Electronic states in a cylindrical quantum dot with the modified Pöschl-Teller potential in the presence of external magnetic field

Energy levels of an electron in a cylindrical quantum dot with a modified Pöschl-Teller potential in the presence of external homogeneous magnetic field are studied. Analytical expressions for the wave function and energy of the particle are obtained. Different regimes of magnetic quantization are considered and peculiarities of behavior of the electron energy spectrum depending on the value of applied magnetic field are revealed.     

Quantum-Confined Stark Effects in a Single GaN Quantum Dot

Using analytical expressions for the polarization field in GaN quantum dot, and an approximation by separating the potential into a radial and an axial, we investigate theoretically the quantum-confined Stark effects. The electron and hole energy levels and optical transition energies are calculated in the presence of an electric field in different directions. The results show that the electron and hole energy levels and the optical transition energies can cause redshifts for the lateral electric field and blueshifts for the vertical field. The rotational direction of electric field can also change the energy shift.     

Effect of magnetic field on beta processes in a relativistic moderately degenerate plasma

The effect of a magnetic field of arbitrary strength on the beta decay and crossing symmetric processes is analyzed. A covariant calculation technique is used to derive the expression for the squares of S-matrix elements of these reactions, which is also valid in reference frames in which the medium moves as a single whole along magnetic field lines. Simple analytic expressions obtained for the neutrino and antineutrino emissivities for a moderately degenerate plasma fully characterize the emissivity and absorbability of the studied medium. It is shown that the approximation used here is valid for core collapse supernovae and accretion disks around black holes; beta processes in these objects are predominantly neutrino reactions. The analytic expressions obtained for the emissivities can serve as a good approximation for describing the interaction of electron neutrinos and antineutrinos with the medium of the objects in question and hold for an arbitrary magnetic field strength. Due to their simplicity, these expressions can be included in the magnetohydrodynamic simulation of supernovae and accretion disks to calculate neutrino and antineutrino transport in them. The rates of beta processes and the energy and momentum emitted in them are calculated for an optically transparent matter. It is shown that the macroscopic momentum transferred in the medium increases linearly with the magnetic field strength and can substantially affect the dynamics of supernovae and accretion disks in the regions of a degenerate matter. It is also shown that the rates of beta processes and the energy emission for a magnetic field strength of B ? 10¹⁵ G typical of supernovae and accretion disks are lower than in the absence of field. This suppression is stronger for reactions with neutrinos.     

Some dynamical properties of a two-dimensional Wigner crystal

Results for the static part of the ground state energy of the square and hexagonal two-dimensional Wigner lattices are given. The hexagonal lattice has the lower energy. Phonon dispersion curves and the vibrational zeropoint energy are calculated for the hexagonal lattice. The dielectric susceptibility tensor of a two-dimensional Wigner crystal χ_αβ(q) has been determined in the long wavelength limit in the presence of a static magnetic field perpendicular to the crystal, and explicit expressions have been obtained for the hexagonal lattice. Applying the analysis developed by Chiu and Quinn, the results for the susceptibility have been used to obtain the dispersion relation for the plasma oscillations in the electron crystal on the assumption that the crystal is embedded in a dielectric medium. The dispersion curves have been calculated for differing magnitudes of the applied magnetic field.     

The above-threshold ionization spectrum in a strong linearly polarized laser field

We use the saddle-point method to derive analytical expressions for the spectral-angular probability distributions of the ionization by a strong linearly polarized laser field in Keldysh’s model that are valid for an arbitrary electron energy and adiabaticity parameter. We obtain asymptotic expansions of the general formulas in the multiphoton and tunneling regimes, analyze their accuracy, and formulate the validity conditions. We provide literal estimates of the parameters that characterize the properties and evolution of the distributions.     

Spontaneous emission by an electron in an arbitrary plane-wave electromagnetic field

On the basis of general expressions obtained for the total emission probability and the probability of a radiation transition with spin reversal of an electron moving in an arbitrary plane-wave electromagnetic field, the particular case of a plane-wave field is considered. It is shown that under certain conditions self-polarization of the electron spin is possible during the emission by an electron in a field which is the superposition of a constant crossed field and a plane, elliptically polarized, electromagnetic wave.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 93–98, October, 1982.     

