Neutrino Quantum Kinetics

We present a formulation of the quantum kinetic equations (QKEs) which govern the evolution of neutrino flavor at high density and temperature. Here, the QKEs are 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 QKE's 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.Comment: Revised version, published in Physical Review

Spin dependent recombination based magnetic resonance spectroscopy of bismuth donor spins in silicon at low magnetic fields

Low-field (6-110 mT) magnetic resonance of bismuth (Bi) donors in silicon has been observed by monitoring the change in photoconductivity induced by spin dependent recombination. The spectra at various resonance frequencies show signal intensity distributions drastically different from that observed in conventional electron paramagnetic resonance, attributed to different recombination rates for the forty possible combinations of spin states of a pair of a Bi donor and a paramagnetic recombination center. An excellent tunability of Bi excitation energy for the future coupling with superconducting flux qubits at low fields has been demonstrated.Comment: 5 pages, 4 figure

A New Spin on Neutrino Quantum Kinetics

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.Comment: 11 pages, 3 figures, Major changes compared to v1, accepted for publication in Physics Letters

Multimedia technology in teaching mathematics pupils 1 – 4 classes

We describe the use of multimedia technology in teaching mathematics in elementary school. The synthesis, systematization, synthesis of existing theoretical positions that make it possible to organize teaching mathematics elementary school students using multimedia technology. Used systematic and comparative analysis of scientific-methodological and psycho-pedagogical literature. The concept multimedia support teaching mathematics in elementary school. Developed requirements and proposed guidelines for creating and using multimedia learning support during lessons in mathematics 1 – 4 classes: presentations, simulators, dynamic models, educational expert systems. Proved that the use of the investigated technologies grounded in multimedia teaching mathematics accompanied by elementary school students during development is important to ensure the selection of appropriate methods of components that should create new opportunities prepare students while changing living conditions, encourage self-education.Keywords: teaching mathematics, primary school, multimedia technology, multimedia support training requirements.Описано використання мультимедійних технологій у навчанні математики в початковій школі. Здійснено синтез, систематизацію, узагальнення наявних теоретичних положень, що вможливлюють організацію навчання математики учнів початкової школи з використанням мультимедійних технологій.  Використано системний і порівняльний аналіз науково-методичної та психолого-педагогічної літератури. Уточнено поняття мультимедійного супроводу навчання математики в початковій школі. Розроблено вимоги та запропоновано методичні рекомендації щодо створення та використання мультимедійного супроводу навчання під час уроків математики у 1 – 4 класах. Показано, що використання досліджуваних технологій ґрунтоване на мультимедійному супроводі навчання математики учнів початкової школи, під час розроблення якого важливо забезпечувати вибір відповідних компонентів методики, що має створювати можливості нової підготовки учнів під час зміни умов життєдіяльності, стимулювати самоосвіту.Ключові слова: навчання математики, початкова школа, мультимедійні технології, мультимедійний супровід навчання, вимоги

Coherent storage of photoexcited triplet states using 29Si nuclear spins in silicon

Pulsed electron paramagnetic resonance spectroscopy of the photoexcited, metastable triplet state of the oxygen-vacancy center in silicon reveals that the lifetime of the ms = \pm1 sub-levels differ significantly from that of the ms =0 state. We exploit this significant difference in decay rates to the ground singlet state to achieve nearly ~100% electron spin polarization within the triplet. We further demonstrate the transfer of a coherent state of the triplet electron spin to, and from, a hyperfine-coupled, nearest-neighbor 29Si nuclear spin. We measure the coherence time of the 29 Si nuclear spin employed in this operation and find it to be unaffected by the presence of the triplet electron spin and equal to the bulk value measured by nuclear magnetic resonance.Comment: 5 pages, 4 figure

Neutrino energy transport in weak decoupling and big bang nucleosynthesis

We calculate the evolution of the early universe through the epochs of weak decoupling, weak freeze-out and big bang nucleosynthesis (BBN) by simultaneously coupling a full strong, electromagnetic, and weak nuclear reaction network with a multi-energy group Boltzmann neutrino energy transport scheme. The modular structure of our code provides the ability to dissect the relative contributions of each process responsible for evolving the dynamics of the early universe in the absence of neutrino flavor oscillations. Such an approach allows a detailed accounting of the evolution of the $\nu_e$, $\bar\nu_e$, $\nu_\mu$, $\bar\nu_\mu$, $\nu_\tau$, $\bar\nu_\tau$ energy distribution functions alongside and self-consistently with the nuclear reactions and entropy/heat generation and flow between the neutrino and photon/electron/positron/baryon plasma components. This calculation reveals nonlinear feedback in the time evolution of neutrino distribution functions and plasma thermodynamic conditions (e.g., electron-positron pair densities), with implications for: the phasing between scale factor and plasma temperature; the neutron-to-proton ratio; light-element abundance histories; and the cosmological parameter \neff. We find that our approach of following the time development of neutrino spectral distortions and concomitant entropy production and extraction from the plasma results in changes in the computed value of the BBN deuterium yield. For example, for particular implementations of quantum corrections in plasma thermodynamics, our calculations show a $0.4\%$ increase in deuterium. These changes are potentially significant in the context of anticipated improvements in observational and nuclear physics uncertainties.Comment: 37 pages, 12 Figures, 6 Table

Neutrino scattering and flavor transformation in supernovae

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 the crucial shock revival/explosion epoch 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 paradigm in supernova modeling.Comment: 5 pages, 3 figure