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.     

Dynamics of a Dirac particle in the theory with Lorentz invariance violation

Solutions to the Dirac equations have been obtained for particles interacting with vector, axial-vector, and tensor condensates within the framework of the Standard Model Extension. Possible applications of these solutions for describing the neutrino behavior in dense matter and electromagnetic field are considered.     

Magnetization reversal of small particles in an oscillating magnetic field

The nonlinear behavior of single spherical particles and many-particle ensembles under an external oscillating magnetic field was studied using the Landau-Lifshitz-Gilbert approach. The exact analytical formulae for calculating field frequency and the dependence of the configuration of the initial moment on the system mean magnetization were obtained. Using asymptotic decomposition we obtained simple expressions for describing the nonlinear dynamics of spherical particles in the cases of large and small frequencies. These solutions are in good agreement with numerical calculations of the Landau-Lifshitz-Gilbert equation for the considering systems.     

Relativistic dynamics of cylindrical shells of counter-rotating particles

Although infinite cylinders are not astrophysical entities, it is possible to learn a great deal about the basic qualitative features of generation of gravitational waves and the behavior of the matter conforming such shells in the limits of very small radius. We study an analytical model of a relativistic cylindrical shell of counter-rotating particles using kinetic theory for the matter and the junction conditions through the shell to obtain its equation of motion. The nature of the static solutions are analyzed, both for a single shell as well as for two coaxial shells. In the latter case, we integrate numerically the time dependent equation of motion of the external shell, when we neglect the wave components of the gravitational field at the shells locations. We obtain solutions that correspond to shells that perform damped oscillations, collapse, or are locally expanding. The collapse ends (numerically) when the external shell hits the interior shell. The numerically work also shows that the radiation becomes important after the bounce of the external shell.     

Coherent polarization driven by external electromagnetic fields

The coherent interaction of the electromagnetic radiation with an ensemble of polarizable, identical particles with two energy levels is investigated in the presence of external electromagnetic fields. The coupled non-linear equations of motion are solved in the stationary regime and in the limit of small coupling constants. It is shown that an external electromagnetic field may induce a macroscopic occupation of both the energy levels of the particles and the corresponding photon states, governed by a long-range order of the quantum phases of the internal motion (polarization) of the particles. A lasing effect is thereby obtained, controlled by the external field. Its main characteristics are estimated for typical atomic matter and atomic nuclei. For atomic matter the effect may be considerable (for usual external fields), while for atomic nuclei the effect is extremely small (practically insignificant), due to the great disparity in the coupling constants. In the absence of the external field, the solution, which is non-analytic in the coupling constant, corresponds to a second-order phase transition (super-radiance), which was previously investigated.     

中性粒子在Ioffe阱中的经典运动方程的Floquet解

研究中性粒子在Ioffe阱中近原点区域的囚禁时,阱中的磁场可以呈现出一种简明的形式.磁矩μ反平行于磁场的中性粒子在阱中与磁场发生相互作用,借助相互作用势,可以获得粒子在阱中的经典运动方程.在一定的条件下,采用迭代近似的目的,将方程演化为马丢方程的形式,利用传统的WKBJ目的可实现方程的近似求解.研究阱中中性粒子的囚禁问题时,感兴趣的是马丢方程的Floquet解,即周期为π,2π的全周期和半周期解,欲获得这种周期解,马丢方程中的参数λ和q必须满足一定的关系,为此必须选择阱的特定参数和粒子的特定初始条件,对这一问题进行了探索性的研究.     

Brownian dynamics simulations with spin Brownian motion on the negative magneto-rheological effect of a rod-like hematite particle suspension

We have investigated the behaviour of a suspension of magnetic rod-like hematite particles in a simple shear flow with the addition of an applied magnetic field. A significant feature of the present hematite particle suspension is the fact that the magnetic moment of the hematite particle lies normal to the particle-axis direction. From simulations, we have attempted to clarify the dependence of the negative magneto-rheological effect on the particle aggregation and orientational distribution of particles. The present Brownian dynamics method has a significant advantage in that it takes into account the spin rotational Brownian motion about the particle axis in addition to the ordinary translational and rotational Brownian motion. The net viscosity is decomposed into three components and discussed at a deeper level and in detail: these three viscosity components arise from (1) the torque due to the magnetic particle–field interaction, (2) the torque and (3) the force due to the interaction between particles. It is found that a slight change in the orientational distribution has a significant influence on the negative magneto-rheological effect. In a relatively dense suspension, the viscosity components arising from an applied magnetic field and the interaction between particles come to change rapidly for a certain strength of the magnetic particle–particle interaction, which is due to the onset of the formation of raft-like clusters.     

