Criterion for and the physical interpretation of minimal and nonminimal interactions

A classification of currents for finite- and infinite-component wave equations is proposed depending on their algebraic and convective nature. Algebraic terms with a consistent one-particle interpretation constitute the minimal interactions. The nonminimal interactions are interpreted as effective c-number currents describing many particle effects and/or composite structures. A number of applications are treated.     

Motion invariants for a charge in a linearly polarized wave field

Six motion integrals for a relativistic charge in the field of a transverse linearly polarized electromagnetic wave propagating with an arbitrary phase velocity u>c were obtained by solving the canonical equations of motion. On the basis of these integrals, the charge trajectory as a function of the wave phase is analyzed in a fixed coordinate system. The coordinates, time, and phase are related by elliptic functions.     

Functional quantum statistics of light propagation in a two-level system

The functional Fokker-Planck formalism developed in a preceding paper is applied to the problem of a radiation field propagating in a medium, which contains resonant two-level atoms. Besides the electromagnetic field also the medium is described by continuous space dependent fields. We give the masterequation and transform it into ac-number functional differential equation for a characteristic functional. This equation is reduced considerably by the projection onto one dimension and the introduction of the diffusion approximation. It forms a solid basis for the study of all types of light propagation in resonant media including classical and quantum noise. We give an approximate solution of this equation by considering the problem of an externally pumped optical transmission line, in the case that saturation effects are absent. The spectral function of the electric field strength is obtained which describes a statistical mixture of photons with the quasiparticles of the polarization field. It shows the onset of a condensation of the quasiparticles into a single state. Self excitation of the transmission line is obtained at a certain threshold of the atomic inversion. This threshold is characterized by a finite occupation number of one single quasiparticle state. The influence of a finite length of the transmission line is briefly considered.     

Chiral invariant Gross-Neveu model: Classical versus quantum

We present a unification of different and independently investigated aspects of the chiral invariant Gross-Neveu model. Special emphasis is placed on the relevance of classical (c-number, non Grassmann) spinor solutions of the G-N field equations for the construction, and thus understanding of the respective quantized Fermi model. To get an insight into the “quantum meaning of classical field theory” if specialized to the G-N case, we perform the path integral quantization procedure which first leads to the Fermi oscillator problem, and then, after appropriate generalizations, to the quantum Fermi G-N model. Path integrals are carried out with respect to c-number spinor paths only, and in fact no reference is necessary to the Grassmann algebra methods, which are conventionally used to integrate out fermions.     

A full wave model of high-harmonic EMIC wave propagation in sheared magnetic fields

ABSTRACT

A new dispersion relation, with finite Larmor orbit effects, for oblique propagating electromagnetic ion cyclotron (EMIC) waves in a magnetized plasma medium, is derived including the magnetic shear effect. The approximate, yet accurate, dispersion relation is used to implement the ray tracing model. A parabolic magnetic field is considered to model the geomagnetic field in the magnetosphere. Energetic protons are also considered as resonant particles. The propagation characteristics of EMIC waves in the vicinity of the ion cyclotron resonances are investigated in some detail. The results reveal adiabatic oscillating motion for wave and magnetic field fluctuations where high harmonics limit the wave damping and confines the magnetic fluctuations. For inward propagating EMIC waves we find (1) turning points which depend on the wave launch position, and (2) wave trapped areas playing a role in quasi-coherent wave-particle interaction in agreement with the observational and theoretical studies. This wave trapping is an effective process for particle acceleration in the context of space plasmas.     

Isolation and quantization of the two degrees of freedom of the electromagnetic potential for any gauge

The true dynamical degrees of freedom (TDDF) of the electromagnetic potential are found for any gauge. They are the components of the Fourier transform of the electromagnetic potential on a two-dimensional spacelike plane orthogonal to the lightlike momentum vector for k² = 0 and vanish for k² ≠ 0. Gauge invariance is related to the (two-parameter) indeterminacy of this spacelike plane and the arbitrariness of the component of the electromagnetic potential along the momentum vector. By direct quantization of the TDDF for any gauge (compatible with the equations of motion), some of the well-known problems of the usual treatments are avoided. For instance, the constraint div E = 0 is a c-number (agrees with the commutation relations) without choosing a gauge, there appears no need for an indefinite metric in the space of state amplitudes, the commutators for creation and annihilation operators of every component of the electromagnetic potential (timelike, longitudinal, and transverse) have the same sign, and the energy of the electromagnetic field is positive for any gauge. When gauges are chosen, the results of the literature are recovered. In our treatment, gauge fixation and quantization commute.     

