Unconventional Approach to Orbital-Free Density Functional Theory Derived from a Model of Extended Electrons

An equation proposed by Levy, Perdew and Sahni (Phys. Rev. A 30:2745, 1984) is an orbital-free formulation of density functional theory. However, this equation describes a bosonic system. Here, we analyze on a very fundamental level, how this equation could be extended to yield a formulation for a general fermionic distribution of charge and spin. This analysis starts at the level of single electrons and with the question, how spin actually comes into a charge distribution in a non-relativistic model. To this end we present a space-time model of extended electrons, which is formulated in terms of geometric algebra. Wave properties of the electron are referred to mass density oscillations. We provide a comprehensive and non-statistical interpretation of wavefunctions, referring them to mass density components and internal field components. It is shown that these wavefunctions comply with the Schrödinger equation, for the free electron as well as for the electron in electrostatic and vector potentials. Spin-properties of the electron are referred to intrinsic field components and it is established that a measurement of spin in an external field yields exactly two possible results. However, it is also established that the spin of free electrons is isotropic, and that spin-dynamics of single electrons can be described by a modified Landau-Lifshitz equation. The model agrees with the results of standard theory concerning the hydrogen atom. Finally, we analyze many-electron systems and derive a set of coupled equations suitable to characterize the system without any reference to single electron states. The model is expected to have the greatest impact in condensed matter theory, where it allows to describe an N-electron system by a many-electron wavefunction Ψ of four, instead of 3N variables. The many-body aspect of a system is in this case encoded in a bivector potential.     

Peculiarities of elastic scattering of intermediate-energy electrons related to their capture at quasi-stationary levels of an atom in a continuous spectrum

A theoretical model of electron scattering on an atom is constructed to study elastic atomic scattering of intermediate-energy electrons. The proposed model is based upon the combined Mensing potential with two spheres of atomic electrons, which admits analytical solutions of the radial Schröbinger equation. A procedure for matching the parameters of this scatterer to an approximate electrostatic potential of an atom in the form of a screened Coulomb potential has been determined. The screening radius of the latter potential has been calculated proceeding from the properties corresponding to the Thomas-Fermi method. A model of a scatterer determined according to the aforementioned procedure can be used to calculate the energy dependence of the cross section of elastic electron scattering on some atoms with s, p, and d shells representing elements neighboring zirconium. The main result is the establishment of factors responsible for the appearance of maxima on the energy dependences of the cross section of elastic electron scattering. These maxima are related to the resonant trapping of impinging electrons by quasi-stationary levels in a continuous spectrum.     

Amplification of ultimately-short pulses in graphene in the presence of a high-frequency field

The Maxwell equations for an electromagnetic field propagating in graphene are considered taking into account strong Coulomb repulsion between electrons of the same site possessing opposite spin projections. The derived effective equation has the form of a classical 2D sine-Gordon equation. Electrons are treated in terms of quantum formalism with allowance for the dispersion law in the presence of Coulomb interaction. The effective equation is analyzed numerically and the effect of Coulomb repulsion is revealed. It is shown that the system in an external homogeneous electromagnetic field, with its period much shorter than the characteristic pulse length, may show the amplification of an ultimately short pulse.     

The quantum acoustomagnetoelectric field in a quantum well with a parabolic potential

The acoustomagnetoelectric (AME) field in a quantum well with a parabolic potential (QWPP) has been studied in the presence of an external magnetic field. The analytic expression for the AME field in the QWPP is obtained by using the quantum kinetic equation for the distribution function of electrons interacting with external phonons. The dependence of the AME field on the temperature T of the system, the wavenumber q of the acoustic wave and external magnetic field B for the specific AlAs/GaAs/AlAs is achieved by using a numerical method. The problem is considered for both cases: The weak magnetic field region and the quantized magnetic field region. The results are compared with those for normal bulk semiconductor and superlattices to show the differences, and we use the quantum theory to calculate the AME field in the QWPP.     

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.     

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)     

Electron-acceptor luminescence from a non-Maxwellian distribution of photoexcited electrons in GaAs

Distribution functions are calculated for photoexcited electrons in GaAs, under conditions of continuous, monochromatic excitation. The lattice temperature is taken to be 1.2 K and the excitation intensity such that the density of photoexcited carriers is insufficient for the distribution to be affected by intercarrier scattering. A Boltzmann equation approach is used to take account of the effects of, injection of electrons into the conduction band, at an energy below the threshold for longitudinal optical phonon emission, scattering by acoustic phonons, via the deformation potential and piezoelectric interactions, and recombination. The equation is solved numerically using an iterative technique and the distribution functions are found to differ significantly from a Maxwellian form. Emission spectra due to conduction band to neutral acceptor transitions are derived from the computed distribution functions and are compared with recent experimental results.     

