Green’s function for an electron model with a plane wave

The Green function for a Dirac particle subject to a plane wave field is constructed according to the path integral approach and the Barut’s electron model. Then it is exactly determined after having fixed a matrix U chosen so that the equations of motion are those of a free particle, and by using the properties of the plane wave and also with some shifts.      

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.     

Macroscopic and mesoscopic matter waves

It has been shown earlier [3,6] that matter waves which are known to lie typically in the range of a few angstrom, can also manifest in the macrodomain with a wave length of a few centimeters, for electrons propagating along a magnetic field. This followed from the predictions of a probability amplitude theory by the author [1,2] in the classical macrodomain of the dynamics of charged particles in a magnetic field. It is shown in this paper that this case constitutes only a special case of a generic situation whereby composite systems such as atoms and molecules in their highly excited internal states, can exhibit matter wave manifestation in macro and mesodomains, in one-dimensional scattering. The wave length of these waves is determined, not by the mass of the particle as in the case of the de Broglie wave, but by the frequency ω, of the classical orbital motion of the internal state in the correspondence limit, and is given by a nonquantal expression, λ = 2πv/ω, v being the velocity of the particle. For the electrons in a magnetic field the frequency corresponds to the gyrofrequency, Ω and the nonquantal wave length is given by λ = 2πv _|| /Ω; v _|| being the velocity of electrons along the magnetic field. Received 29 September 2001 / Received in final form 23 May 2002 Published online 19 July 2002     

Spin–orbit stiffness of the spin‐polarized electron gas

In a spin‐polarized electron gas, Coulomb interaction couples the spin and motion degrees of freedom to build propagating spin waves. The spin wave stiffness S_sw quantifies the energy cost to trigger such excitation by perturbing the kinetic energy of the electron gas (i.e. putting it in motion). Here we introduce the concept of spin–orbit stiffness, S_so, as the energy necessary to excite a spin wave with a spin polarization induced by spin–orbit coupling. This quantity governs the Coulombic enhancement of the spin–orbit field acting of the spin wave. First‐principles calculations and electronic Raman scattering experiments carried out on a model spin‐polarized electron gas, embedded in a CdMnTe quantum well, demonstrate that S_so = S_sw. Through optical gating of the structure, we demonstrate the reproducible tuning of S_so by a factor of 3, highlighting the great potential of spin–orbit control of spin waves in view of spintronics applications. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

The AdS5 Black Hole Space-time with the Perturbed?Dilaton Field Background

The AdS ₅ black hole space-time with perturbed dilaton field background considered. We use the holographic AdS/QCD soft-wall model to investigate the wave functions and the effective potential. In this model, glueballs are described by a massless scalar field in an AdS ₅ black hole with a dilaton soft-wall background. For the first time we use modified dilaton field and discuss the consequence of the perturbation. In order to obtain the effective potential we rewrite the equation of motion in the Schr?dinger like equation, then try to find corresponding solution.     

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)     

Zitterbewegung and Quantum Jumps in Relativistic Schrödinger Theory

Within the general framework of the relativistic Schrödinger theory, a new waveequation is identified which stands between Dirac's four-component spinorequation and the scalar one-component Klein–Gordon equation. It is atwo-component, first-order wave equation in pseudo-Riemannian spacetime which onone hand can take account of the Zitterbewegung (similar to the Dirac theory),but on the other hand describes spinless particles (just like the Klein–Gordontheory). In this way it is demonstrated that spin and Zitterbewegung areindependent phenomena despite the fact that both effects refer to a certain kindof internal motion. An extra variable for the internal motion can be introduced(similarly as in the Dirac theory) so that the new wave equation is reduced tothe Klein–Gordon case when the internal variable takes its trivial value and theinternal motion is not excited. The internal degree of freedom admits the occurenceof quasi-pure states (i.e., a special subset of the mixtures), which undergo atransition to a pure state in finite time. If the initial configuration is already apure state, this transition occurs in the form of a sudden jump to the final purestate. The coupling of the new wave field to gravity via the Einstein equationsmakes the Zitterbewegung manifest through the corresponding trembling of theextension of a Friedmann–Robertson–Walker universe.     