Dynamics of a two-dimensional light bullet propagating in a system of carbon nanotubes with a velocity greater than the speed of light in the medium

The behavior of a two-dimensional light bullet propagating with a velocity greater than the speed of light in a medium consisting of semiconducting carbon nanotubes is investigated by means of numerical simulation. The electromagnetic field of the investigated system is described using Maxwell’s equations with allowance for the electric and magnetic properties of the carbon nanotubes and the medium in which they are embedded.     

Reflection and refraction of the electromagnetic field in a semi-infinite plasma

We compute the reflected and refracted electromagnetic fields for an ideal semi-infinite (half-space) plasma, as well as the reflection coefficient, by using a general procedure based on equations of motion and electromagnetic potentials. The approach consists of representing the charge disturbances by a displacement field in the positions of the moving particles (electrons). The propagation of an electromagnetic wave in plasma is treated by means of the retarded electromagnetic potentials, and the resulting integral equations are solved. Generalized Fresnel’s relations are thereby obtained for any incidence angle and polarization and the angles of total polarization and total reflection are derived. Bulk and surface plasmon-polariton modes are identified. As it is well known, the field inside the plasma is either damped (evanescent) or propagating (transparency regime), and the reflection coefficient exhibits an abrupt enhancement on passing from the propagating regime to the damped one (total reflection).     

Master equation approach to propagation of radiation through random media

Master and Fokker-Planck equations are obtained for radiation propagating through a random medium using the q-c-number correspondence of the coherent state technique. The corresponding equation for the antinormal characteristic function is solved by means of the method of characteristics. The master equation method and the recently developed method based on the Heisenberg equations and quantum characteristic function are shown to be equivalent. Some existence problems for the Glauber-Sudarshan weighting function are discussed. New light is thrown on approximations in the photocounting statistics used earlier.     

Wave shaping through finite electromagnetic bandgap structure

Transmission mechanisms and wave steering under localized feeding conditions through a finite electromagnetic bandgap structure are investigated both experimentally and theoretically. The artificial propagating medium consists of a two-dimensional metallic wire structure dimensioned for millimetre wave operation. By analogy with electron propagation in semiconductor heterostructures, the signatures of ‘modal‘ and ‘fluid‘ propagation regimes are experimentally demonstrated. Data are then analysed through electric field patterns calculated by means of a three-dimensional solver of Maxwell‘s equations.     

Eine phasenraumdarstellung für spinsysteme

We start with the definition of two mapping operators, one of them is the projection operator onto coherent spin states. With the help of these operators we derive a mapping theorem which defines a correspondence between the operators in spin space andc-number functions of a certain class. It is shown that this correspondence is one-to-one. The quantum-mechanical expectation value of an operator is found to be expressible in the form of a phase space average of classical statistical mechanics. We also derive a product theorem which allows us to transcribe the equations of motion for operators into equivalent equations for thec-number functions. As an illustration of the theory, some examples are discussed.     

Invariants of motion of a charge in the field of a circularly polarized wave

Six integrals of motion of a relativistic charge in the field of a transverse circularly polarized electromagnetic wave propagating with a phase velocity u > c are obtained from the solution of the Hamilton equations. These integrals form the basis of analysis of the trajectory of the charge depending on the phase of the wave in a stationary system of coordinates. The coordinates and phase are connected via elliptic functions.     

Equilibrium state of charged particles in a wave propagating along the magnetic field

This investigation examines the adiabatic motion of a charged particle near the equilibrium state in a field of a plane, circularly polarized, electromagnetic wave which is propagating with a changing velocity phase along the magnetic field. Approximate equations are found which describe the behavior of the equilibrium state parameters when the wave leaves the medium and enters a vacuum. It is shown that compared to the equilibrium value in this situation under the adiabatic approximation there is a decrease in amplitude of the particle energy fluctuation; this establishes the possibility of a prolonged acceleration of the particle to high energies. It is further demonstrated that a particle moving close to equilibrium state can appear to be in the autoresonance regime when the wave enters vacuum.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 117–122, October, 1976.     

