal contribution to the neutrino refractive index. This topic was unexamined until recently. It has been suggested by Bell, Rawlinson and Sawyer that quantum entanglement could play an essential role in the flavour evolution of the dense neutrino system. In this thesis we examine the validity of the one-body approximation by constructing a many-body neutrino model. The neutrino system is modelled by a system of interacting spins following earlier work of Friedland and Lunardini. We extend this work by generalising the model to initial states with asymmetric flavour composition. We find an exact analytical solution to the system. The investigation has revealed an array of interesting physics including semi-classical behaviour, quantum equilibration and a transition from semi-classical to purely quantum regimes. Further, this study has found no evidence for the violation of the one-body description of a dense neutrino ensemble. We also note that our analysis is valid for any two state system with equal strength interactions.