Maxim Dvornikov

We study a new form of mean-field equations in the presence of an axion. The key role is played by asymptotic ergodic invariants of magnetic lines, which determine the type of MHD spectrum of solutions.

We study the evolution of neutrinos electroweakly interacting with a rotating matter. The description of neutrinos is based on the Dirac equation in the corotating noninertial frame where matter is at rest. We find the solution of this Dirac equation, where the matter angular velocity is accounted for exactly, for massless neutrinos. In case of massive particles, this solution is obtained for a slowly rotating matter. Our findings are compared with previous research. We consider two applications of our results. First, we compute the electroweak contribution to the vector current of neutrinos along the rotation axis, which is analogous to the chiral vortical effect. This current is shown to be nonzero for both massless and massive particles. Then, we take into account the nonzero mixing between different mass eigenstates. It allows us to study neutrino flavor oscillations in rotating matter and account for noninertial effects. We derive the transition probability which reveals the resonance. These findings generalize the description of neutrino oscillations in a nonmoving matter. Some astrophysical applications are briefly discussed.

In this work, we study the propagation and spin oscillations of neutrinos in their scattering by a supermassive black hole (SMBH) surrounded by a realistic accretion disk. We review various descriptions of the fermion spin evolution in a curved spacetime under the influence of external fields. The overview of the test particle motion in the gravitational field of a rotating SMBH is also present. The external fields which a neutrino spin interacts with are the electroweak forces in plasma and the toroidal magnetic field in the accretion disk surrounding SMBH. Spin precession of neutrinos, which are supposed to be Dirac particles, is caused by the interaction of the neutrino magnetic moment with the magnetic field in the disk. We use a semi-analytical model of a thick accretion disk and review its characteristics. The cases of co-rotating and counter-rotating disks with respect to BH are discussed. We consider the incoming flux of neutrinos having an arbitrary angle with respect to the BH spin since the recent results of the Event Horizon Telescope indicate that the BH spin in the galactic center is not always perpendicular to the galactic plane. For our study, we consider a large number of incoming test neutrinos. We briefly discuss our results and their applications in the observations of astrophysical neutrinos.

In this paper, we study the evolution of interacting large scale magnetic and axionic fields. Based on the new induction equation accounting for the contribution of spatially inhomogeneous axions, we consider the evolution of a magnetized spherical axion structure. Using the thin layer approximation, we derive the system of the nonlinear ordinary differential equations for harmonics of poloidal and toroidal magnetic fields, as well as for the axion field. In this system, we account for up to four modes. Considering this small and dense axion clump to be in a solar plasma, we numerically simulate the evolution of magnetic fields. We obtain that the behavior of magnetic fields depends on the initial fields configuration. Moreover, we find an indication on a magnetic field instability in the magnetohydrodynamics with inhomogeneous axions.

We study neutrino clusters formed owing to the interaction of neutrinos with a light scalar boson. This interaction is attractive. We consider one of the model of the cluster cooling, which must provide the energy losses by the neutrino gas during its compression while a cluster is formed. Assuming that a cluster appears in the early Universe after the electroweak phase transition, we suggest that the neutrino gas is cooled owing to the emission of Cherenkov plasmons. We establish the temperature interval where the cluster cooling rate is greater than that of the Universe expansion. Thus, the temperature of the neutrino gas inside the cluster drops to the temperature of relic neutrinos. Moreover, we find that the neutrino decoupling temperature is within this interval. Thus, thermal fluctuations of the electroweak plasma do not affect the cluster formation.

We study the problem of breaking non-Abelian gauge symmetry for solving the Yang–Mills equation in an expanding space with a parameter of negative scalar curvature, which becomes flat at large expansion times and which is called the geodesic flow space of the Lobachevsky plane. We use the following: the physical properties of the magnetic field are related to the Kolmogorov scale, which made it possible to estimate the α-effect of the space curvature parameter at each moment of time. On the other hand, in an expanding hyperbolic space, a change in the density of magnetic helicity is observed, unrelated to the α-effect. We compare the two indicated factors of change in magnetic helicity and conclude that, at a fairly stable stage of expansion, the α-effect caused by the influence of scalar curvature on the Kolmogorov MHD spectrum becomes small.

We study neutrino oscillations in background matter within the quantum field theory formalism where neutrino mass eigenstates are virtual particles. In this case, neutrino mass eigenstates are mixed owing to the interaction with matter. Assuming that neutrinos are Majorana particles, we find the exact propagators for massive neutrinos accounting for the interaction with matter by solving the analog of the Dyson equation. These propagators are used to calculate the transition probability, which coincides with the prediction of the standard quantum-mechanical treatment of neutrino flavor oscillations in uniform matter. Finally, we analyze the approximations made in our analysis.

We summarize our recent achievements in the description of neutrino oscillations in various gravitational fields. After the short review of the previous st