Kinetics of ion admixture in a native gas in an external harmonic electric field

We have considered the spatially homogeneous problem of the behavior of an ion admixture in a background gas after applying a harmonic electric field with arbitrary parameters for various laws of interaction of particles. The Boltzmann equation has been solved using the modified method of moments. The ion distribution function and its first moments have been analyzed. It has been shown that the universal analytic expressions for the current density and the ion energy that we derived earlier for a small field amplitude-tofrequency ratio have a considerably wider range of applications.     

Threshold behavior of the dielectric nonlinearity in ferroelectric crystals of triglycine sulfate

The threshold behavior of the effective permittivity and harmonic amplitudes of the polarization switching-current spectrum is studied for triglycine-sulfate crystals with various defects as a function of the ac electric field amplitude. The interaction energies are calculated for domain walls with defects. The relaxation behavior of the effective permittivity at a constant amplitude of the switching field is studied.     

Resonances in the one-dimensional Dirac equation in the presence of a point interaction and a constant electric field

We show that the energy spectrum of the one-dimensional Dirac equation in the presence of a spatial confining point interaction exhibits a resonant behavior when one includes a weak electric field. After solving the Dirac equation in terms of parabolic cylinder functions and showing explicitly how the resonant behavior depends on the sign and strength of the electric field, we derive an approximate expression for the value of the resonance energy in terms of the electric field and delta interaction strength.     

Sources,potentials and fields in Lorenz and Coulomb gauge: Cancellation of instantaneous interactions for moving point charges

We investigate the coupling of the electromagnetic sources (charge and current densities) to the scalar and vector potentials in classical electrodynamics, using Green function techniques. As is well known, the scalar potential shows an action-at-a-distance behavior in Coulomb gauge. The conundrum generated by the instantaneous interaction has intrigued physicists for a long time. Starting from the differential equations that couple the sources to the potentials, we here show in a concise derivation, using the retarded Green function, how the instantaneous interaction cancels in the calculation of the electric field. The time derivative of a specific additional term in the vector potential, present only in Coulomb gauge, yields a supplementary contribution to the electric field which cancels the gradient of the instantaneous Coulomb gauge scalar potential, as required by gauge invariance. This completely eliminates the contribution of the instantaneous interaction from the electric field. It turns out that a careful formulation of the retarded Green function, inspired by field theory, is required in order to correctly treat boundary terms in partial integrations. Finally, compact integral representations are derived for the Liénard–Wiechert potentials (scalar and vector) in Coulomb gauge which manifestly contain two compensating action-at-a-distance terms.     

Shift and damping of optical phonons caused by interaction with electrons

Frequency shift and damping of long-wave optical phonons caused by interaction with electrons are calculated. The equations of the dynamic theory of elasticity are considered together with the Maxwell equations and the kinetic equation for determining the deformation field, the electric field, and the distribution function of electrons. Changes in the spectrum of electrons are described using a local potential. Coulomb screening of the longitudinal electric field is taken into account.     

Das Mikrofeld im Plasma

By taking full account of the Coulomb interaction and energy conservation, the probability distribution of the electric and magnetic microfield in an ionized gas is calculated. It results a Gaussian distribution instead of the hitherto used Holtsmark function and its variants which exhibit certain deficiencies. The mean square electric field is found to be proportional to the temperature, in analogy to the Nyquist formula. The probability of finding an atomic charge in the vicinity of another is established. With this, the time correlation function of the microfield and an average of the correlation time is deduced. Applications to the theory of transport phenomena and spectral line broadening are briefly discussed.     

Interaction of two dielectric macroparticles

The electrostatic interaction of two charged dielectric spherical particles with a nonuniform freecharge distribution over their surfaces in an external homogeneous electric field is considered. An exact solution for the electric field potential is obtained, and an analytical expression for the interaction force between these two particles is found. The case of a uniform free-charge distribution is considered in detail, and the region of parameters in the plane “the ratio of the radii vs. the ratio of the charges,” where repulsion between two like-charged particles turns into attraction as the interparticle distance decreases is established.     

