The special theory of relativity as applied to the Born–Oppenheimer–Huang approach

In two recent publications (Int. J. Quant. Chem. 114, 1645 (2014) and Mole. Phys. 114, 227 (2016)) it was shown that the Born–Hwang (BH) treatment of a molecular system perturbed by an external field yields a set of decoupled vectorial wave equations, just like in electro-magnetism. This finding led us to declare on the existence of a new type of Fields, which were termed Molecular Fields. The fact that such fields exist implies that at the vicinity of conical intersections exist a mechanism that transforms a passing-by electric beam into a field which differs from the original electric field. This situation is reminiscent of what is encountered in astronomy where Black Holes formed by massive stars may affect the nature of a near-by beam of light. Thus, if the non-adiabatic-coupling-terms (NACT) with their singular points may affect the nature of such a beam (see the above two publications), then it would be interesting to know to what extend NACTs (and consequently also the BH equation) will be affected by the special theory of relativity as introduced by Dirac. Indeed, while applying the Dirac approach we derived the relativistic affected NACTs as well as the corresponding BH equation.     

Momentum Space Diffusion from Spatially Amplified Waves in a Plasma in a Magnetic Field

Quasilinear equations for relativistic plasmas in external magnetic fields are derived for the case of spatially growing wave turbulence. This generalizes the well-known quasilinear approach to an amplifying relativistic plasma. The equations can be cast in condensed momentum-space diffusive form. The diffusion tensor is given. As a result an inhomogeneity is produced in the space charge distribution giving rise to the development of a second-order field-aligned dc electric field. A general formula for the electrostatic potential is presented, which is specialised to the case of ion-cyclotron turbulence. Here the field points out of the interaction region.     

New Concepts from the Evans Unified Field Theory. Part One: The Evolution of Curvature,Oscillatory Universe Without Singularity,Causal Quantum Mechanics,and General Force and Field Equations

No Heading The Evans field equation is solved to give the equations governing the evolution of scalar curvature R and contracted energy-momentum T. These equations show that R and T are always analytical, oscillatory, functions without singularity and apply to all radiated and matter fields from the sub-atomic to the cosmological level. One of the implications is that all radiated and matter fields are both causal and quantized, contrary to the Heisenberg uncertainty principle. The wave equations governing this quantization are deduced from the Evans field equation. Another is that the universe is oscillatory without singularity, contrary to contemporary opinion based on singularity theorems. The Evans field equation is more fundamental than, and leads to, the Einstein field equation as a particular example, and so modifies and generalizes the contemporary Big Bang model. The general force and conservation equations of radiated and matter fields are deduced systematically from the Evans field equation. These include the field equations of electrodynamics, dark matter, and the unified or hybrid field.     

Energy spectra and quantum crystallization in two-electron quantum dots in a magnetic field

Quantum crystallization of electrons in a quantum dot (QD) subjected to an external magnetic field is considered. Two-electron QDs with two-dimensional (2D) parabolic confining potential in an external transverse magnetic field are calculated. The Hamiltonian is numerically diagonalized in the basis of one-particle functions to find the energy spectra and wave functions for the relative motion of electrons with inclusion of electron-electron interaction for a broad range of the confining-potential steepness (α) and external magnetic fields (B). The region of the external parameters (α, B) within which a gradual transition to quantum crystalline order occurs is numerically determined. In contrast to a 2D unbounded system, a magnetic field acts nonmonotonically on “crystallization” in a quantum dot with several electrons because of a competition between two effects taking place with increasing B, namely, decreasing spread of the electron wave functions and increasing effective steepness of the confining potential, which reduces the average separation between electrons. Fiz. Tverd. Tela (St. Petersburg) 40, 1753–1759 (September 1998)     

Liouville and Fokker–Planck dynamics for classical plasmas and radiation

We consider a nonequilibrium statistical system formed by many classical non‐relativistic particles of opposite electric charges (plasma) and by the classical dynamical electromagnetic (EM) field. The charges interact with one another directly through instantaneous Coulomb potentials and with the dynamical degrees of freedom of the transverse EM field. The system may also be subject to external influences of: i) either static, but spatially inhomogeneous, electric and magnetic fields (case 1)), or ii) weak distributions of electric charges and currents (case 2)). The particles and the dynamical EM field are described, for any time t > 0, by the classical phase‐space probability distribution functional (CPSPDF) f and, at the initial time (t = 0), by the initial CPSPDF f_in. The CPSPDF f and f_in, multiplied by suitable Hermite polynomials (for particles and field) and integrated over all canonical momenta, yield new moments. The Liouville equation and f_in imply a new nonequilibrium linear infinite hierarchy for the moments. In case 1), f_in describes local equilibrium but global nonequilibrium, and we propose a long‐time approximation in the hierarchy, which introduces irreversibility and relaxation towards global thermal equilibrium. In case 2), the statistical system, having been at global thermal equilibrium, without external influences, for t ≤ 0, is subject to weak external charge‐current distributions: then, new hierarchies for moments and their long‐time behaviours are discussed in outline. As examples, approximate mean‐field (Vlasov) approximations are treated for both cases 1) and 2).     