Specific dynamics of faster-than-light (in the medium) extremely short optical pulses in an array of carbon nanotubes

Maxwell’s equations for an electromagnetic field propagating in an array of carbon nanotubes have been considered in the case when the velocity of the incident pulse is greater than the speed of light in the medium. The equation for the vector potential of the electromagnetic field has been derived and solved numerically. The dependence of the pulse on its velocity at the entrance to the array of carbon nanotubes has been revealed.     

Analytic evaluation of high-order susceptibilities in multiwave mixing

A dynamical system consisting of a multilevel atomic gas medium subject to an electromagnetic field is analyzed by the density-matrix equations of motion. All stochastic processes such as elastic and inelastic atomic collisions and spontaneous emission are described by a damping matrix. Analytical expressions for the density-matrix elements to any order of perturbation theory (without any multipolar and rotating wave approximations) are obtained by means of the Laplace-transform method in a diagonal representation of the damping matrix. Closed formulae for the high-order susceptibilities are derived.     

Retardation and nonstationarity effects on the generation of terahertz radiation by the e-h plasma in a semiconductor

Radiative processes in a nonequilibrium e-h plasma are theoretically studied using a self-consistent solution of the kinetic equation and Maxwell’s equations. The terahertz emission from a finite-thickness semiconductor sample is due to the retardation and nonstationarity of the electromagnetic interaction of the photocurrent in the e-h plasma and the radiation field. The duplex waveform of the terahertz electromagnetic pulse for an arbitrary ratio of the radiation formation length and the plate thickness originates due to coherent radiative processes accompanying the generation of the e-h plasma at the input boundary and its extinction at the output boundary of a semiconductor plate through which a weakly absorbed ultrashort laser pulse propagates. The theoretical conclusions show analogies with the radiative phenomena accompanying the start-stop motion of external currents (Tamm problem) and the nonlinear interaction of optical waves in a finite-thickness medium.     

Vortices with fermions

Vortex-like solutions of two models involving fermions are found. A method is presented for extracting the anticommuting c-number parameters in the solutions and reducing the equations to ones containing only ordinary numbers.     

太赫兹偏振测量系统及其应用

麦克斯韦方程中的介质响应特性一般由本构关系中的介电函数ε(ω)和磁导率μ(ω)来描述,对于介质中传播的电磁场,通常存在两个独立的本征传播模式,它们是齐次麦克斯韦方程组的特解,各自具有特定的色散关系和偏振态。如果介质中传播的电磁场为两个本征模分量的线性迭加,其偏振态将会随着传播的过程而改变。常见的现象有各向异性晶体中的双折射、超材料中的偏振调制效应、自然界中手性材料的旋光响应以及外磁场作用下产生的Faraday效应等。本文从测量方法、数据处理、测量精度等方面介绍太赫兹时域偏振检测系统及其发展状况,特别是利用线栅、超材料以及光学手段调制太赫兹电场偏振态的方法。对近几年太赫兹偏振检测系统在分析手性超材料、太赫兹圆二色谱以及Faraday效应等实验中的应用进行了总结和讨论。最后展望了太赫兹偏振检测系统未来进一步的发展空间及应用前景。     

The scale-transformation of electromagnetic theory and its applications

The scale-transformation of electromagnetic theory is investigated in detail based on the form of Maxwell equations in scale-transformation being unchanged in different coordinate systems. The relations of electromagnetic parameters in a rectangular coordinate system and in a spherical coordinate system are presented respectively. The scale-transformation invariants for electromagnetic field are derived and their physical meaning is also presented. It is indicated by simulation that the electromagnetic waves located in medium can be considered to be isotropic due to the fact that the size of propagating vector affected by the scale factors and observing azimuth is on a size of 10^-9, which provides a new approach for investigating the electromagnetic characteristics of ellipsoidal targets.     

The electromagnetic two-body problem in special relativity

A system of two point charged particles is considered. Each particle moves in the electromagnetic field created by the other particle according to Maxwell's equations. A scheme of successive approximations is developed to study the field and the motion of the charges. The field (potentials and intensities) are exapanded in powers of c^?1 using a retarded time coordinate. The variables of the motion (position vectors, velocities, etc) are expanded in powers of c^?1 with coefficients depending on t only. The field is evaluated in the first three approximations. The equations of motion are derived in the same approximations and the corresponding conserved quantities are explicitly given. Thus, the usual assumption of an action-at-a-distance principle is avoided and the original nonlinear integrodifferential equations are reduced to a sequence of linear equations.