Dielectric tensor of low-dimensional metal systems

The dielectric tensor of a low-dimensional metal system has been introduced on the basis of the density matrix in the relaxation time approximation. The properties of this tensor have been analyzed. It has been proved that anisotropy and nonlocality are decisive features of the response of low-dimensional systems to an electromagnetic field. In particular, the expression has been derived for the dielectric tensor of nanometer- thick metal films. It has been shown that the dielectric tensor components can be reduced to the Drude dielectric function for a homogeneous metal in the case when the film thickness considerably exceeds the effective electron mean free path. The application of the classical distribution function for describing electrons in the film is justified under these conditions.     

Computer study of the physical properties of a copper film on a heated graphene surface

The structural, kinetic, and mechanical properties of a copper film deposited on single-layer and two-layer graphenes have been studied in a molecular-dynamics model in the temperature range 300 K ≤ T ≤ 3300 K. The film sizes are reduced in the “zigzag” direction more slowly than in the “armchair” direction. The differences have been found to appear in the behavior of copper atoms on single-layer and two-layer graphenes with increasing temperature. Copper atoms on the two-layer graphene have higher horizontal mobility over entire temperature range. However, Cu atoms on the single-layer graphene become more mobile in the vertical direction beginning from a temperature of ～1500 K. The stress tensor components of the copper film characterizing the action of forces on the horizontal areas have a sharp extremum at T = 1800 K in the case of the single-layer graphene and are characterized by quite smooth behavior in the case of the two-layer graphene.     

Dynamic magnetic susceptibility of a two-layer film in a strong magnetic field

A theoretical study is reported of the effect of interlayer exchange coupling on the resonance properties of a two-layer magnetic film with “easy-axis” and “easy-plane” anisotropic layers in a strong tilted magnetic field. The dependence of the resonance fields on the tilting angle of the external magnetic field to the film has been obtained, the tensor of integrated high-frequency film susceptibility has been found, and its dependence on the strength and orientation of the external field, as well as on layer thickness, has been analyzed. The results obtained agree with the available experimental data.     

A simple method for the determination of strains in epitaxial films: application to Eu(110) deposited on a Nb(110) buffer

In order to determine the strain tensor in a 375 nm thick Eu(110) epitaxial thin film, we have developed a new method, based on the accurate determination of the lattice vectors by high resolution X-ray diffraction. We show that a biaxial strain model gives a good representation of the state of the strains field in the film.     

Plastic relaxation anisotropy in epitaxial films grown on miscut Si(001) substrates

A way of calculating the structural parameters of semiconductor epitaxial layers grown on miscut (0 0 1) substrates is developed. It is shown that the difference between the tensor of film elastic strains and the spherical tensor of strains translating the film’s crystal lattice into the substrate’s lattice is a tensor whose components are proportional to X-ray strains. The technique is used to analyze GaAs and Ge_0.2Si_0.8 films grown on (1 1 13) Si substrates. The anisotropy of the degree of plastic relaxation is established for lateral directions perpendicular and parallel to the interfacial steps in the GeSi film. It is proposed that noninteger Miller indices be used to denote the direction and value of the rotation of the film’s crystal lattice with respect to the substrate lattice.     

Study of the mechanical interaction between an electromagnetic field and a nanoscopic thin film near electronic resonance

The mechanical interaction between an electromagnetic field and a nanoscopic thin film near electronic resonance is theoretically studied by calculation of Maxwell's stress tensor. As a result of numerical demonstrations for both propagating and evanescent incident waves, the following effects that are specific to this condition have been clarified: (1) The force exerted on a nanoscopic thin film is greatly enhanced near the resonance frequency to the same order of magnitude as for a film with macroscopic thickness. (2) The peak position of the gradient force in its spectrum is highly sensitive to the change in nanoscopic thickness that is due to the polaritonic effect. (3) In a total-reflection region a large enhancement of the repulsive force between the two thin films occurs when the films act as an optical cavity.     

Magneto-optics in the ultrafast regime: thermalization of spin populations in ferromagnetic films

We have characterized by pump-probe polarimetry the time-dependent dielectric tensor in a CoPt3 ferromagnetic film excited by 20 fs laser pulses. It is shown that, after the thermalization time of the electrons (approximately 50 fs), the dynamics of the real and the imaginary parts of the Voigt vector are identical. In addition, their relative variation is 10 times larger than that of the diagonal elements of the tensor, which allows one to infer that the spins dominate the magneto-optical response. During the thermalization process, the temporal behavior of the tensor elements opens new questions concerning the dynamics of the spins associated to a nonthermal electronic population in a ferromagnet.     

