Quantum Phase for an Electric Multipole Moment in Noncommutative Quantum Mechanics

We study the noncommutative nonrelativistic quantum dynamics of a neutral particle, which possesses an electric multipole moment, in the presence of an external magnetic field. First, by introducing a shift for the magnetic field we give the Schrödinger equations in the presence of an external magnetic field both on a noncommutative space and a noncommutative phase space, respectively. Then by solving the Schrödinger equations, we obtain quantum phases of the electric multipole moment both on a noncommutative space and a noncommutative phase space. We demonstrate that these phase are geometric and dispersive.     

Super scattering phenomenon in active spherical nanoparticles

Localized surface electromagnetic resonances in spherical nanoparticles with gain are investigated by using the Mie theory. Due to the coupling between the gain and resonances, super scattering phenomenon is raised and the total scattering efficiency is increased by over six orders of magnitude. The dual frequency resonance induced by the electric dipole term of the particle is observed. The distributions of electromagnetic field and the Poynting vector around nanoparticles are provided for better understanding different multipole resonances. Finally, the scattering properties of active spherical nanoparticles are investigated when the sizes of nanoparticles are beyond the quasi-static limit. It is noticed that more highorder multipole resonances can be excited with the increase of the radius. Besides, all resonances dominated by multipole magnetic terms can only appear in dielectric materials.     

Rotation of a Spherical Particle with Electrical Dipole Moment Induced by Steady Irradiation in a Static Electric Field

Rotation of a spherical particle in a static electric field and under steady irradiation that induces an electric dipole moment in the particle is studied for the first time. Along with the general treatment of the phenomenon, we analyze possible mechanisms underlying the photoinduction of dipole moment in the particle. Estimations of the angular velocity and the power expended by the rotating particle are provided. The indicated characteristics reach their maximum values if the size of particles is within the range of 10 nm to 10 μm.     

Spherical magnetic multipole moments system of currents

Concepts of spherical magnetic multipoles that represent distributions of electric currents over a spherical surface are introduced. Vector potentials of magnetic multipoles meet solenoidal- and harmonic-field conditions outside of the spherical surface and are continuous on it. Within the sphere, the vector potential of currents flowing outside of it is represented by the sum of vector potentials of basis magnetic multipoles with coefficients expressed by spherical multipole moments of system of currents. This expansion of the vector potential is in many respects analogous to the multipole expansion known from electrostatics. The first three terms of the expansion represent components of the well-known magnetic moment, the next five terms represent components of the magnetic quadrupole moment, etc. Possible applications of the magnetic spherical multipole technique are discussed. Krasnoyarsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 66–72, October, 1999.     

Controlling electric field distribution by graded spherical core-shell metamaterials

This paper investigates analytically the electric field distribution of graded spherical core-shell metamaterials, whose permittivity is given by the graded Drude model. Under the illumination of a uniform incident optical field, the obtained results show that the electrical field distribution in the shell region is controllable and the electric field peak’s position inside the spherical shell can be confined in a desired position by varying the frequency of the optical field as well as the parameters of the graded dielectric profiles. It has also offered an intuitive explanation for controlling the local electric field by graded metamaterials.     

The electric moment of a spherical particle,with the conductivity of the particle and medium taken into account

The behavior of a solid particle in an inhomogeneous electric field depends on the size and sign of the electric dipole moment of the particle. The dipole moment of a spherical particle is calculated, taking into account the conductivity of the particle and the surrounding medium.     

Dynamics of the Photoinduced Rotation of a Spherical Particle in a Constant Electric Field

Technical Physics - The rotation of a spherical particle in a constant electric field (an effect found earlier) has been analyzed. The particle is illuminated to induce the electric dipole moment...     

Angular spectrum representation of the electromagnetic multipole fields, and their reflection at a perfect conductor

Angular spectrum representations are derived for electric and magnetic multipole fields of arbitrary order. The result involves generalized spherical harmonics and generalized vector spherical harmonics, and the representations are in the form of integrals over the k_∥-plane. The representations are especially useful for the study of reflection and transmission of multipole radiation by a plane interface. As an example, we have considered the reflection at a perfect conductor. The reflected field of a multipole field could be expressed in the form of an angular spectrum with a very simple relation to the angular spectrum of the source field. The radiation pattern of a multipole near the perfect conductor is obtained with the method of stationary phase. We also introduce a method for determining the mirror image of the source of an arbitrary multipole.     

