Radiation reaction

I solve Maxwell's equation for a current produced by a classical, point electron. My solution, which represents the self electromagnetic field of the electron, can be found along the electron trajectory, where the conventional retarded-time solution is singular. The solution is in the form of an integral over all spectral frequencies of the field and has an Ehrenfest correspondence with the operator field of quantum electrodynamics (QED). Use of the field in the equation of motion for a harmonically-bound electron leads to an equation having the same form as the Schrödinger equation for a two-level atom interacting with the QED vacuum field.     

Certain general questions of fast-electron transport II. Kinetic equations and conditions governing the accelerated motion of fast electrons in dielectrics in an electric field

A general kinetic equation for the differential density of fast particles moving in a medium in an external field is derived on the basis of the continuity equation in phase space. An equation is written for the differential flux in the case of fixed target particles. This equation is used to derive equations for fast electrons; account is taken of the coupling of energy-loss and scattering events in an electric field for various particular problems analogous to those studied in the theory of electron transport in the absence of a field. The kinetic equations are used to analyze the conditions governing accelerated motion of electrons in a dielectric in an external electric field in the continuous-deceleration approximation. Account is taken of fluctuations in the energy loss and of multiple scattering. There are two energy ranges of particles moving in a dielectric in which accelerated motion can occur; in the case of an electron beam with a continuous energy spectrum, this acceleration would be accompanied by monochromatization of the beam.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 7–12, February, 1972.     

A new representation of the interaction between an atom and an intense elliptically polarized electromagnetic field

A new representation of the interaction between a laser field and an atom is obtained. The Fourier component of the interaction is represented as a multipole expansion dependent on the force parameter of the field, a ₀=F/ω², and the degree of its ellipticity, η. This representation provides the analytical separation of the angles in the time-dependent Schrödinger equation. The stationary spherically symmetric part of the potential V ₀(r, a ₀, η) of a “field-dressed” atom is singled out. The application of the new representation to the calculation of nonlinear effects and electron scattering by an atom in a field are discussed     

Nonlinear diffraction of super-gaussian laser beams in an array of quantum-dot chains with coulomb interaction taken into account

We consider the propagation of super-Gaussian monochromatic laser beams in a three-dimensional array of quantum dots coupled by the tunneling effect along one axis. The electron energy spectrum of the system corresponds to the Hubbard model, where the Coulomb interaction of electrons in quantum dots is taken into account. The field of the laser beam is described by the Maxwell equations, from which a nonhomogeneous wave equation for the vector potential is obtained. In the approximation of slowly varying amplitudes and phases, the wave equation is reduced to a phenomenological equation describing the electromagnetic field in an array of chains of quantum dots. We study the influence of the system parameters and the frequency of the laser-beam field on the propagation in the medium by solving numerically the phenomenological equation. We obtain the dependence of the factor characterizing the diffraction blooming of the beam in an array of chains of quantum dots on the parameters of the system’s electron energy spectrum.     

Two-dimensional light bullets in an array of carbon nanotubes

The problem of the propagation of two-dimensional solitary electromagnetic waves in an array of carbon nanotubes has been considered. The electromagnetic field and the electron system of carbon nanotubes have been treated on the basis of the Maxwell’s equations and the Boltzmann kinetic equation in the relaxation-time approximation, respectively. The derived effective equation has been analyzed and the state of the electromagnetic field that is localized in two spatial dimensions has been found.     

Equations of Relativistic and Quantum Mechanics and Exact Solutions of Some Problems

Relativistic invariant equations are proposed for the action function and the wave function based on the invariance of the representation of the generalized momentum. The equations have solutions for any values of the interaction constant of a particle with a field, for example, in the problem of a hydrogen-like atom, when the atomic number of the nucleus Z > 137. Based on the parametric representation of the action, the expression for the canonical Lagrangian, the equations of motion and the expression for the force acting on the charge during motion in an external electromagnetic field are derived. The Dirac equation with the correct inclusion of the interaction for a particle in an external field is presented. In this form, the solutions of the equations are not limited by the value of the interaction constant. The solutions of the problem of charge motion in a constant electric field, problems for a particle in a potential well, and penetration of a particle through a potential barrier, as well as problem of a hydrogen atom are presented.     