Dynamics of thin free liquid films stabilized with ionic surfactants

To study the dynamics of free liquid films which are stabilized with ionic surfactants, an electrohydrodynamic theory is developed. The long-range interaction forces, namely the repulsive force arising from the overlap of diffuse electric double layers and the attractive Van der Waals-London force, are described by the Maxwell stress tensor with its related field equations and the Van der Waals potential. The short-range surface force has a normal Laplace component and a tangential surface tension gradient component. The total set of first-order equations and their boundary conditions, which describes the capillary waves on the surfaces and the induced flow motion in the film, has been solved. The dispersion relation for the “squeezing mode” is obtained. The cases of no-slip condition and the long-wavelength limit have been studied in more detail. The testability of the dispersion relation using laser beat spectroscopy is reported.     

Effects of the tensor force on low-energy heavy-ion fusion reactions: a mini review

In recent several years, the tensor force, one of the most important components of the nucleon–nucleon force, has been implemented in time-dependent density functional theories and it has been found to influence many aspects of low-energy heavy-ion reactions, such as dissipation dynamics, sub-barrier fusions, and low-lying vibration states of colliding partners. Especially, the effects of tensor force on fusion reactions have been investigated from the internuclear potential to fusion crosssections systematically. In this work, we present a mini review on the recent progress on this topic. Considering the recent progress of low-energy reaction theories, we will also mention more possible effects of the tensor force on reaction dynamics.     

Local-field anisotropy of a light wave in quasi-two-dimensional soft-matter objects

Experimental values of the Lorentz tensor components L _j for uniaxial quasi-two dimensional “soft matter” objects on substrates (bilayer lipid membranes, multilayer Langmuir films, smectics A, hexatic smectics B, submicron films of discotics Col _hd , micron anisotropic films of liquid-crystal comblike polymers and macromolecular polymers, submicron films of conjugated conductive polymers), freely suspended submicron films of smectics A, and uniaxially stretched micron films of conjugated conductive polymers have been determined using dispersion of refractive indices in the visible range. The dependences of the components L _j on the type of orientation (axial, planar) of uniaxial molecules (structural units of the film) with respect to the optical axis of the film, the film thickness, the substrate type, the chemical structure of molecules, and their long-range orientational order are established. It is revealed that the smectic A-hexatic B phase transition and two-dimensional crystallization of the smectic layer lead to changes in the components L _j due to the change in the orientational ordering of molecules as a result of the relation between the orientational and hexatic order parameters. All the above objects are characterized by isotropization of the Lorentz tensor L and the local-field tensor f with a simultaneous decrease in the birefringence of the sample and in the anisotropy of the molecular polarizability due to the change in the electronic structure of molecules. The correction for the anisotropy of the local-field tensor f to the orientational order parameter or the anisotropy of the molecular polarizability increases. The existing model approaches to calculating the components L _j for the objects under consideration are compared with the experimental data.     

On the algebraic types of the Bel–Robinson tensor

The Bel–Robinson tensor is analyzed as a linear map on the space of the traceless symmetric tensors. This study leads to an algebraic classification that refines the usual Petrov–Bel classification of the Weyl tensor. The new classes correspond to degenerate type I space-times which have already been introduced in literature from another point of view. The Petrov–Bel types and the additional ones are intrinsically characterized in terms of the sole Bel–Robinson tensor, and an algorithm is proposed that enables the different classes to be distinguished. Results are presented that solve the problem of obtaining the Weyl tensor from the Bel–Robinson tensor in regular cases.     

类硼离子基态的精细结构(英文)

以多电子精细结构哈密顿的球张量形式为基础,借助不可约张量理论,建立了类硼离子基态精细结构能量的解析表达式.完成了所有角向积分和自旋求和计算,使精细结构能量表示为若干个径向积分之和.在此基础上计算了类硼体系(Z=5~8)基态精细结构能量,计算结果与实验数据符合得较好.     

类氟离子基态的精细结构

以多电子精细结构哈密顿的球张量形式为基础,借助不可约张量理论,建立了类氟离子基态精细结构能量的解析表达式.完成了所有角向积分和自旋求和计算,使精细结构能量表示为若干个径向积分之和.在此基础上对类氟体系(Z=9～13)基态的精细结构能量进行了具体计算,计算结果与实验数据符合得较好.     

Concircular Curvature Tensor and Fluid Spacetimes

In the differential geometry of certain F-structures, the importance of concircular curvature tensor is very well known. The relativistic significance of this tensor has been explored here. The spacetimes satisfying Einstein field equations and with vanishing concircular curvature tensor are considered and the existence of Killing and conformal Killing vectors have been established for such spacetimes. Perfect fluid spacetimes with vanishing concircular curvature tensor have also been considered. The divergence of concircular curvature tensor is studied in detail and it is seen, among other results, that if the divergence of the concircular tensor is zero and the Ricci tensor is of Codazzi type then the resulting spacetime is of constant curvature. For a perfect fluid spacetime to possess divergence-free concircular curvature tensor, a necessary and sufficient condition has been obtained in terms of Friedmann-Robertson-Walker model.     