Orbital-angular-momentum based origin of Rashba-type surface band splitting

We propose that the existence of local orbital angular momentum (OAM) on the surfaces of high-Z materials plays a crucial role in the formation of Rashba-type surface band splitting. Local OAM state in a Bloch wave function produces an asymmetric charge distribution (electric dipole). The surface-normal electric field then aligns the electric dipole and results in chiral OAM states and the relevant Rashba-type splitting. Therefore, the band splitting originates from electric dipole interaction, not from the relativistic Zeeman splitting as proposed in the original Rashba picture. The characteristic spin chiral structure of Rashba states is formed through the spin-orbit coupling and thus is a secondary effect to the chiral OAM. Results from first-principles calculations on a single Bi layer under an external electric field verify the key predictions of the new model.     

Multiple mobility edges in a 1D Aubry chain with Hubbard interaction in presence of electric field: Controlled electron transport

Electronic behavior of a 1D Aubry chain with Hubbard interaction is critically analyzed in presence of electric field. Multiple energy bands are generated as a result of Hubbard correlation and Aubry potential, and, within these bands localized states are developed under the application of electric field. Within a tight-binding framework we compute electronic transmission probability and average density of states using Green's function approach where the interaction parameter is treated under Hartree–Fock mean field scheme. From our analysis we find that selective transmission can be obtained by tuning injecting electron energy, and thus, the present model can be utilized as a controlled switching device.     

On the Interaction of an Alternating Electrical Field with a Magnetized Fully Ionized Plasma

The electron distribution function for a plasma interacting with an alternating electric field is studied, without using the Fourier expansion in terms of time. For this distribution function a more complete expression was deduced. Also the expressions for the current density are computed. Recurrently, we find the general form of the solution for our problem. A dependence of the current density of the form E and EEE was obtained. This dependence being characteristic to the nonlinear interaction of the waves in a plasma with the collision frequency depending on the velocity.     

Two identical conducting spheres with same potential in a uniform electric field

Interaction, polarization, and charges or electric field distribution of conducting spheres in applied electric field are in many fields including electrorheological fluids, electrophoresis, and electrical engineering. A system with two equipotential conducting spheres in an applied uniform electric field is analyzed by image method. A new method is put forward to calculate the image charges distribution when using image method, which ensures the validity of image method to analyze equipotential cases. An apparatus is constructed to measure the force experimentally as well. Results show that the distribution of electric field and electric interaction are different with the case not equipotential.     

Evolution of the ion velocity distribution after sudden turn-on of a periodic electric field: A charge exchange model

An analytical solution to the problem of the ion velocity distribution evolution after turn-on of a periodic electric field is derived. The solution is constructed for the case of resonance charge exchange at a constant collision frequency (charge exchange model). The specific features of the transient process at the early stage of evolution are revealed. The phase shift between the applied field and the ion current at the periodic stage of the process is analyzed. The distribution function exhibits abrupt steps propagating in the velocity space. A method is proposed to study the ion-atom interaction cross section using a periodic electric field. The method is based on analysis of the current toward the electrode with a retarding potential.     

Electric field distribution around the chain of composite nanoparticles in ferrofluids

Composite nanoparticles (NPs) have the ability of combining materials with different properties together, thus receiving extensive attention in many fields. Here we theoretically investigate the electric field distribution around core/shell NPs (a type of composite NPs) in ferrofluids under the influence of an external magnetic field. The NPs are made of cobalt (ferromagnetic) coated with gold (metallic). Under the influence of the external magnetic field, these NPs will align along the direction of this field, thus forming a chain of NPs. According to Laplace's equations, we obtain electric fields inside and outside the NPs as a function of the incident wavelength by taking into account the mutual interaction between the polarized NPs. Our calculation results show that the electric field distribution is closely related to the resonant incident wavelength, the metallic shell thickness, and the inter-particle distance. These analytical calculations agree well with our numerical simulation results. This kind of field-induced anisotropic soft-matter systems offers the possibility of obtaining an enhanced Raman scattering substrate due to enhanced electric fields.     

On the electron energy distribution in the gas discharge positive column: Langmuir paradox

The results of calculations of electron drift characteristics in a dc spatially inhomogeneous periodic electric field are presented. It is shown that the effect of field inhomogeneities on the drift velocity and the average electron energy is insignificant under typical conditions of experiments with gas-discharge plasma at low gas pressures. However, the intensity of the processes of excitation, ionization, and plasma spatial distribution are strongly affected by the inhomogeneity (variance) and field variation behavior. It is shown that the electric field inhomogeneity in the gas discharge positive column leads to maxwellization of the electron energy distribution function.     