强光场中电子系统与多光子的相互作用

在非相对论量子场论框架下,给出电子场和光子场相互作用时整个系统的哈密顿量H_tot,研究在强光场中非线性项即A²项的作用.电子系统用Fermi-Dirac统计的Schr?dinger量子波场描述.采用“自洽平均场”和“有效质量”近似,并基于位移谐振子的相干态方法,得到电子波光量子场算子函数的Lee-Low-Pines表式f(b⁺),再利用算子函数f(b⁺)对算子b+的微商公式,导出了相关理论计算公式,其中包括电子能量E< 关键词： 强光场 多光子 非线性光学     

Absorption of electromagnetic energy by slow electrons under scattering from Coulomb centers

Simple analytical expressions are obtained for the rate of the inverse stimulated bremsstrahlung absorption under electron scattering from a Coulomb center with charge Z in the presence of the electromagnetic field. The initial and final values of electron energy are assumed to be small compared to the Rydberg energy Z ² (atomic units are used throughout). Single-photon processes of absorption and induced radiation of photon by electron are treated. It is assumed that the electromagnetic field frequency ω is rather low, so that the condition Zω/p ³ ? 1, where p is the electron momentum, and the condition ?ω ? p ² are valid. However, this frequency is assumed to be fairly high compared to the electron-Coulomb center collision frequency: ω ? v _nei. The dependences of the rates of photon absorption and induced radiation on the angle θ between the direction of incident electron and the electromagnetic field polarization vector (assumed to be linearly polarized) are obtained. It is demonstrated that, for any angles θ, the rate of photon absorption is higher than the rate of induced radiation and, therefore, the Marcuse effect for slow electrons (electromagnetic field amplification) is absent. It is further demonstrated that a slow electron on the average absorbs double ponderomotive energy per collision with an ion (Coulomb center) in Maxwellian plasma. This agrees both with the known results calculation for fast electrons and with the known results of the calculation based on the classical Boltzmann kinetic equation for plasma.     

Electron heat transport in the magnetic filter of a volume plasma-based source of H−/D− ions

A time-independent one-dimensional model of the electron energy balance in the region of the magnetic filter of a volume plasma-based ion source is justified. The local electron energy balance equation and the steady density profiles of the plasma components are used to determine the transverse (with respect to the mag-netic field) electron temperature profile, which is found to agree well with the experimental profile. The temperature profile obtained analytically is then used to refine the particle balance in a plasma with two ion species and, accordingly, to find the optimum conditions for the formation of an H⁻/D⁻ beam and for extracting the beam from the source.     

A simple analysis of the subband energies in quantum-confined non-parabolic semiconductors in the presence of a parallel magnetic field

Summary We study the subband energies in quantum wells and quantum wires in the presence of a parallel magnetic field in non-parabolic semiconductors, on the basis of a generalized dispersion relation considering all types of anisotropies of the energy-band parameters within the framework ofk·p formalism, by formulating the respective electron energy spectra. It is found, by takingn-Cd₃As₂ as an example, that the subband energies are greater for quantum wires and smaller for quantum wells, respectively. The magnetic field diminishes the above values and the corresponding well-known results for quantum-confined parabolic semiconductors have also been obtained from our generalized expressions under certain limiting conditions.     

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.     

On the gate capacitance of mos structures in N-Channel inversion layers on ternary chalcopyrite semiconductors

An attempt is made to investigate the gate capacitance of MOS structures in n-channel inversion layers on ternary chalcopyrite semiconductors at low temperatures, taking n-channel inversion layers on CdGeAs₂ as examples, under both the weak and strong electric field limits, respectively. We have formulated the gate capacitance on the basis of newly derived 2D electron energy spectra for both the limits by considering the various anisotropies of the band parameters within the framework ofk·p formalism. It has been observed that, the gate capacitance increases with increasing surface electric field in an oscillatory manner and the theoretical results are in good agreement with the experimental observations as reported elsewhere. In addition, the corresponding well-known results for n-channel inversion layers on isotropic parabolic semiconductors are also obtained from the generalized expressions derived under certain limiting conditions.     

托卡马克电场电子注入的漂移电子束研究

 研究了漂移电子束中电子的运动规律, 得到了电子在外加电场、纵磁场和电子束自场中的运动轨迹和漂移速度表达式, 并就它们的成束条件、成束形状和电压要求以及束的稳定性条件进行了比较和讨论, 认为阴极垂直于纵磁场放置更好一些。     

Application of obliquely interfering TE10 modes for electron energy gain

Two fundamental TE₁₀ modes are considered to interfere at a small angle θ and then propagate along the z-axis in an evacuated rectangular waveguide. The electron trajectory in the resultant field and the expressions for energy gain and the acceleration gradient are obtained, when the electron is injected along the z-axis. A 50 keV electron gains 718 keV energy in a 4.0 cm × 2.5 cm waveguide, when the microwave with intensity of 1 × 10¹⁰ W/cm² and frequency 5.577 GHz is used and the modes superpose at an angle of 10°; here the maximum acceleration gradient is obtained as 251 MeV/m. The energy gain and acceleration gradient are decreased with increasing width of the waveguide and microwave frequency. Higher gradient and larger energy gain are obtained for the higher microwave intensity, smaller angle of superposition and also when the electron is injected with larger initial energy.     