Suppression of the radiation limit through autoresonant acceleration of charged particles by an electrostatic field

We consider the autoresonant motion of a charged particle in the field of a transverse electromagnetic wave propagating with the speed of light along a stationary homogeneous magnetic field with allowance for radiative friction. It is shown that the loss of wave-particle synchronism due to radiative friction can be suppressed by an external electrostatic field that is parallel to the magnetic field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 4, pp. 458–463, April, 1996.     

Acceleration of charged particles and radiation reaction in strong plane and spherical waves. II

Particle motion in a superstrong wave field (Laser or Pulsar field) is considered in the presence of an additional longitudinal magnetic field. It is shown that the particle motion is distinctly different from that in a previously considered pure wave field and that the maximum obtainable energy is substantially reduced. We also reconsider the effects of radiation reaction on a particle moving in a plane linearily polarized wave.     

Nonlinear quantum theory of interaction of charged particles and monochromatic radiation in a medium

We study the quantum theory of nonlinear interaction of charged particles and a given field of plane-transverse electromagnetic radiation in a medium. Using the exact solution of the generalized Lamé equation, we find the nonlinear solution of the Mathieu equation to which the relativistic quantum equation of particle motion in the field of a monochromatic wave in the medium reduces if one ignores the spin-spin interaction (the Klein-Gordon equation).We study the stability of solutions of the generalized Lamé equation and find a class of bounded solutions corresponding to the wave function of the particle. On the basis of this solution we establish that the particle states in a stimulated Cherenkov process form bands. Depending on the wave intensity and polarization, such a band structure describes both bound particle-wave states (capture) and states in the continuous spectrum. It is obvious that in a plasma there can be no such bands, since bound states of a particle with a transverse wave whose phase velocity v _ph is higher than c are impossible in this case. The method developed in the paper can be applied to a broad class of problems reducible to the solution of the Mathieu equation. Zh. éksp. Teor. Fiz. 113, 43–57 (January 1998)     

Exact treatment of the Jaynes–Cummings model under the action of an external classical field

We consider the usual Jaynes–Cummings model (JCM), in the presence of an external classical field. Under a certain canonical transformation for the Pauli operators, the system is transformed into the usual JCM. Using the equations of motion in the Heisenberg picture, exact solutions for the time-dependent dynamical operators are obtained. In order to calculate the expectation values of these operators, the wave function has been constructed. It has been shown that the classical field augments the atomic frequency ω₀ and mixes the original atomic states. Changes of squeezing from one quadrature to another is also observed for a strong value of the coupling parameter of the classical field. Furthermore, the system in this case displays partial entanglement and the state of the field losses its purity.     

Model basis states for photons and "empty waves"

From the perspective of physical realism (PR), a photon is a localized entity that carries energy and momentum, and which is surrounded by a wave packet (anempty wave) that is devoid of observable energy or momentum. In creating quantized PR basis states for a photon wave packet, three requirements must be met:(1) The basis states must each carry the frequency of the wave;(2) They must closely resemble the photon, so that e.g. they scatter in the same manner from an optical mirror;(3) They must have infinitesimal energy, linear momentum, and angular momentum. An essentially zero-energy "empty wave" quantum-a "zeron"-is defined which meets these requirements. It is created as an asymmetric single-particle (or single-antiparticle) excitation of the vacuum state, with the "particle" (or "antiparticle") and its associated "hole" (or "antihole") forming a rotational bound state. The photon is reproduced as a symmetric particle-antiparticle excitation of the vacuum state, with the "particle" and "antiparticle" also forming a rotational bound state. The relativistic transformation problem is discussed. A key point in this development is the deduction of the correct equation of motion for a "hole" state in an external electrostatic field.     

Relativistic theory of inverse beta-decay of polarized neutron in strong magnetic field

The relativistic theory of the inverse beta-decay of polarized neutron,ν _e +n → > p +e ^-, in strong magnetic field is developed. For the proton wave function we use the exact solution of the Dirac equation in the magnetic filed that enables us to account exactly for effects of the proton momentum quantization in the magnetic field and also for the proton recoil motion. The effect of nucleons anomalous magnetic moments in strong magnetic fields is also discussed. We examine the cross-section for different energies and directions of propagation of the initial neutrino accounting for neutron polarization. It is shown that in the super-strong magnetic field the totally polarized neutron matter is transparent for neutrinos propagating antiparallel to the direction of polarization. The developed relativistic approach can be used for calculations of cross-sections of the other URCA processes in strong magnetic fields.     