Propagation and interaction of ion-acoustic solitary waves in a quantum electron-positron-ion plasma

This paper discusses the existence of ion-acoustic solitary waves and their interaction in a dense quantum electron-positron-ion plasma by using the quantum hydrodynamic equations.The extended Poincar’e-Lighthill-Kuo perturbation method is used to derive the Korteweg-de Vries equations for quantum ion-acoustic solitary waves in this plasma.The effects of the ratio of positrons to ions unperturbation number density p and the quantum diffraction parameter H e (H p) on the newly formed wave during interaction,and the phase shift of the colliding solitary waves are studied.It is found that the interaction between two solitary waves fits linear superposition principle and these plasma parameters have significantly influence on the newly formed wave and phase shift of the colliding solitary waves.The investigations should be useful for understanding the propagation and interaction of ion-acoustic solitary waves in dense astrophysical plasmas (such as white dwarfs) as well as in intense laser-solid matter interaction experiments.     

The interaction of three fields in ECE theory: The inverse Faraday effect

The simultaneous interaction of three fundamental fields is illustrated in Einstein Cartan Evans (ECE) theory with reference to the effect of gravitation on the inverse Faraday effect. The three-field interaction in this case is that of the fermionic, electromagnetic and gravitational fields. The interaction of the first two is developed in a well-defined semi-classical approximation of the ECE wave equation and the effect of gravitation incorporated through the index reduced canonical energy momentum density T. The exercise is repeated using the ECE wave equations and a general rule developed for the effect of gravitation on the fermionic, electromagnetic weak and strong fields.     

A treatise on the interaction of molecular systems with short-pulsed highly-intense external fields

In this review, we consider two gauges: one, the field-free gauge, is formed by the field-free electronic eigenstates and the other, the field-dressed gauge, is formed by the field-dressed electronic basis set. The field-free gauge is used, of course, in the case of time-independent systems but then it is also the more common one to be used in the case of molecular systems exposed to external fields. This gauge is conceptually simple and therefore numerically friendly — two features which make it versatile for numerical application. The field-dressed gauge is, eventually, more involved but yields deeper insight which might lead to a better understanding of the complicated interaction between a molecular system and external fields. In addition, these features can be exploited to develop efficient and reliable approximations that may save CPU (computer processing unit) time in numerical applications. These two gauges are the main topics of the present review.     

Decay of a negative molecular ion in a constant electric field

The problem of the shift and broadening of the electron energy levels in the field of two 3D short-range potentials (e.g., the model of a negative molecular ion) by a constant electric field F is considered. The interaction of an electron with attraction centers is taken into account in the effective range approximation. We analyze the cases when both centers maintain weakly bound s states and when the electron state in the field of one of the centers is a p state. Exact numerical results for the shift and the width of the energy levels of a quasi-molecule as functions of field F, distance R between atomic centers, and the orientation of the quasi-molecule axis relative to vector F are presented, as well as the results of analytic treatment for a number of limiting cases. The exact values of complex energies of the quasi-molecule are compared with analytic results for a weak field in the case of identical s centers [26], as well as nonequivalent s centers and s-p centers; the applicability boundaries of the weak field approximation are established. It is shown that for large values of R, the position and width of the levels in a strong field are correctly described in perturbation theory in the exchange interaction. We analyze the field-induced quasi-intersection of molecular energy levels of the system with nonequivalent atomic centers and peculiarities in the energy level widths associated with this intersection. The results make it possible to qualitatively interpret the results of numerical calculations of the probability of homo- and heteronuclear molecules being ionized by a low-frequency laser field.     

Electrodynamics of Balanced Charges

We introduce here a new “neoclassical” electromagnetic (EM) theory in which elementary charges are represented by wave functions and individual EM fields to account for their EM interactions. We call so defined charges balanced or “b-charges”. We construct the EM theory of b-charges (BEM) based on a relativistic field Lagrangian and show that: (i) the elementary EM fields satisfy the Maxwell equations; (ii) the Newton equations with the Lorentz forces hold approximately when b-charges are well separated and move with non-relativistic velocities. When the BEM theory is applied to atomic scales it yields a hydrogen atom model with a frequency spectrum matching the Schrodinger model with desired accuracy. An important feature of the theory is a mechanism of elementary EM energy absorption established for retarded potentials.     

Dirac equation for the Hulthén potential within the Yukawa-type tensor interaction

Using the Nikiforov-Uvarov (NU) method, pseudospin and spin symmetric solutions of the Dirac equation for the scalar and vector Hulthén potentials with the Yukawa-type tensor potential are obtained for an arbitrary spin-orbit coupling quantum number κ. We deduce the energy eigenvalue equations and corresponding upper- and lower-spinor wave functions in both the pseudospin and spin symmetry cases. Numerical results of the energy eigenvalue equations and the upper- and lower-spinor wave functions are presented to show the effects of the external potential and particle mass parameters as well as pseudospin and spin symmetric constants on the bound-state energies and wave functions in the absence and presence of the tensor interaction.     

