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Yunfan Zhang
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We derive a suite of generalized Boltzmann equations, based on the density-matrix formalism, that incorporates the physics of neutrino oscillations for two- and three-flavor oscillations, matter refraction, and self-refraction. The resulting equations are straightforward extensions of the classical transport equations that nevertheless contain the full physics of quantum oscillation phenomena. In this way, our broadened formalism provides a bridge between the familiar neutrino transport algorithms employed by supernova modelers and the more quantum-heavy approaches frequently employed to illuminate the various neutrino oscillation effects. We also provide the corresponding angular-mome
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In the standard approaches to neutrino transport in the simulation of core-collapse supernovae, one will often start from the classical Boltzmann equation for the neutrinos spatial, temporal, and spectral evolution. For each neutrino species, and its anti-particle, the classical density in phase space, or the associated specific intensity, will be calculated as a function of time. The neutrino radiation is coupled to matter by source and sink terms on the right-hand-side of the transport equation and together with the equations of hydrodynamics this set of coupled partial differential equations for classical densities describes, in principle, the evolution of core collapse and explosion. However, with the possibility of neutrino oscillations between species, a purely quantum-physical effect, how to generalize this set of Boltzmann equations for classical quantities to reflect oscillation physics has not been clear. To date, the formalisms developed have retained the character of quantum operator physics involving complex quantities and have not been suitable for easy incorporation into standard supernova codes. In this paper, we derive generalized Boltzmann equations for quasi-classical, real-valued phase-space densities that retain all the standard oscillation phenomenology, including resonant flavor conversion (the MSW effect), neutrino self-interactions, and the interplay between decohering matter coupling and flavor oscillations. With this formalism, any code(s) that can now handle the solution of the classical Boltzmann or transport equation can easily be generalized to include neutrino oscillations in a quantum-physically consistent fashion.
In the context of core-collapse supernovae, Strack and Burrows (Phys. Rev. D 71, 093004 (2005)) have recently developed an extension of the classical Boltzmann kinetic formalism that retains all the standard neutrino oscillation phenomenology, including resonant flavor conversion (the MSW effect), neutrino self-interactions, and the interplay between neutrino-matter coupling and flavor oscillations. In this thesis, I extend the Strack & Burrows formalism to incorporate general relativity, spin degrees of freedom, and a possible neutrino magnetic-moment/magnetic-field interaction.
Two and three flavor oscillating neutrinos are shown to exhibit the properties bipartite and tripartite quantum entanglement. The two and three flavor neutrinos are mapped to qubit states used in quantum information theory. Such quantum bits of the neutrino state can be encoded on a IBMQ computer using quantum computing as a tool. We show the implementation of entanglement in the two neutrino system on the IBM quantum processor.
The texture zero mass matrices for the leptons and the seesaw mechanism are used to derive relations between the matrix elements of the lepton mixing matrix and the ratios of the neutrino masses.
Since most of the neutrino parameters are well-measured, we illustrate precisely the prediction of the Standard Model, minimally extended to allow massive neutrinos, for the electron neutrino magnetic moment. We elaborate on the effects of light sterile neutrinos on the effective electron neutrino magnetic moment measured at the reactors. We explicitly show that the kinematical effects of the neutrino masses are negligible even for light sterile neutrinos.
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