arXiv subjects

Maxim Dvornikov

Publications and source records attributed to Maxim Dvornikov.

At least 127 records · Page 7Linked to original sources

arXiv2009

Oscillations of Dirac and Majorana neutrinos in matter and a magnetic field

We study the evolution of massive mixed Dirac and Majorana neutrinos in matter under the influence of a transversal magnetic field. The analysis is based on relativistic quantum mechanics. We solve exactly the evolution equation for relativistic neutrinos, find the neutrino wave functions, and calculate the transition probability for spin-flavor oscillations. We analyze the dependence of the transition probability on the external fields and compare the cases of Dirac and Majorana neutrinos. The evolution of Majorana particles in vacuum is also studied and correction terms to the standard oscillation formula are derived and discussed. As a possible application of our results we discuss the spin-flavor transitions in supernovae.

hep-ph↗

arXiv2009

Formation of Cooper pairs in quantum oscillations of electrons in plasma

We study low energy quantum oscillations of electron gas in plasma. It is shown that two electrons participating in these oscillations acquire additional negative energy when they interact by means of a virtual plasmon. The additional energy leads to the formation a Cooper pair and possible existence of the superconducting phase in the system. We suggest that this mechanism supports slowly damping oscillations of electrons without any energy supply. Basing on our model we put forward the hypothesis the superconductivity can occur in a low energy ball lightning.

physics.plasm-ph↗

arXiv2008

Evolution of Mixed Particles Interacting with Classical Sources

We study the systems of scalar and spinor particles with mixing emitted by external classical sources. The particles wave functions exactly accounting for external sources are obtained directly from the Lorentz invariant wave equations in (3+1)-dimensional space-time. Then we discuss sources which are localized in space and emit harmonic radiation. We obtain that the considered scalar and spinor fields can be converted from one type to another due to the presence of the vacuum mixing. This phenomenon is shown to be analogous to neutrino flavor oscillations in vacuum since the calculated transition and survival probabilities coincide with the corresponding expressions for neutrino oscillations. When we discuss the evolution of spinor particles, the situation of general mass matrix, which has both Dirac and Majorana mass terms, is studied. In this case we analyze the appearance of antiparticles in the initial particles beam. The relevance of the developed technique to the description of neutrino flavor oscillations is examined.

hep-ph↗

arXiv2007

Neutrino oscillations in matter and in twisting magnetic fields

We find the solution to the Dirac equation for a massive neutrino with a magnetic moment propagating in background matter and interacting with the twisting magnetic field. In frames of the relativistic quantum mechanics approach to the description of neutrino evolution we use the obtained solution to derive neutrino wave functions satisfying the given initial condition. We apply the results to the analysis of neutrino spin oscillations in matter under the influence of the twisting magnetic field. Then on the basis of the yielded results we describe spin-flavor oscillations of Dirac neutrinos that mix and have non-vanishing matrix of magnetic moments. We again formulate the initial condition problem, derive neutrinos wave functions and calculate the transition probabilities for different magnetic moments matrices. The consistency of the obtained results with the quantum mechanical treatment of spin-flavor oscillations is discussed. We also consider several applications to astrophysical and cosmological neutrinos.

hep-ph↗

arXiv2007

Evolution of Mixed Dirac Particles Interacting with an External Magnetic Field

We study in the framework of relativistic quantum mechanics the evolution of a system of two Dirac neutrinos that mix with each other and have non-vanishing magnetic moments. The dynamics of this system in an external magnetic field is determined by solving the Pauli-Dirac equation with a given initial condition. We consider first neutrino spin-flavor oscillations in a constant magnetic field and derive an analytical expression for the transition probability of spin-flavor conversion in the limit of small magnetic interactions. We then investigate ultrarelativistic neutrinos in an transversal magnetic field and derive their wave functions and transition probabilities with no limitation for the size of transition magnetic moments. Although we consider neutrinos, our formalism is straightforwardly applicable to any spin-1/2 particles.

hep-ph↗

arXiv2007

Neutrino spin-flavor oscillations in electromagnetic fields of various configurations