Toward a nonlinear theory of acceleration of charged particles in a linearly polarized EH-ubitron field

The motion of charged particles in a linearly polarized EH-ubitron field with sinusoidal time dependence of the variable component of the magnetic field is investigated. It is shown that, depending on the parameters of the system and the initial conditions of entry of the particle into the EH-field region, three different types of motion are possible: ballistic motion, capture in the vicinity of one of the maxima of the magnetic field, and escape of particles from the EH-field region. An analytical expression is found for the criterion determining the type of motion of the particles, along with analytical solutions for the energy of the particles in the approximation of slow variation of the magnetic field amplitude in time. Peculiarities of the motion of the particles in EH fields with arbitrary rate of change of the magnetic field amplitude in time are investigated numerically. Zh. Tekh. Fiz. 69, 87–93 (January 1999)     

The influence of a varying field on the non-Markovian migration of particles

The influence of an external varying field on the non-Markovian migration of particles described in the continuous-time random walk model (CTRWM) was analyzed theoretically. In terms of the Markovian representation for the CTRWM suggested earlier, a rigorous method for describing the influence of an external force was developed. This method reduced the problem to solving the non-Markovian stochastic Liouville equation (SLE) for the particle distribution function. An analysis of the derived SLE and its comparison with the earlier equations were performed. The method was used to study the characteristic features of the time dependence of the first and second moments of the distribution function for particles involved in subdiffusion motion in a uniform varying external field. Both oscillating and fluctuating fields were considered. In both cases, anomalously strong field effects on the second particle distribution moment (variance) were observed. This influence was especially strong for a fluctuating field, and in the limit of anomalously slow fluctuations at that.     

Solving a two-electron quantum dot model in terms of polynomial solutions of a Biconfluent Heun equation

The effects on the non-relativistic dynamics of a system compound by two electrons interacting by a Coulomb potential and with an external harmonic oscillator potential, confined to move in a two dimensional Euclidean space, are investigated. In particular, it is shown that it is possible to determine exactly and in a closed form a finite portion of the energy spectrum and the associated eigenfunctions for the Schrödinger equation describing the relative motion of the electrons, by putting it into the form of a biconfluent Heun equation. In the same framework, another set of solutions of this type can be straightforwardly obtained for the case when the two electrons are submitted also to an external constant magnetic field.     

Localized and delocalized motion of colloidal particles on a magnetic bubble lattice

We study the motion of paramagnetic colloidal particles placed above magnetic bubble domains of a uniaxial garnet film and driven through the lattice by external magnetic field modulation. An external tunable precessing field propels the particles either in localized orbits around the bubbles or in superdiffusive or ballistic motion through the bubble array. This motion results from the interplay between the driving rotating signal, the viscous drag force and the periodic magnetic energy landscape. We explain the transition in terms of the incommensurability between the transit frequency of the particle through a unit cell and the modulation frequency. Ballistic motion dynamically breaks the symmetry of the array and the phase locked particles follow one of the six crystal directions.     

Density waves in quark matter within the Nambu-Jona-Lasinio model in an external magnetic field

The possibility of forming static dual scalar and pseudo-scalar density wave condensates in dense quark matter is considered for the Nambu-Jona-Lasinio model in an external magnetic field. Within a mean-field approximation, the effective potential of the theory is obtained and its extrema are numerically studied and a phase diagram of the system is constructed. It is shown that the presence of a magnetic field favors the formation of spatially inhomogeneous condensate configurations at low temperatures.     