A particle in a box in the presence of an electric field and applications to disordered systems

The Green's function and energy eigenvalues of an electron under the influence of a uniform electric field in a box with infinitely high sides is investigated. The second order correction to the energy eigenvalues is calculated by finding zeros of the wronskian and comparing with the value obtained from second order perturbation theory. Comparison is made with the limiting conditions in which the size of the box tends to infinity and the electric field tends towards zero. The results of the investigation suggest a possible criterion for localisation. The value obtained for the ground state energy is used to extend a model of Edwards to study the tail of the density of states of a disordered system in the presence of an electric field.     

Ionization of atoms in strong low-frequency electromagnetic field

The ionization of atoms in a low-frequency linearly polarized electromagnetic field (the photon energy is much lower than the ionization potential of an atom) is considered under new conditions, in which the Coulomb interaction of an electron with the atomic core in the final state of the continuum cannot be considered in perturbation theory in the interaction of the electron with the electromagnetic field. The field is assumed to be much weaker that the atomic field. In these conditions, the classical motion of the electron in the final state of the continuum becomes chaotic (so-called dynamic chaos). Using the well-known Chirikov method of averaging over chaotic variations of the phase of motion, the problem can be reduced to non-linear diffusion on the energy scale. We calculate the classical electron energy in the final state, which is averaged over fast chaotic oscillations and takes into account both the Coulomb field and the electromagnetic field. This energy is used to calculate the probability of ionization from the ground state of the atom to a lower-lying state in the continuum using the Landau-Dykhne approximation (to exponential accuracy). This ionization probability noticeably depends on the field frequency. Upon a decrease in frequency, a transition to the well-known tunnel ionization limit with a probability independent of the field frequency is considered.     

Zero-field spin splitting in a two-dimensional electron gas with the spin-orbit interaction revisited

We consider a two-dimensional electron gas (2DEG) with the Rashba spin-orbit interaction (SOI) in the presence of a perpendicular magnetic field. We derive analytical expressions of the density of states (DOS) of a 2DEG with the Rashba SOI in the presence of a magnetic field by using the Green's function technique. The DOS allows us to obtain the analytical expressions of the magnetoconductivities for spin-up and spin-down electrons. The conductivities for spin-up and spin-down electrons oscillate with different frequencies and give rise to the beating patterns in the amplitude of the Shubnikov-de Haas (SdH) oscillations. We find a simple equation which determines the zero-field spin splitting energy if the magnetic field corresponding to any beat node is known from the experiment. Our analytical results reproduce well the experimentally observed non-periodic beating patterns, number of oscillations between two successive nodes and the measured zero-field spin splitting energy.     

Nonlinear response to external magnetic fields

The purpose of this paper is to study conditions under which a system of itinerate spin-$\text{1}\text{2}$ fermions might exhibit a macroscopic linear response to external magnetic fields after long times. Exact expressions are obtained for the nonlinear response of the magnetization and the total energy. We find that for a constant field there is no response (our model contains no mechanism for the relaxation of spins). For an oscillatory field there is a response in which secular terms (in the time) appear which are associated both with nonlinear terms in the external field and with contributions from the background medium. The secular terms involving the magnetic field would not be seen if one used the usual approximations of microscopic linear response theory. They give rise to new conditions which must be satisfied if the system is to exhibit a macroscopic linear response in the long-time limit.     

新型二次电子倍增阴极构型设计与动力学过程

提出了一种可由脉冲功率驱动的新型二次电子倍增阴极构型,并对其进行了动力学过程的初步理论研究。首先,针对该二次电子倍增阴极,建立了动力学模型,获得了二次电子的位移和速度方程,讨论了电子初始出射速度对其轨迹、渡越时间和碰撞能量的影响,理论给出了渡越时间和碰撞能量的近似解析表达式。其次,通过动力学方程与Vaughan二次电子产额经验公式的耦合求解,获得了该二次电子倍增阴极的工作区间,并对其进行了细致讨论。结果表明:该新型二次电子倍增阴极二极管概念上是可行的,在涂敷高二次电子产额系数材料的圆柱形介质上施加合适的轴向和径向静电场(MV/m量级)以及轴向静磁场(T量级),可以达到电子沿阴极表面螺旋行进过程中实现二次电子倍增并最终获得电流沿轴向放大的设计目标。另外,讨论了正电荷沉积引发的二次电子倍增饱和现象,并对阴极发射电流密度进行了理论粗估,结果表明:阴极发射电流密度可达kA/cm2水平,具备强流发射特性;增加外加径向场强幅值可有效提升阴极发射电流密度。     

直流空心阴极放电中鞘层区电子的输运过程

采用蒙特－卡洛方法对空心阴极放电中鞘层区电子的输运过程进行了研究，电子在鞘层区被非均匀电场加速，两次碰撞之间的步长是由电子与中性粒子的碰撞频率确定。模型中三种碰撞截面积是由实验和理论数据拟合而来。研究了电子平均能量、电子密度和电离系数在径向的分布。电子能量的空间分布结果与实验很好地符合。 关键词：