Quantization effects in the plasma universe

It is suggested that a unification of the morphology of the solar system, anomalous intrinsic red shifts of quasars and galaxies, the structure of the hydrogen atom, the Einstein equations of general relativity, and Maxwell's equations can be accomplished by a basic consideration of the minimum-action states of cosmic and/or virtual vacuum field plasmas. A formalism of planetary formation theory leads naturally to a generalization which describes relativistic gravitational field theory in terms of a `pregeometry'. A virtual plasma associated with the vacuum state is postulated. It is demonstrated that the relaxed state of the virtual plasma underlies Einstein's field equation and predicts the proper form for the effective gravitational potential generated by the Schwarzschild solution of those equations. A further extension of the theory demonstrates that it also predicts the structure of the hydrogen atom described in terms of the Schrodinger equation of quantum mechanics. These concepts are applied in an attempt to explain the quantized anomalous red shifts in related galaxies as observed by H. Arp and J.H. Sulentic (1985). A possible unified field theory is suggested based on the above-mentioned concepts     

The Level-split of the Two-level Entangled Atom in an Optical Field

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The Level-split of the Two-level Entangled Atom in an Optical Field

The behavior of a two-level entangled atom in an optical field with circular polarization is studied in this paper. The interaction of an optical field and one of the entangled atoms is analyzed in detail. A general solution of the SchrAo¨Gdinger equation about the motion of the entangled atom is obtained. The properties of the action are dependent on the initial state of the atom. By detecting the entangled atom out of the field, we can obtain the state of the other atom moving in the field. It is shown that the state of the atom out of the field will influence the energies of the split-levels of the atom in the field.     

Models of the Dynamics of Spatially Separated Broadband Electromagnetic Fields Interacting with Resonant Atoms

The Markov model of spontaneous emission of an atom localized in a spatial region with a broadband electromagnetic field with zero photon density is considered in the conditions of coupling of the electromagnetic field with the broadband field of a neighboring space. The evolution operator of the system and the kinetic equation for the atom are obtained. It is shown that the field coupling constant affects the rate of spontaneous emission of the atom, but is not manifested in the atomic frequency shift. The analytic expression for the radiative decay constant for the atom is found to be analogous in a certain sense to the expression for the decay constant for a singly excited localized ensemble of identical atoms in the conditions when the effect of stabilization of its excited state by the Stark interaction with the vacuum broadband electromagnetic field is manifested. The model is formulated based on quantum stochastic differential equations of the non- Wiener type and the generalized algebra of the Ito differential of quantum random processes.     

Electron Density and Temperature Rise Time of a Weakly Ionized Oxygen Plasma Subject to an Alternating Electric Field

Macroscopic balance equations for particle number, momentum and energy of the electrons are derived from the Boltzmann equation which describe the time evolution of a weakly ionized oxygen plasma exposed to an alternating homogeneous electric field. The equations are applied to estimate the rise time of electron temperature and density when a rf pulse is emitted from a satellite into the ionospheric plasma.     

Relaxation in an entangled thermostat

A generalized Lindblad equation is derived that describes the relaxation of two systems of an arbitrary physical nature in an entangled thermostat. The relaxation of an atom and a mode of the electromagnetic field selected by a high-Q cavity is considered as an example. Using the introduced collective operators for an atom and a mode, it is shown that the entangled state of the thermostat can lead to the coherent and squeezed state of the atom and the mode.     

Effect of the self-field of an intense relativistic electron beam on its interaction with matter

The effect of the self-field of an intense relativistic electron beam on its interaction with a dense medium was studied by solving a system of equations consisting of the kinetic equation for the fast electrons, the hydrodynamic equations for the plasma electrons, and Maxwell's equations for the electromagnetic field. It was assumed that the macroscopic parameters of the medium (its density, conductivity, and electron collision frequency) were independent of time. The system of equations was solved using high-order perturbation theory. The results show that a magnetic field is formed by the beam of fast electrons and to an equal degree by a current of thermalized electrons, which has not been taken into account before. It is shown also that the magnetic field of the beam affects its transmission through matter. In particular, the penetration depth of the electrons in matter and the transverse dimensions of the beam are both smaller than in a weak-current beam.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 10, pp. 19–24, October, 1987.The author deeply thanks K. A. Dergobuzov for support of the work, and A. V. Arzhannikov, V. A. Klimenko, and A. V. Lapp for useful discussions.     