General magnetized Weyl solutions: disks and motion of charged particles

We construct three families of general magnetostatic axisymmetric exact solutions of Einstein-Maxwell equations in spherical coordinates, prolate, and oblates. The solutions obtained are then presented in the system of generalized spheroidal coordinates which is a generalization of the previous systems. The method used to build such solutions is the well-known complex potential formalism proposed by Ernst, using as seed solutions vacuum solutions of the Einstein field equations. We show explicitly some particular solutions among them a magnetized Erez-Rosen solution and a magnetized Morgan-Morgan solution, which we interpret as the exterior gravitational field of a finite dislike source immersed in a magnetic field. From them we also construct using the well known “displace, cut and reflect” method exact solutions representing relativistic thin disks of infinite extension. We then analyze the motion of electrically charged test particles around these fields for equatorial circular orbits and we discuss their stability against radial perturbations. For magnetized Morgan-Morgan fields we find that inside of disk the presence of magnetic field provides the possibility of to find relativist charged particles moving in both prograde and retrograde direction.     

Exact relativistic models of perfect fluid disks in a magnetic field

Using the well-known “displace, cut and reflect” method we construct thin disks made of a perfect fluid in presence of a magnetic field. The models are based in a magnetic Reissner-Nordstrom metric of Einstein-Maxwell equations for a conformastatic spacetime. The influence of the magnetic field on the matter properties of the disk are analyzed. We also study the motion of charged test particles around the disks. We construct models of perfect fluid disks satisfying all the energy conditions.     

On the theory of phase transitions in magnetic fluids

Particles of magnetic fluids (ferrofluids), as is known from experiments, can condense to bulk dense phases at low temperatures (that are close to room temperature) in response to an external magnetic field. It is also known that a uniform external magnetic field increases the threshold temperature of the observed condensation, thus stimulating the condensation process. Within the framework of early theories, this phenomenon is interpreted as a classical gas-liquid phase transition in a system of individual particles involved in a dipole-dipole interaction. However, subsequent investigations have revealed that, before the onset of a bulk phase transition, particles can combine to form a chain cluster or, possibly, a topologically more complex heterogeneous cluster. In an infinitely strong magnetic field, the formation of chains apparently suppresses the onset of a gas-liquid phase transition and the condensation of magnetic particles most likely proceeds according to the scenario of a gas-solid phase transition with a wide gap between spinodal branches. This paper reports on the results of investigations into the specific features of the condensation of particles in the absence of an external magnetic field. An analysis demonstrates that, despite the formation of chains, the condensation of particles in this case can proceed according to the scenario of a gas-liquid phase transition with a critical point in the continuous binodal. Consequently, a uniform magnetic field not only can stimulate the condensation phase transition in a system of magnetic particles but also can be responsible for a qualitative change in the scenario of the phase transition. This inference raises the problem regarding a threshold magnetic field in which there occurs a change in the scenario of the phase transition.     

A class of stationary charged dust solutions of Einstein's field equations

We consider a special class of stationary rotating charged dust solutions of Einstein's field equations without cosmological constant. In these space-times, the motion of freely falling particles and of light rays can be visualized by the motion of charged particles in an appropriate model magnetic field. Any curl-free magnetostatic field, given on an open subset of Euclidean 3-space, can serve as a model magnetic field for a charged dust solution in this sense. The simplest example, corresponding to a homogeneous model magnetic field, is given by Som-Raychaudhuri space-time. Some other examples are worked out.     

Deformation and motion by gravity and magnetic field of a droplet of water-based magnetic fluid on a hydrophobic surface

Motion and deformation of a water-based magnetic fluid on a hydrophobic surface were investigated under gravity and a magnetic field. Surface energy and the resultant contact angle of the magnetic fluid depend on the surfactant concentration. The fluid viscosity is governed mainly by magnetite concentration. The front edge of the droplet moved under a weak external field. The rear edge required a higher external field for movement. The forces of gravity and the magnetic field for moving of the front edge are almost equal. However, those of the rear edge are different. The motion of magnetic fluids by an external field depends on concentrations of surfactants and magnetic particles, the external field, and experimental assembly.