We study spin-flavor oscillations of Dirac neutrinos with mixing and having non-zero matrix of magnetic moments in magnetic fields of various configurations. We discuss constant transversal and twisting magnetic fields. To describe the dynamics of Dirac neutrinos we use relativistic quantum mechanics approach based on the exact solutions to the Dirac-Pauli equation in an external electromagnetic field. We derive transition probabilities for different neutrino magnetic moments matrices.

hep-ph↗

arXiv2007

Neutrino flavor oscillations in background matter

We study the evolution of two mixed Dirac neutrinos in an external axial-vector field. The dynamics of this system is described in the framework of relativistic wave equations approach on the basis of the known solutions of the Dirac equation in an external field with a given initial condition. The general solution of the initial condition problem, exactly accounting for the external field, is obtained. Then we consider special form of the external field which corresponds to the standard model neutrino interactions with the background matter. In this limit we derive the transition probability and compare it with the previously known results.

hep-ph↗

arXiv2007

Spectral Properties of Numerical Differentiation

We study the numerical differentiation formulae for functions given in grids with arbitrary number of nodes. We investigate the case of the infinite number of points in the formulae for the calculation of the first and the second derivatives. The spectra of the corresponding weight coefficients sequences are obtained. We examine the first derivative calculation of a function given in odd-number points and analyze the spectra of the weight coefficients sequences in the cases of both finite and infinite number of nodes. We derive the one-sided approximation for the first derivative and examine its spectral properties.

math.NA↗

arXiv2007

Coriolis force corrections to g-mode spectrum in 1D MHD model

The corrections to g-mode frequencies caused by the presence of a central magnetic field and rotation of the Sun are calculated. The calculations are carried out in the simple one dimensional magnetohydrodynamical model using the approximations which allow one to find the purely analytical spectra of magneto-gravity waves beyond the scope of the JWKB approximation and avoid in a small background magnetic field the appearance of the cusp resonance which locks a wave within the radiative zone. These analytic results are compared with the satellite observations of the g-mode frequency shifts which are of the order one per cent as given in the GOLF experiment at the SoHO board. The main contribution turns out to be the magnetic frequency shift in the strong magnetic field which obeys the used approximations. In particular, the fixed magnetic field strength 700 KG results in the mentioned value of the frequency shift for the g-mode of the radial order n=-10. The rotational shift due to the Coriolis force appears to be small and does not exceed a fracton of per cent, α_Ω< 0.003.

astro-ph↗

arXiv2007

Evolution of Coupled Scalar and Spinor Particles in Classical Field Theory

We study the evolution of mixed scalar as well as spinor fields within the context of the classical field theory. The initial condition problem is solved and the fields distributions, exactly accounting for the initial conditions, are obtained for both scalar and spinor fields. In the system of two coupled fields we consider the special case of the initial conditions which are rapidly oscillating functions. It is demonstrated that the energy densities of the scalar fields and the intensities of the spinor fields coincide with the usual transition and survival probabilities of neutrino flavor oscillations in vacuum.

hep-ph↗

arXiv2006

Neutrino spin-flavor oscillations in rapidly varying magnetic fields

The general formalism for the description of neutrino oscillations in arbitrary rapidly varying external fields is elaborated. We obtain the new effective Hamiltonian which determines the evolution of the averaged neutrino wave function. The general technique is applied to the neutrino oscillations in rapidly varying magnetic fields. We evaluate the transition probabilities of the neutrino spin-flavor oscillations in magnetic fields of the Sun and compare them with the numerical solutions of the Schroedinger equation with the exact Hamiltonian.

hep-ph↗

arXiv2006

Evolution of coupled fermions under the influence of an external axial-vector field

The evolution of coupled fermions interacting with external axial-vector fields is described with help of the classical field theory. We formulate the initial conditions problem for the system of two coupled fermions in (3+1)-dimensional space-time. This problem is solved using the perturbation theory. We obtain in the explicit form the expressions for the leading and next to the leading order terms in the expansion over the strength of external fields. It is shown that in the relativistic limit the intensity of the fermion field coincides with the transition probability in the two neutrinos system interacting with moving and polarized matter.