Force acting on an atom and a classical oscillator in an electromagnetic field

The expression for the force exerted by the field on an atom and averaged over the field period is derived in quantum-mechanical perturbation theory, in which a quasi-monochromatic electromagnetic field plays the role of a perturbation. An approximate solution is obtained to the classical (Newton) equation of motion in the same field for a harmonic isotropic oscillator. In both problems, the expressions for the force acting on a particle are completely identical if they are written in terms of the polarizability (of the atom and the oscillator). These results conform with the data obtained in macroscopic electrodynamics for rarefied media.     

Hydrodynamics of Plasma Interaction with an Intense Laser Field

A set of moment relations, which can describe the charged fluids response to an intense pump laser, and a linearization substitution relation, which is more appropriate as compared with the past treatment, are given by theoretical analyses. The relevant equations of state (adiabatic and isothermal), momentum and energy equations are derived self-consistently.The dispersion relations of the electron plasma wave and the ion acoustic wave driven by an intense pump laser field are-obtained. The results show that the frequencies of both the excited electron plasma wave and the excited ion acoustic wave have a great modification in the case of strong pump. The former bears out the theoretical result obtained from Vlasov equation and the later is consistent with experimental observations. It is proved that the zero-frequency component of the laser light wave contribution to the plasma pressure tensor is un-neglected,which implies a greatly change to the wave excitation properties, particularly in the direction of parallel or approximately parallel to the laser field vector.     

Response of an atom interacting with an arbitrarily polarized electromagnetic field

We develop the theory of interaction of the electromagnetic field and a single atom being in an arbitrary state and having an arbitrary direction of the angular momentum of the atomic electron with respect to the direction of the field polarization vector. It is shown that the atom response current has a tensor structure and depends on both the direction of the angular momentum of the atom, and the polarization vector of the external field. The tensor character of the response is determined by the externally induced anisotropic distribution of the probability density of spatial localization of the atomic electron. It is shown that the induced-anisotropy effects clarify the harmonic generation mechanism at play during the non-resonance interaction of laser radiation with atomic media. The developed theory is applied to the analysis of the problem about the generation of terahertz waves in a two-color laser field. It is shown that the change in the mutual orientation of wave polarization vectors leads to a significant increase in the efficiency of conversion of high-frequency fields to low-frequency ones. It is shown for the first time that the generation of terahertz waves is possible in the preionization regime, when the generation mechanism is related to atomic nonlinearity.     

螺旋线行波管注波互作用时域理论

研究了螺旋线行波管中电子注与高频场互作用的时域理论.电子对场的作用由高频场方程和空间电荷场方程模拟,场对电子注的作用由运动方程模拟.在螺旋导电面模型下利用安培环路定理和法拉第电磁感应定律得到了时域高频场方程.利用空间电荷波模型处理空间电荷场,得到了空间电荷场方程.将高频场和空间电荷场代入洛伦兹力方程,得到了运动方程.利用耦合阻抗处理高频场方程的激励源,使得高频场方程的求解能够借助诸如HFSS或HFCS等高频模拟软件来实现,增强了时域理论的灵活性.基于上述理论,编写软件数值模拟某螺旋线行波管,验证了时域理论的可行性.     

Space charge solution of Rittner photoconductor equation for a HgCdTe detector

The steady-state charge continuity equations are linearized to derive a space charge field that accompanies the ambipolar diffusion and drift described by the Rittner equation. The space charge field is evaluated for a typical 14.2 μm cutoff wavelength HgCdTe detector operating at 85 K. It is found that the space charge density is ∼10⁻⁵ times the hole and electron population density generated by photon flux. This corroborates that Rittner's equation gives an accurate solution for the hole and electron densities. But, at relatively high photon flux levels that are found in some Geostationary Operational Environment Satellite instrument channels, the small average space charge field can have a noticable effect on the linearity of detector response. Divergence of electric field terms in the continuity equations, which are absent from the Rittner equation, can also contribute a non-linearity to detector response.     

Scaling of wave-packet dynamics in an intense midinfrared field

A theoretical investigation is presented that examines the wavelength scaling from near-visible (0.8 micro m) to midinfrared (2 micro m) of the photoelectron distribution and high harmonics generated by a "single" atom in an intense electromagnetic field. The calculations use a numerical solution of the time-dependent Schr?dinger equation (TDSE) in argon and the strong-field approximation in helium. The scaling of electron energies (lambda2), harmonic cutoff (lambda2), and attochirp (lambda -1) agree with classical mechanics, but it is found that, surprisingly, the harmonic yield follows a lambda -(5-6) scaling at constant intensity. In addition, the TDSE results reveal an unexpected contribution from higher-order returns of the rescattering electron wave packet.