Spin-flavor oscillations of Dirac neutrinos described by relativistic quantum mechanics

Spin-flavor oscillations of Dirac neutrinos in matter and a magnetic field are studied using the method of relativistic quantum mechanics. Using the exact solution of the wave equation for a massive neutrino, taking into account external fields, the effective Hamiltonian governing neutrino spin-flavor oscillations is derived. Then the The consistency of our approach with the commonly used quantum mechanical method is demonstrated. The obtained correction to the usual effective Hamiltonian results in the appearance of the new resonance in neutrino oscillations. Applications to spin-flavor neutrino oscillations in an expanding envelope of a supernova are discussed. In particular, transitions between right-polarized electron neutrinos and additional sterile neutrinos are studied for realistic background matter and magnetic field distributions. The influence of other factors such as the longitudinal magnetic field, the matter polarization, and the non-standard contributions to the neutrino effective potential, is also analyzed.     

Neutrino oscillations in the field of a linearly polarized electromagnetic wave

Neutrino oscillations ν _iL ? ν _jR in the field of a linearly polarized electromagnetic wave are studied on the basis of a recently proposed effective Hamiltonian that describes the evolution of a spin in an arbitrary electromagnetic field. The condition of resonance amplification of the oscillations is analyzed in detail. A method is developed for qualitatively studying solutions to the equation of neutrino evolution in the resonance region. This method can be used to explore neutrino oscillations in fields of various configurations.     

Evolution of mixed particles interacting with classical sources

Systems of scalar and spinor particles that underwent mixing and which originated from external classical sources were investigated. Particle wave functions that take exactly into account external sources were obtained on the basis of solving Lorentz-invariant wave equations in four-dimensional space. Sources localized in space that emit harmonic radiation were considered. It was found that, owing to the presence of vacuum mixing, the scalar and spinor fields in question might oscillate—that is, go over to one another. It was shown that this phenomenon was analogous to neutrino flavor oscillations in a vacuum, since the calculated transition probabilities were coincidentwith their counterparts for neutrino oscillations. The situation of an arbitrarymassmatrix (that is, that which involved bothDirac andMajoranamass terms) was studied for the case of spinor-field evolution. The possibility of the appearance of antiparticles in a beam that originally involved only particles was analyzed. The question of whether the use of this method in describing neutrino flavor oscillations is legitimate was studied.     

Neutrino in matter and external fields

A technique for describing various processes proceeding in matter and involving neutrinos and electrons is discussed. This technique is based on “the method of exact solutions,” which implies the use of solutions to proper Dirac equations for particle wave functions in matter. Exact solutions for the neutrino and the electron in the cases of uniform nonmoving and rotating matter are discussed. On studying relativistic neutrino motion and associated neutrino-energy quantization in rotating matter, a semiclassical interpretation of particle finite motion is developed. In the general case of neutrino and electron motion in matter with varying parameters, the corresponding effective force acting on the particles is determined. The possibility of electromagnetic-wave radiation by an electron that moves in a dense neutrino flux of varying density and which is accelerated by this kind of force is predicted.     

Scattering of spatially inhomogeneous sound waves by a spherical particle

The problem of monopole, dipole, and rotational scattering of a spatially inhomogeneous time-harmonic sound field by an arbitrary spherical particle is solved for the cases of the medium being a viscous compressible liquid or an isotropic elastic medium. Equations for the spherical mean fields at the particle are obtained. These equations are used to derive the formulas for the scattered fields. Different limiting cases of particle behavior are considered. In particular, it is shown that the dipole scattering is determined by two components of particle oscillations, one of which corresponds to translational oscillatory motion and the other to oscillations of two antiphase monopoles. For these types of particle oscillations, a scattering matrix, which determines the scattering of an arbitrary field by a particle, is constructed. The matrix allows the formalization of the processes of multiple sound scattering by particles and is valid for any distances between the particles down to their contact.     