Metric and Ricci tensors for a certain class of space-times ofD type

The class of space-times has been determined at the connection level, assuming the existence of some symmetrical relations between the Ricci rotation coefficients. It has been assumed, for instance, that at least two shear-free congruences of null geodesics exist. We have shown that onlyD type or conformally flat space-times can belong to this class. The theorem has been proved that a system of coordinates exists in which the metric tensor can depend on two coordinates, only. The metric tensor has been determined with an accuracy to two functions, each of which is a function of only one coordinate. Linear, second-order differential expressions have been found for these two functions. They determine the Ricci tensor. Several solutions of the Einstein-Maxwell equations with a cosmological constant are given.On leave from the Institute of Theoretical Physics, Warsaw University, Warsaw, Poland.     

类碳体系基态能量的精细结构(英文)

以多电子原子精细结构哈密顿的球张量形式和不可约张量理论为基础,建立了计算多电子原子精细结构(包括自旋-轨道相互作用、自旋-其它轨道相互作用和自旋-自旋相互作用)能量的一般性解析理论形式,应用所建立的理论对类碳体系(Z=6～8)基态的精细结构能量进行了具体计算,计算结果与实验数据符合得较好.     

Control of extraordinary light transmission through perforated metal films using liquid crystals

We calculate the effective dielectric tensor of a metal film penetrated by cylindrical holes filled with a nematic liquid crystal (NLC). We assume that the director of the NLC is parallel to the film, and that its direction within the plane can be controlled by a static magnetic field, via the Freedericksz effect. To calculate the effective dielectric tensor, we consider both randomly distributed holes (using a Maxwell-Garnett approximation) and a square lattice of holes (using a Fourier technique). Both the holes and the lattice constant of the square lattice are assumed small compared to the wavelength. The films are found to exhibit extraordinary light transmission at special frequencies related to the surface plasmon resonances of the composite film. Furthermore, the frequencies of peak transmission are found to be substantially split when the dielectric in the holes is anisotropic. For typical NLC parameters, the splitting is of order 5–10% of the metal plasma frequency. Thus, the extraordinary transmission can be controlled by a static magnetic or electric field whose direction can be rotated to orient the director of the NLC. Finally, as a practical means of producing the NLC-filled holes, we consider the case where the entire perforated metal film is dipped into a pool of NLC, so that all the holes are filled with the NLC, and there are also homogeneous slabs of NLC on both sides of the film. The transmission in this geometry is shown to have similar characteristics to that in which the NLC-filled screen is placed in air.     

Comments on the properties of one- and two-body double tensor operators

Recently, the parity, charge, time and Hermitian conjugation properties of one-body tensor operators have been reexamined and the Racah algebra has been formally extended to two-body tensor operators. In this paper we consider several important aspects related to these problems. First, we present a proof of the communication relations for two-body operators which was previously postulated. Then, comparing the reduced matrix elements for one- and two-body operators we find the normalization constant for the latter. We subsequently show that the P- and T-conjugation relations for tensor operators are relativistically invariant. Finally, we analyze the question of Hermitian conjugation of double tensor operators and conclude that previously stated conditions on their ranks were too restrictive and resulted in omissions of some terms from theoretical analyses. We show examples of tensor operators which were customarily neglected but indeed should be retained in the effective Hamiltonian.     

张量力在16O+16O熔合动力学中的效应（英文）

利用时间相关Hartree-Fock 理论和完整Skyrme 有效相互作用研究了16O+16O 碰撞在库仑位垒附近的熔合动力学。数值计算是在没有任何对称性约束的三维笛卡尔基下完成。将时间相关Hartree-Fock 理论和冻结密度近似下的能量密度泛函方法给出的库仑位垒与实验结果进行了比较,发现同位旋标量的张量项能降低自旋饱和体系16O+16O的库仑位垒,而库仑位垒高度随着同位旋矢量的张量项的耦合常数减小而降低。并计算了包含和不包含张量力的16O+16O熔合截面,发现张量力对16O+16O碰撞在库仑位垒附近的熔合动力学影响较小。The fusion dynamics of 16O+16O around Coulomb barrier has been studied in the timedependent Hartree-Fock (TDHF) theory with the full Skyrme effective interaction. The calculations have been carried out in three-dimensional Cartesian basis without any symmetry restrictions. We have included the full tensor force and all the time-odd terms in Skyrme energy density functional (EDF). The Coulomb barrier obtained from the dynamical TDHF calculations and EDF with frozen density approximation has been compared with the available experimental data. The isoscalar tensor terms and the rearrangement of other terms are found to decrease the barrier height in the spin-saturated system 16O+16O, while the energy of Coulomb barrier tends to decrease as the isovector coupling constant decreases. The fusion cross section for 16O+16O collision has been calculated with and without the tensor force. We found that the tensor force has minor effect on the fusion dynamics of 16O+16O at the energies around Coulomb barrier.