Calculation of Electric Mult ipole Moment Integrals Using Translation Formulas for Slater-Type Orbitals

Using translation formulas for Slater-type orbitals the infinite series through the overlap integrals are derived for the electric multipole moment integrals. By the use of the derived expressions the electric multipole moment integrals, and therefore, the electric properties of molecules can be evaluated most efficiently and accurately. The convergence of the series is tested by calculating concrete cases. An accuracy of for 10^-5 the computer results is obtained for 1 ≤ v ≤ 5, and for the arbitrary values of internuclear distances and screening constants of atomic orbitals.     

The theory of particle diffusion in a strong random magnetic field with an allowance for higher multipole moments of the distribution function

The kinetic equation including a small-scale collisional integral for the particles propagating in a strong random and regular magnetic field [29] is solved by expanding the distribution function into series in spherical harmonics of the particle momentum angles. Using methods of the quantum theory of the angular moment [41], the equations for higher multipole moments of the distribution function in the space of momentum angles are derived and solved in the stationary case for the galactic cosmic rays in interplanetary space. The observed amplitudes and phases of the diurnal variation harmonics can be explained using the results of measurements of the interplanetary magnetic field performed on board the Ulysses spacecraft [12–14] and other satellites [45, 46] with an allowance for redistribution of the interplanetary and interstellar magnetic field lines. The spatial structure of the convection and diffusion fluxes of the galactic cosmic rays is refined. Formulas taking into account a change in the Earth’s axis tilt relative to the direction toward the Sun are derived, which allow the annual changes in contributions to the diurnal variation harmonics to be determined. The equation of diffusion taking into account the 2nd harmonic is obtained, and the contribution of this effect to the relative particle density in the cosmic rays in a spherically symmetric case is analyzed.     

Contribution from cosmological scalar perturbations to the angular velocity spectrum of extragalactic sources

The possibility of the influence of adiabatic scalar perturbations on the angular velocity spectrum of extragalactic sources is considered. The multipole expansion coefficients of the angular velocity field in terms of vector spherical harmonics are calculated. We show that there is no contribution from adiabatic perturbations to the angular spectrum for a spatially flat Universe at the dusty stage, while there is a contribution only to the electric multiple coefficients at the stage of ??-term domination. The cases of long-wavelength and short-wavelength perturbations are considered separately. The relationship between the multipole angular velocity spectrum and the primordial scalar perturbation spectrum is discussed.     

Control of the motion of nanoelectromechanical systems based on carbon nanotubes

A new method is proposed for controlling the motion of nanoelectromechanical systems based on carbon nanotubes. In this method, a single-walled nanotube acquires an electric dipole moment owing to the chemical adsorption of atoms or molecules at open ends of the nanotube and, then, the electric dipole moment thus induced can be set in motion under the effect of a nonuniform electric field. The electric dipole moments of chemically modified nanotubes are calculated for the first time. The possibility of controlling the motion of nanotube-based nanoelectromechanical systems with the proposed method is demonstrated using a gigahertz oscillator as an example. The operating characteristics of the gigahertz oscillator and the controlling electric field are calculated.     

Semiconductor Nanoparticle in an Electric Field

The distributions of electrons and positive charges within a spherical semiconductor nanoparticle with surface electron traps in a uniform applied electric field are studied. The minimization of the total free energy gives the resulting effective electric field, which depends on the densities of donors and surface traps, as well as on the distance from the center of the nanoparticle. It is shown that the near-surface field at a relatively low donor density in the region of its entrance to the nanoparticle significantly differs from that in the region of its departure from the nanoparticle. The induced dipole moment of the nanoparticle is calculated and different contributions to it are determined. The ranges of applicability of the results are indicated.     