Spin-flavor oscillations of neutrinos in rapidly varying external fields

Spin-flavor oscillations of neutrinos in rapidly varying external fields are studied. A method for describing neutrino oscillations in arbitrary rapidly varying external fields is developed. An effective Hamiltonian that describes the evolution of the averaged neutrino wave function is obtained. Neutrino oscillations in rapidly varying magnetic fields are considered on the basis of the general formalism developed in this study. Neutrino transitions in a superposition of a constant and a rotating (in space) magnetic field that are transverse with respect to the neutrino velocity are studied. The probabilities of transitions in spin-flavor oscillations of neutrinos in the magnetic fields of the Sun are estimated. Numerical solutions to the Schrödinger equation for the Hamiltonian that describes neutrino interaction with a constant and a rotating (in space) magnetic field are given. It is shown that the approximate analytic formula obtained in the present study for the probability of neutrino transitions is consistent with the respective numerical solution to the evolution equation at high frequencies of the rotating magnetic fields.     

Neutrino oscillations in a homogeneous moving medium

The quasi-classical equation that describes both neutrino flavor oscillations and spin rotation in dense matter is obtained in the framework of quantum field theory. The solution of this equation for homogeneous medium is found. The probabilities of the spin-flavor transitions in unpolarized moving matter are calculated in the two-flavor model. We show that if the medium is at rest the neutrino helicity is conserved and the flavor transition probabilities are equal to those obtained using the phenomenological approach.     

Relativistic quantum theory of cyclotron resonance in a medium

The relativistic quantum theory of cyclotron resonance in a medium with arbitrary dispersive properties is presented. The quantum equation of motion for a charged particle in the field of a plane electromagnetic wave and in the uniform magnetic field in a medium is solved in the eikonal approximation. The probabilities of induced multiphoton transitions between the Landau levels in a strong laser field are calculated.     

Parametric resonance in neutrino oscillations in periodically varying electromagnetic fields

It is shown that a parametric resonance may arise in neutrino oscillations in varying electromagnetic fields. For two types of electromagnetic fields—an amplitude-modulated electromagnetic wave and a transverse magnetic field that is constant in time, but which has an amplitude periodically varying in space—the probabilities of the ν _i ? ν _j neutrino transitions are found, and it is shown that the probability amplitudes increase with time for a specific choice of the parameters of external electromagnetic fields.     

A relativized quark model for radiative baryon transitions

In this paper we investigate the electromagnetic form factors of baryons and their resonances using the framework of a relativized constituent quark model. Beyond the usual single-quark transition ansatz, we incorporate relativistic corrections which are welldetermined by the intrinsic interaction and confinement forces between the quarks. Furthermore we separate off for the compound three-quark system the relativistic center-of-mass motion by an approximately Lorentz-invariant approach. In this way for the first time recoil effects could be explicity studied. Using the harmonic oscillator wavefunctions with the configuration mixing as derived in the Isgur-Karl model, after restoring gauge invariance our relativized interaction hamiltonian can be used to calculate the transversely and longitudinally polarized photon transition form factors of the baryons.     

Electromagnetic excitation of infrasound in a conducting medium

A comparative analysis is made of the mechanisms of interaction between the electromagnetic fields of a global resonator and hydrodynamic and acoustic disturbances in a conducting medium. A universal boundary condition at the interface between air and the conducting medium, which takes into account the motion of the electrolyte, is obtained in an explicit analytical form to calculate the long-wavelength electromagnetic fields. The intensity of the electromagnetic field excited by a vertical hydroacoustic wave is estimated together with the efficiency of excitation of infrasonic oscillations of a conducting medium in the field of a global resonator. Zh. Tekh. Fiz. 68, 80–83 (January 1998)     

A laser accelerator

We show that a laser can efficiently accelerate charged particles if a magnetic field is introduced to improve the coupling between the particle and the wave. Solving the relativistic equations of motion for an electron in a uniform magnetic field and superposed, circularly polarized electromagnetic wave, we find that in energy-position phase space an electron traces out a curtate cycloid: it alternately gains and loses energy. If, however, the parameters are chosen so that the electron's oscillations in the two fields are resonant, it will continually accelerate or decelerate depending on its initial position within a wavelength of light. A laboratory accelerator operating under these resonant conditions appears attractive: in a magnetic field of 10⁵ Gauss, and the fields of a 5×10¹² W, 10 μm wavelength laser, an optimally positioned electron would accelerate to 700 MeV in only 10m. Supported by NASA Grant NSG-7490     

Weak and electromagnetic mechanisms of neutrino-pair photoproduction in a strongly magnetized electron gas

Expressions for the power of neutrino radiation from a degenerate electron gas in a strong magnetic field are derived for the case of neutrino-pair photoproduction via the weak and electromagnetic interaction mechanisms (it is assumed that the neutrino possesses electromagnetic form factors). It is shown that the neutrino luminosity of a medium in the electromagnetic reaction channel may exceed substantially the luminosity in the weak channel. Relative upper bounds on the effective neutrino magnetic moment are obtained.     