Exact electrostatic solitons in a magnetoplasma with degenerate electrons

Fully nonlinear planar ion-acoustic solitary waves (IASWs) moving obliquely to an external magnetic field are studied in a collisionless magnetoplasma with degenerate electrons. The features of the nonlinear IASWs are investigated through the derivation of an energy balance-like equation involving the Sagdeev-type potential as well as the nonlinear dispersion relation.     

On the confinement potential formation in a two-electron quantum dot

A model of a quantum dot for two interacting electrons is proposed and analyzed. The properties of the ambient determining the form of the confinement potential for electrons are simulated using the electrostatic field of the image charge. Analytic expressions for the eigenvalues of each subsystem are derived taking into account the external magnetic field and using the representation of the system Hamiltonian as the sum of the Hamiltonians of the center of mass and of relative motion on the basis of the method of oscillator representation [M. Dineykhan and G. V. Efimov, Element. Chast. At. Yadra 26, 651 (1995); M. Dineykhan, G. V. Efimov, G. Ganbold, and S. N. Nedelko, Oscillator Representation in Quantum Physics, Lecture Notes in Physics, Vol. 26, Springer, Berlin (1995)]. The relative motion of electrons is responsible for a confinement potential which differs from the parabolic confinement potential and is a function of the electron effective mass as well as the characteristics of the image charge.     

Quantum dynamics in a thin film,I. Propagation of localized perturbations

In the one-particle approximation, the quantum behavior of a (quasi-)particle is studied in a thin waveguide having the form of a thin curvilinear film (in three-dimensional space) placed in external magnetic and electric fields. Objects of this type arise in the actively developing physics of nano-structures and, in particular, in the theory of ballistic transport of electrons. The corresponding quantum-mechanical equation is a Pauli-type equation with nonrelativistic Rashba spin-orbital interaction for a two-dimensional vector function. Asymptotic solutions of the Cauchy problem with special localized initial data and those of the spectral problem are obtained. The construction of asymptotic solutions is carried out in two stages. At the first stage, in the framework of the adiabatic approximation, using the “operator separation of variables” (the “generalized adiabatic principle”) for a rather broad class of quantum states, the original three-dimensional equation is reduced to a two-dimensional surface (the limit film), and then diverse solutions of this reduced equation are constructed. The first part of the paper is devoted to the reduction and the solutions of the Cauchy problem. Spectral problems will be treated in the second part. Dedicated to the memory of V. A. Geyler Supported by the RFBR grant no. 05-01-00968 and by the DFG-RAS project DFG 436 RUS 113/785.     

Modulation of the exciton density in a hybrid electron-exciton system

The induced modulation of the exciton density in a system consisting of spatially separated layers of a two-dimensional electron gas and indirect dipolar excitons is studied theoretically. In particular, it is shown that an external potential causes Friedel oscillations in the density of excitons due to their interaction with electrons. Possibilities for experimental observation of this effect are briefly discussed.     

Coupled ripplon-plasmon modes in a multielectron bubble

In multielectron bubbles, the electrons form an effectively two-dimensional layer at the inner surface of the bubble in helium. The modes of oscillation of the bubble surface (the ripplons) are influenced by the charge redistribution of the electrons along the surface. The dispersion relation for these charge redistribution modes (‘longitudinal plasmons’) is derived and the coupling of these modes to the ripplons is analysed. We find that the ripplon-plasmon coupling in a multielectron bubble differs markedly from that of electrons on a flat helium surface. An equation is presented relating the spherical harmonic components of the charge redistribution to those of the shape deformation of the bubble.     

Mathematical and physical aspects of controlling the exact solutions of the 3D Gross-Pitaevskii equation

The possibility of the decomposition of the three-dimensional (3D) Gross-Pitaevskii equation (GPE) into a pair of coupled Schrödinger-type equations, is investigated. It is shown that, under suitable mathematical conditions, it is possible to construct the exact controlled solutions of the 3D GPE from the solutions of a linear 2D Schrödinger equation coupled with a 1D nonlinear Schrödinger equation (the transverse and longitudinal components of the GPE, respectively). The coupling between these two equations is the functional of the transverse and the longitudinal profiles. The applied method of nonlinear decomposition, called the controlling potential method (CPM), yields the full 3D solution in the form of the product of the solutions of the transverse and longitudinal components of the GPE. It is shown that the CPM constitutes a variational principle and sets up a condition on the controlling potential well. Its physical interpretation is given in terms of the minimization of the (energy) effects introduced by the control. The method is applied to the case of a parabolic external potential to construct analytically an exact BEC state in the form of a bright soliton, for which the quantitative comparison between the external and controlling potentials is presented.     

Towards a theory of the field emission of electrons

Application of a generalized WKB method to the investigation of the field emission of electrons from conductors and semiconductors is considered. Formulas are obtained for estimating the coefficients of transmission of electrons through a potential barrier created by an external electric field and the image force.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 7–13, November, 1972.     