Nichtlineare Wechselwirkung elektromagnetischer Wellen im Plasma mit konstantem Magnetfeld

The nonlinear interaction of waves in anisotropic plasmas is considered. Solving the hydrodynamics equations with a n-th order perturbation procedure, an equation for the nonlinear electric field is derived. The n-th order current produced by interaction of waves with lower order is represented by means of a nonlinear tensor of conductivity, which is calculated for n = 2. It is shown, that a miced plasma wave with combination frequencies is excited as the result of interaction of two transverse (ordinary) waves propagating perpendicular to the magnetic field.     

Infrared wave interaction with an electron in the rectangular and circular plasma waveguide

In this article, the effect of the electron collision frequency with background ions on TM mode field components, the trajectory, and the electron energy gain in interaction infrared radiation with collisional plasma is studied. The field components of the TM mode in the rectangular and circular collisional plasma waveguides are obtained. The deflection angle and acceleration gradient of an electron in the fields associated with a transverse magnetic (TM) wave propagating inside a plasma waveguide for TM mode is studied. The relativistic momentum and energy equations for an electron are solved, which was injected initially along the propagation direction of the infrared. The results for collisionless and collisional plasma are graphically represented. Finally, the results for rectangular and circular waveguides are compared.     

Electromagnetic momentum in frontiers of modern physics

We review the role of the momentum of the electromagnetic (EM) fields P _e in several areas of modern physics. P _e represents the EM interaction in equations for matter and light waves propagation. As an application of wave propagation properties, a first order optical experiment which tests the speed of light in moving rarefied gases is presented. Within a classical context, the momentum P _e appears also in proposed tests of EM interactions involving open currents and angular momentum conservation laws. Moreover, P _e is the link to the unitary vision of the quantum effects of the Aharonov-Bohm (AB) type and, for several of these effects, the strength of P _e is evaluated. These effects provide a quantum approach to evaluate the limit of the photon mass m _ph. A new effect of the AB type, together with the scalar AB effect, provides the basis for table-top experiments which yield the limit m _ph = 9.4 × 10⁻⁵²g, a value that improves the results achieved with recent classical and quantum approaches.      

Functional differential equation approach to the large N expansion and mean field perturbation theory

An apparent difference between formulating mean field perturbation theory for λφ⁴ field theory via path integrals or via functional differential equations when there are external sources present is shown not to exist when mean field theory is considered as the N = 1 limit of the 0(N)λφ⁴ field theory. A simple method is given for determining the 1/N expansion for the Green's functions in the presence of external sources by directly solving the functional differential equations order by order in 1/N. The 1/N expansion for the effective action Γ(φ, χ) is obtained by directly integrating the functional differential equations for the fields φ and χ ( ) in the presence of two external sources j = −δΓ/δφ, S = −δΓ/δχ.     

一维分子晶体激子-孤子运动的激子运动学和动力学非线性效应

基于一维分子晶体相邻分子间静态作用势和分子间的(电)偶极-偶极相互作用,采用分子投影算符表示一维分子晶体激子系统的模型哈密顿量.在谐振近似下,根据激子运动学和动力学非线性效应的理解,推导了晶格运动和激子-孤子运动的非线性Klein-Gordon(K-G)耦合运动方程组.发现激子运动学和动力学非线性效应不但对孤子波函数的³,²{²}\{x²}有重要贡献,且导致重要的高阶非线性项,分别对⁵非线性和⁷非线性方程给出了解析解.详细分析非线性方程的Bell型孤子和Kink型孤子解结果,发现激子运动学和动力学非线性效应对激子的有效质量m有显著增加贡献,对激子-孤子能量(Ω)有更负的修正,孤子局域范围更小.对Bell型孤子以超声速(v＞c_s)沿一维键传播,而Kink型孤子以亚声速传播(v＜c_s),它们分别出现在激子能带底部和顶部. 关键词： 一维分子晶体 激子-孤立子 运动学和动力学非线性效应 非线性Klein-Gordon方程     

载流子在金属/聚对苯乙炔/金属结构中注入及输运的动力学研究

采用紧束缚的Su-Schrieffer-Heeger模型,利用非绝热动力学方法研究了载流子在金属/聚对苯乙炔(poly(p-phenylene vinylene,简记为PPV))/金属三明治结构中注入与输运的动力学过程.发现由于强的电子-晶格相互作用,注入的电荷在PPV链中形成波包,波包的形成与施加在金属电极上的偏压、PPV链上的电场强度及金属电极与PPV之间的界面耦合强度密切相关.在无外电场的情况下,当偏压达到临界值时电荷能够从金属电极注入到PPV链中并形成波包.随着电场强度的增大,波包能 关键词： 金属/聚对苯乙炔/金属结构 载流子输运 波包     

Diffraction of an electromagnetic wave from an infinitely long slit in an infinite metallic sheet

The diffraction of anE-polarized and anH-polarized wave by an imperfectly conducting slit (on which impedance boundary conditions are imposed) in an infinite metallic plane is investigated. The two independent problems are solved by using integral transforms, the Wiener-Hopf technique and asymptotic approximations. It is found that the diffracted field consists of the sum of fields produced by the two edges of the planes formed by the slit and a field due to the interaction of the two edges.