Magnetic multipole moments

Literature definitions of magnetic multipole moment operators are shown to be at variance, and new definitions are formulated which are consistent with a general multipole interaction hamiltonian and with the radiation field of a dynamic charge distribution. The applicability of traceless multipole moments is examined.

The multipole hamiltonian is used to derive expressions for some magnetic quadrupole distortion tensors. For those describing the quadrupole moment induced by a magnetic field and by a field gradient the number of independent components for various molecular symmetries is evaluated.     

Influence of a high-speed dielectric spherical particle''s movement on its scattering characteristics

The scattered field and differential scattered section (DSS) of a moving spherical particle with a high speed are investigated numerically. The coordinate and vector transformations are used to establish a theoretical basis for studying the laser scattering of a moving particle. The DSS of a moving spherical particle is explained by the electric and magnetic field from Mie scattering theory. Assuming the laser wavelength of 1.06 μm, we compute the ratio of the laser DSS of the moving dielectric spherical particle to that of the static dielectric spherical particle, which changes with radii, speeds and scattering angles of the particle. The numerical results show that the laser DSS of the oving pherical particle is tightly connected with its speed and scattering zenith angle. If a spherical particle moves with high speed, the laser DSS due to movement of the particle could not be neglected. If the speed of the dielectric spherical particle is fluctuating, the Doppler effect and the frequency spectrum expansion play important roles.     

Effect of electric field on the magnetic characteristics of a ferromagnetic nanosemiconductor

A theory is developed to describe the effect of an electric field on the magnetization of a thin ferromagnetic semiconductor plate. It is shown that the magnetic moment density is nonuniform under these conditions and that the total magnetic moment and its density depend on the electric field and the temperature. An electric field is found to increase the Curie temperature, and an inflection point is detected in the temperature dependence of the derivative of the total magnetic moment with respect to temperature.     

Plasma coating of nanoparticles in the presence of an external electric field

Film deposition onto nanoparticles by low-pressure plasma in the presence of an external electric field is studied numerically. The plasma discharge fluid model along with surface deposition and heating models for nanoparticles, as well as a dynamics model considering the motion of nanoparticles, are employed for this study. The results of the simulation show that applying external field during the process increases the uniformity of the film deposited onto nanoparticles and leads to that nanoparticles grow in a spherical shape. Increase in film uniformity and particles sphericity is related to particle dynamics that is controlled by parameters of the external field like frequency and amplitude. The results of this work can be helpful to produce spherical core-shell nanoparticles in nanomaterial industry.     

Anisotropic solutions of the Einstein-Boltzmann equations: I. General formalism

Given a choice of a timelike vector field, a particle distribution function in a general curved space-time can be analysed into spherical harmonics; the Liouville and Boltzmann equations can then be written as a set of equations relating these spherical harmonic components. We obtain these equations and the resulting equations for the spherical harmonic moments of the distribution function. An orthonormal tetrad formalism is used as an aid in our calculations; the set of moment equations used can be completed by giving Einstein's field equations as equations for the rotation coefficients of this tetrad. We discuss time and space reversal symmetry properties of the Boltzmann equation, but leave applications of the set of equations obtained to further papers.     

Self-interaction and massive vector field in the Schwarzschild space-time

Using a multipole expansion, we determine formally the massive vector field generated by a point source held fixed in the Schwarzschild space-time. We prove that its limit, when the mass of the Proca field goes to zero, does not tend to the corresponding massless vector field. In this limit we evaluate the expression of the self-force acting on the particle. The result is in accordance with that of Vilenkin, without the assumption that the point source is at a large distance from the horizon, that we extend to the case of a Reissner-Nordström space-time. We also investigate a further case: a point source within a spherical shell of matter for which the Proca field tends to the corresponding massless vector field.     

On atomic analogue of Landau quantization

We have studied the physics of atoms with permanent electric dipole moment and nonvanishing magnetic moment interacting with an electric field and inhomogeneous magnetic field. This system can be demonstrated as the atomic analogue of Landau quantization of charged particles in a uniform magnetic field. This Landau-like atomic problem is also studied with space-space noncommutative coordinates.