hep-ph↗

arXiv2006

Neutrino spin oscillations in gravitational fields

We study neutrino spin oscillations in gravitational fields. The quasi-classical approach is used to describe the neutrino spin evolution. First we examine the case of a weak gravitational field. We obtain the effective Hamiltonian for the description of neutrino spin oscillations. We also receive the neutrino transition probability when a particle propagates in the gravitational field of a rotating massive object. Then we apply the general technique to the description of neutrino spin oscillations in the Schwarzschild metric. The neutrino spin evolution equation for the case of the neutrino motion in the vicinity of a black hole is obtained. The effective Hamiltonian and the transition probability are also derived. We examine the neutrino oscillations process on different circular orbits and analyze the frequencies of spin transitions. The validity of the quasi-classical approach is also considered.

hep-ph↗

arXiv2006

Formulae of numerical differentiation

We derived the formulae of central differentiation for the finding of the first and second derivatives of functions given in discrete points, with the number of points being arbitrary. The obtained formulae for the derivative calculation do not require direct construction of the interpolating polynomial. As an example of the use of the developed method we calculated the first derivative of the function having known analytical value of the derivative. The result was examined in the limiting case of infinite number of points. We studied the spectral characteristics of the weight coefficients sequence of the numerical differentiation formulae. The performed investigation enabled one to analyze the accuracy of the numerical differentiation carried out with the use of the developed technique.

math.NA↗

arXiv2006

Neutrino spin-flavor oscillations in rapidly varying external fields

We study neutrino spin-flavor oscillations in presence of rapidly varying external fields. The general formalism for the description of neutrino oscillations in arbitrary rapidly varying external fields is elaborated. We obtain the effective Hamiltonian which determines the evolution of the averaged neutrino wave function. We apply the general technique to neutrino oscillations in rapidly varying magnetic fields. The special case of the constant transversal and twisting magnetic fields is studied. We evaluate the effect of neutrino spin-flavor oscillations in rapidly varying magnetic fields of the Sun. The numerical solutions of the Schroedinger equation with the Hamiltonian accounting for the constant transversal and twisting magnetic fields are presented. We compare them with our approximate analytical transition probability formula and reveal good agreement at high frequencies of the twisting magnetic field.

hep-ph↗

arXiv2006

Neutrino spin relaxation in medium with stochastic characteristics

The helicity evolution of a neutrino interacting with randomly moving and polarized matter is studied. We derive the equation for the averaged neutrino helicity. The type of the neutrino interaction with background fermions is not fixed. In the particular case of a tau-neutrino interacting with ultrarelativistic electron-positron plasma we obtain the expression for the neutrino helicity relaxation rate in the explicit form. We study the neutrino spin relaxation in the relativistic primordial plasma. Supposing that the conversion of left-handed neutrinos into right-handed ones is suppressed at the early stages of the Universe evolution we get the upper limit on the tau-neutrino mass.

hep-ph↗

arXiv2005

Electron gas oscillations in plasma. Theory and applications

We analyze the obtained solutions of the non-linear Shroedinger equation for spherically and axially symmetrical electrons density oscillations in plasma. The conditions of the oscillations process existence are examined. It is shown that in the center or on the axis of symmetry of the systems the static density of electrons enhances. This process results in the increasing of density and pressure of the ion gas. We suggest that this mechanism could occur in nature as rare phenomenon called the fireball and could be used in carrying out the research concerning controlled fusion. The description of the experiments, carried out for the purpose to generate long-lived spherical plasma structures, is presented.

physics.plasm-ph↗

arXiv2005

Evolution of coupled classical fields

We study the evolution of the coupled scalar and fermion fields within the classical field theory. We examine the case of N coupled fields in 1+3 dimensional space. The general expressions for the fields distributions are obtained. The particular case of two fields in 1+1 dimensional space is carefully studied. We obtain the expressions for the averaged fields intensities and show that in the relativistic limit they are similar to the usual transition probabilities formulae of neutrino oscillations.

hep-ph↗