Excitonic Rabi oscillations in a quantum dot: local field impact

The influence of local fields on the excitonic Rabi oscillations in an isolated, arbitrary shaped quantum dot (QD) has been theoretically investigated. QD interaction with both a classical electromagnetic field and quantum light has been considered. In the classical light, time harmonic and ultrashort pulse excitations are analyzed. The general formalism has been formulated for quantum light and applied to the case of a Fock qubit. Noticeable modification of the Rabi oscillation dynamics induced by the local fields is predicted to be observable in QDs exposed to both classical and quantum light. In particular, the bifurcation and anharmonism in the Rabi oscillations have been revealed under time harmonic excitation and a dependence of the Rabi oscillation period on the QD depolarization has been obtained.     

Quantum vacuum contribution to the momentum of dielectric media

Momentum transfer between matter and electromagnetic field is analyzed. The related equations of motion and conservation laws are derived using relativistic formalism. Their correspondence to various, at first sight self-contradicting, experimental data (the so-called Abraham-Minkowski controversy) is demonstrated. A new, Casimir-like, quantum phenomenon is predicted: contribution of vacuum fluctuations to the motion of dielectric liquids in crossed electric and magnetic fields. Velocities of about 50 nm/s can be expected due to the contribution of high frequency vacuum modes. The proposed phenomenon could be used in the future as an investigating tool for zero fluctuations. Other possible applications lie in fields of microfluidics or precise positioning of micro-objects, e.g., cold atoms or molecules.     

f(R,L m ) gravity

We generalize the f(R) type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R and of the matter Lagrangian L _m . We obtain the gravitational field equations in the metric formalism, as well as the equations of motion for test particles, which follow from the covariant divergence of the energy-momentum tensor. The equations of motion for test particles can also be derived from a variational principle in the particular case in which the Lagrangian density of the matter is an arbitrary function of the energy density of the matter only. Generally, the motion is non-geodesic, and it takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equation of motion is also considered, and a procedure for obtaining the energy-momentum tensor of the matter is presented. The gravitational field equations and the equations of motion for a particular model in which the action of the gravitational field has an exponential dependence on the standard general relativistic Hilbert–Einstein Lagrange density are also derived.     

Relativistic ponderomotive forces

The interaction of a relativistic classical electron with an inhomogeneous electromagnetic field is investigated. In second-order perturbation theory the motion is separated into fast and slow motions, and the relativistic Newtonian equation is averaged over the fast oscillations. The rate of change obtained for the slow component of the electron momentum is interpreted as a relativistic ponderomotive force. The result is generalized to the relativistic case of the wellknown expression for the Gaponov-Miller force acting on an electron at rest. The expressions obtained for the relativistic ponderomotive forces are very complicated in the general case. They simplify in the limit of a stationary field (pulses of long duration) and a small gradient. The most typical and simplest special case of an inhomogeneous field—a stationary plane-focused beam—is investigated. The main difference between relativistic ponderomotive forces and their nonrelativistic limit is they have multiple components. In addition to the usual force directed along the gradient of the field, the relativistic case is also characterized by force components that do not have the form of the gradient of a potential and are parallel to the wave vector and the direction of the field polarization. It is shown that when a relativistic electron travels in a direction close to the direction of the wave vector of a focused laser beam, these components can greatly exceed the gradient force. A force directed along the field polarization vector arises even when the gradient of the field in this direction is zero. Zh. éksp. Teor. Fiz. 116, 1198–1209 (October 1999)     

Quark mixing in the discrete dark matter model

We consider a model in which dark matter is stable as it is charged under a Z₂ symmetry that is residual after an A₄ flavour symmetry is broken. We consider the possibility to generate the quark masses by charging the quarks appropriately under A₄. We find that it is possible to generate the CKM mixing matrix by an interplay of renormalisable and dimension-six operators. In this set-up, we predict the third neutrino mixing angle to be large and the dark matter relic density to be in the correct range. Low energy observables - in particular meson-antimeson oscillations - are hard to facilitate. We find that only in a situation where there is a strong cancellation between the Standard Model contribution and the contribution of the new Higgs fields, B meson oscillations are under control.