Analytic study on solitons in the nonlinear fibers with time-modulated parabolic law nonlinearity and Raman effect

In this paper, the nonlinear optical transmission equation with time-modulated cubic–quintic nonlinearity and Raman effect term, describing the ultrashort optical pulse propagate along the nonlinear media, has been studied by using the non-auto-Bäcklund transformation (NATB) and subsidiary ordinary differential equation (sub-ODE) expansion method. As a result, analytical solution expressions to that equation are obtained. Finally, two simple examples, including systems with the external potential in exponential form and periodic form, are provided to show the solution steps.     

Master equation for the density matrix and Boltzmann equation of localized electrons in crystals

A Master equation for the density matrix and a Boltzmann equation for the occupation number of electrons in a crystal are derived. The wave function of an electron is localized within a sub crystal by a superposition of the corresponding Wannier functions. The electrons are coupled to an external electrical field, to phonons, and to a particle reservoir, describing phenomena as transport, damping, and electron sources on the surface of contact.     

Quantum kinetic theory of trapped particles in a strong electromagnetic field

The idea of treating quantum systems by semiclassical representations using effective quantum potentials (forces) has been successfully applied in equilibrium by many authors, see e.g. [D. Bohm, Phys. Rev. 85 (1986) 166 and 180; D.K. Ferry, J.R. Zhou, Phys. Rev. B 48 (1993) 7944; A.V. Filinov, M. Bonitz, W. Ebeling, J. Phys. A 36 (2003) 5957 and references cited therein]. Here, this idea is extended to nonequilibrium quantum systems in an external field. A gauge-invariant quantum kinetic theory for weakly inhomogeneous charged particle systems in a strong electromagnetic field is developed within the framework of nonequilibrium Green’s functions. The equation for the spectral density is simplified by introducing a classical (local) form for the kinetics. Nonlocal quantum effects are accounted for in this way by replacing the bare external confinement potential with an effective quantum potential. The equation for this effective potential is identified and solved for weak inhomogeneity in the collisionless limit. The resulting nonequilibrium spectral function is used to determine the density of states and the modification of the Born collision operator in the kinetic equation for the Wigner function due to quantum confinement effects.     

变像管相机中空间电荷效应的统计动力学分析

 从Boltzmann积分微分方程出发推出了保守势场中电子数密度按势能的分布规律,即Boltzmann统计分布。以此为基础,从统计动力学的角度详细分析了变像管相机中超短电子脉冲内部的空间电荷效应,通过求解Poisson方程得出了表征空间电荷效应的两个特征参量：空间电荷密度分布函数和速度分布函数,并对其按电位的动态变化规律进行了定性讨论。结果表明,限制变像管中的低电位区域和其中光电子脉冲从高电位向低电位传输的区域都将有助于优化整个变像管的性能。同时也重新讨论了光电阴极附近强加速场对光电子脉冲时间弥散的抑制作用,最终确定了其物理机制为不等位区间中电子脉冲空间分布的高度集中性。     

Pressure anisotropy effects on nonlinear electrostatic excitations in magnetized electron-positron-ion plasmas

The propagation of linear and nonlinear electrostatic waves is investigated in a magnetized anisotropic electron-positron-ion (e-p-i) plasma with superthermal electrons and positrons. A two-dimensional plasma geometry is assumed. The ions are assumed to be warm and anisotropic due to an external magnetic field. The anisotropic ion pressure is defined using the double adiabatic Chew-Golberger-Low (CGL) theory. In the linear regime, two normal modes are predicted, whose characteristics are investigated parametrically, focusing on the effect of superthermality of electrons and positrons, ion pressure anisotropy, positron concentration and magnetic field strength. A Zakharov-Kuznetsov (ZK) type equation is derived for the electrostatic potential (disturbance) via a reductive perturbation method. The parametric role of superthermality, positron content, ion pressure anisotropy and magnetic field strength on the characteristics of solitary wave structures is investigated. Following Allen and Rowlands [J. Plasma Phys. 53, 63 (1995)], we have shown that the pulse soliton solution of the ZK equation is unstable to oblique perturbations, and have analytically traced the dependence of the instability growth rate on superthermality and ion pressure anisotropy.     

Microscopic theory of sound propagation in dielectric crystals

The time evolution of the atomic displacement field in a dielectric crystal subjected to an external force is studied in the domain of linear response by means of imaginary time Green's functions. For slowly varying disturbances two coupled equations have to be solved: a differential equation for the amplitude of an acoustic wave and a linearized Boltzmann equation. The latter results from the integral equation for the vertex part and includes an additional integral operator. The collision equation is solved for different relative magnitudes of the sound frequency and the frequencies for normal and Umklapp processes using the method developed by Weiss. Some of the expressions showing up in the velocity and damping of the sound wave are estimated numerically for rare gases with two-body forces in the form of the Morse potential.