Electric field and the charge distribution on the surface of an insulator in a vacuum

The free charge steady-state distribution over the insulator surface that arises in a strong electric field in a vacuum can be found by solving the boundary-value problem for the electrostatic field strength if the angle between the field vector and vacuum-insulator interface is given. A general solution to this boundary-value problem is derived for the case of an in-plane field and rectilinear interfaces. Laws of charge and field formation that follow from the solution obtained are considered. Formulas for the electric field strength and charge density in terms of elementary functions are obtained for a number of particular cases. Power-type expressions for the electric field and a critical angle between the electrode and insulator surface that describe the field behavior and charge distribution near the vacuum-insulator-electrode contact are derived.     

Dielectric catastrophe at the Mott transition

We study the Mott transition as a function of interaction strength in the half-filled Hubbard chain with next-nearest-neighbor hopping t' by calculating the response to an external electric field using the density matrix renormalization group. The electric susceptibility chi diverges when approaching the critical point from the insulating side. We show that the correlation length xi characterizing this transition is directly proportional to fluctuations of the polarization and that chi approximately xi2. The critical behavior shows that the transition is infinite order for all t', whether or not a spin gap is present, and that hyperscaling holds.     

Determination of nonlinear optical properties using the Voigt function: Stochastic considerations

In this work, the absorptive and dispersive profiles of a molecular system have been calculated through a methodology based on the averaging of the coherence obtained by the resolution of the optical stochastic Bloch equations. To this aim, a generalized Lorentzian approximation to the Voigt function has been used as a probability distribution, which allows a more generalized analysis of the interactions between the solvent and the molecule. This has been modeled with the parameters of the standard organic dye Green Malaquite, which exhibits a nonlinear behavior under the interaction with a high intensity electric field.     

Probability of electron emission in photoemission from doped semiconductor

Electron motion is investigated in a strong-field region —in the region of bending of the band close to the surface of a semiconductor. In this region there is a change in the electron distribution function under the action of the electric field and interaction mechanisms leading to energy loss of the hot electrons. The main characteristics of the external photoeffect are determined by the energy lost by the electron in the region of band bending and the size of the barrier at the semiconductor-vacuum interface. The electron-emission probability from a crystal containing a space-charge region is determined from the solution of the Boltzmann kinetic equation. The energy dependence of the energy scattering length of the hot electrons is taken into account in the calculation. The calculation is made for photoemission from GaAs in conditions when the interaction with polar optical phonons is the most effective energy-scattering mechanism. An expression is obtained for the energy distribution function of the emitted electrons for the case of strong electric fields. The position of the distribution-function maximum depends on the electric field and the effective interaction constant with phonons. The current and quantum yield of the photoeffect are calculated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 81–87, October, 1978.In conclusion, it remains to extend profound thanks to V. L. Bonch-Bruevich for Ms constant interest in the work.     

Inelastic electron-acoustic-phonon interaction in quantum-well wires

Due to the lack of transverse momentum conservation for the electron-acoustic-phonon interaction in quantum wires this interaction becomes strongly inelastic within a wide range of electron energies. As a result the electron distribution function has to be found from an integro-differential equation. We derive the new nonequilibrium distribution functions for these conditions and present the electric field dependences for the kinetic coefficients. Our approach can be applied as well for two-dimensional electron systems or for electrons subjected to an external quantizing magnetic field. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 6, 441–446 (25 March 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Stark Effect of Polarons in Parabolic Quantum Wells

We report the study of Stark effect of polarons in infinite parabolic quantum wells under an electric field, taking into account the effects of interaction with bulk LO-phonons. The electron-phonon interaction and the.effective mass in the plane perpendicular to the growth direction for excited states of free polarons have been calculated as functions of the degree of confinement. The general behavior of the excited states is found to be in agreement with previous works on the ground state. It is shown that in the limit of strong confinement the differences in electron-phonon interaction and effective mass between the ground state and excited states vanish. Although the applied electric field has no effect on the electronphonon interaction or the effective mass of a free polaron system, our numerical results for an AlGaAs parabolic quantum well have demonstrated its significance in determining the coupling of electrons with bulk LO-phonons of bound polaron systems.