Toward a nonlinear theory of acceleration of charged particles in a linearly polarized EH-ubitron field

The motion of charged particles in a linearly polarized EH-ubitron field with sinusoidal time dependence of the variable component of the magnetic field is investigated. It is shown that, depending on the parameters of the system and the initial conditions of entry of the particle into the EH-field region, three different types of motion are possible: ballistic motion, capture in the vicinity of one of the maxima of the magnetic field, and escape of particles from the EH-field region. An analytical expression is found for the criterion determining the type of motion of the particles, along with analytical solutions for the energy of the particles in the approximation of slow variation of the magnetic field amplitude in time. Peculiarities of the motion of the particles in EH fields with arbitrary rate of change of the magnetic field amplitude in time are investigated numerically. Zh. Tekh. Fiz. 69, 87–93 (January 1999)     

Derivation of Nonperturbative Relativistic Two-Body Equations from the Action Principle in Quantumelectrodynamics

For two fermion fields Ψ₁(x) and Ψ₂(x) interacting with the electromagnetic field via the minimal and Pauli-couplings we introduce a composite field ϕ(x₁, x₂). The total action can be rewritten in terms of ϕ and its time derivatives if we use the physical retarded Green's functions D^ret (corresponding to an effective to (1/2)(D^ret + D^adv) = D ) between two particles. The variation of the action with respect to ϕ gives then exact covariant two-body, one-time, equations with relativistic potentials. The center of motion can be covariantly separated leading to an infinite component wave equation for the composite system, which reduces to the well-known covariant wave equation for the moving H-atom in the limit m₂ → ∞.     

Stochastically excited waves in a 1D random medium – the mean field and power spectrum

Scalar wave propagation is examined when both the wave source and the propagation speed are random. Results are derived for the mean field and the power spectrum using the second-order Born approximation. The results depend on whether the source S(x, t) and the propagation speed c(x, t) are correlated or not. When they are uncorrelated, the mean field is zero. When they are correlated, the mean field is non-zero only when the source is non-stationary. The power spectrum is incoherent to leading order. There is a transfer of energy from lower to higher frequencies owing to wave scattering. The corresponding frequency upshift of the power profile in the (k, ω) domain is mainly caused by the cross power between the direct and the twice scattered field, which represents a second-order incoherent power contribution. The results are confirmed using a numerical solution of the wave equation where the scattered field is expanded to fifth order.     

Shapiro steps in the torsion of a quasi-one-dimensional conductor TaS<Subscript>3</Subscript>

Features have been observed in the current dependences of the torsion angle, φ(I), for samples of a quasi-one-dimensional conductor TaS₃ irradiated by a high-frequency (HF) field. The features appear at the same current values as the Shapiro steps on the current-voltage characteristics, i.e., correspond to the synchronization of the motion of a charge-density wave (CDW) by the HF field. The shape of the features in the φ(I) dependences indicates a decrease in the inhomogeneous deformation of the CDW under the synchronization conditions. The investigation of torsion appears to be a highly sensitive method for determining the spatial coherence of the CDW.     

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.     

Influence of magnetic fields on taylor vortex formation in magnetic fluids

The flow of a magnetic fluid placed inside a small gap between concentric rotating cylinders is investigated for axial, radial and azimuthal magnetic fields. An equation of motion is derived phenomenologically to describe the hydrodynamics of magnetic fluids. Studied are the changes in the critical Taylor numberT _c and wave numberT _c which characterize the instability of primary circular Couette flow towards Taylor vortices. It is found that all above magnetic fields have a stabilizing effect on circular Couette flow and thatT _c increases or decreases, depending on the direction of the magnetic field. Besides this, the influence of the magnetic fields on the correlation length ₀, the wave number of maximal growthk _m and the linear growth rate amplitude ₀ is determined.