Screening of charge in a semiinfinite electron gas

Within linear response and the self-consistent field approximation an equation for the screening of a chargee ^iwt δ(r?r ₀),r ₀=(0, 0,z ₀) by an electrongas confined to the half-spacez>0 is derived. From this 3 cases are discussed: 1. Application to a homogeneous electron gas bounded by an infinite potential. 2. Thomas-Fermi approximation. 3. Image potential approximation.     

Some estimates for magnetic fluctuations in a turbulent medium

A new integral relationship between the fluctuations b(r, t) of a magnetic field and its mean B ₀(r, t) is derived for the steady-state magnetic field in a turbulent medium. This formula provides the estimate 〈b?curlb〉=?B ₀?curlB ₀. Simultaneously, the coefficient of amplification of the mean magnetic field α effect) is obtained: α=(η+β)B ₀? curlB ₀/B ₀ ² . The formula for α allows for a decrease in this coefficient owing to the back action of the magnetic field on the turbulent velocity field. It is shown that the Zel’dovich’s estimate 〈 b ²〉?β/η B ₀ ² for two-dimensional turbulence holds for magnetic fields at the instant the fluctuations 〈a ²〉 of the vector potential, rather than 〈b ²〉, reach a maximum. Here, η and β are the ohmic (molecular) and turbulent diffusion coefficients, respectively. This estimate is refined with allowance made for the fact that the condition for diffusion approximation itself relates the β, b, and B ₀ quantities to each other.     

Quantum dissipation: Dynamics of a particle in a symmetric double well in the presence of non-ohmic friction

We investigate the equilibrium value and the approach to equilibrium of a particle in a symmetric double-well potential and subjected to dissipation, within the model of Caldeira and Leggett, Ann. Phys. (N.Y.) 149 (1983) 374, but without the ohmic assumption. For subohmic friction, the critical value of the coupling with the bath above which the particle localizes is found to be dependent on the ratio (tunnelling frequency)/(bandwidth of the bath); for an infinite bandwidth, the results given by Leggett et al., Rev. Mod. Phys. 59 (1987) 1, are recovered. For superohmic dissipation, the particle never localizes and its coordinate always goes to zero by following, at large times, a power law in time of the form t^−ν; the exponent ν is shown to have a non-intuitive variation as a function of the non-ohmicity.     

Spin and orbital angular momenta defined for electromagnetic fields in planar anisotropic media

The spin and orbital angular momenta (S and L) of the radiation fields were defined newly to satisfy the duality transformation and to hold for planar anisotropic media, by introducing an entirely new vector potential. Some features of them are discussed in connection with the anisotropy in the permittivity and permeability of a medium.     

HCNO as a semirigid bender

The semirigid bender Hamiltonian [Bunker and Landsberg, J. Mol. Spectrosc., 67, 374–385 (1977)] is used to fit the rotation-vibration energy level separations in the fulminic acid (HCNO) molecule. The allowance made in the model for the variation of the CH and CN bond lengths with the HCN bending angle proves to be very important, and as well as achieving a good fit we are able to make a detailed investigation of the shape of the HCN bending potential function.From the results we conclude that the equilibrium structure of HCNO is linear but that excitation of the ν₁ or ν₂ stretching vibrations gives rise to an effective HCN bending potential function having its minimum at a nonlinear configuration. Even in the ground state the zeropoint vibrational contributions from ν₁ and ν₂ to the effective HCN bending potential give a small barrier (11.5 cm^?1) to linearity, and we determine that the zero-point HCN bending vibrational amplitude is ±34°.     

Sufficient conditions for the existence of bound states in a potential without spherical symmetry

We give in this paper several suffieient conditions for the existence of negative energy bound states in a purely attractive potential without spherical symmetry. These conditions generalize the condition obtained recently by K. Chadan and A. Martin (C. R. Acad. Sci. Paris290 (1980), 151), and can ensure the existence of n bound states. For the spherically symmetric case, one gets simple formulae which are also new.     

Theory of light scattering from a system of interacting Brownian particles

Starting from a N-particle diffusion equation for a system of N interacting spherical Brownian particles, a non-linear transport equation for concentration fluctuations δc(r, t) of the particles is derived. This dynamic equation is transformed into a hierarchy of equations for retarded propagators of increasing numbers of concentration fluctuations. A cluster expansion to lowest order in the average concentration results in a set of two coupled equations. The spectrum of light scattered by the interacting particles is in general not a Lorentzian, due to the non-linear term in the transport equation. For small scattering wave vectors k the width is D(ω)k², where ω is the transferred frequency. It is shown that D(0) = D_e, the effective diffusion coefficient. For a hardcore interaction potential the spectrum is Lorentzian and it is found that D_e = D₀(1 + φ), where D₀ is the diffusion constant for independent particles and φ the volume concentration of Brownian particles.     

An SU(4) invariant compactification of d = 11 supergravity on a stretched seven-sphere

We construct on S⁷ an SU(4) invariant solution of d = 11 supergravity in which the metric on the seven-sphere, regarded as a U(1) bundle overCP³, is distorted by stretching the U(1) fibers, and the four-index field strength F_MNPQ is non-zero in the S⁷ directions. This solution presumably corresponds to the SU(4) invariant extremum of the de Wit-Nicolai potential.     

Theory of the Senftleben-Beenakker effects for NH3 and ND3: Collision integrals

The distorted wave Born approximation is used as a basis for understanding the cross sections which govern the production and relaxation of internal state polarizations, in gaseous ammonia, in the presence of shear flow or thermal gradients. For viscous flow, it is shown that the dominant dipole-dipole interaction leads to the production of [W]⁽²⁾J polarization, but not to any appreciable [J]⁽²⁾ polarization. The essential absence of the usual [J]⁽²⁾ polarization, as produced by the anisotropic dispersion interaction (P₂-potential), is consistent with the smallness of the anisotropy of the dipole polarizability in ammonia and with the suppression of the effect of such shorter ranged interactions (e.g. the P₂ potential) in the presence of a dominant longer ranged interaction (there the dipole-dipole potential). For thermal conduction, it is shown that the dominant dipole-dipole interaction apparently produces predominantly a $\text{WJ(W}{}^2\text{?}\text{5}\text{2}\text{)}$ polarization. The shorter ranged dipole-quadrupole interaction as well as higher multipole potentials produce a W[J]⁽²⁾ polarization, while a cross term between the dipole-dipole and quadrupole-dipole potentials can produce a velocity-independent dipolar polarization, denoted here as Jh¹.     

Andreev reflection between a normal metal and the FFLO superconductor II: A self-consistent approach

We consider Andreev reflection in a two dimensional junction between a normal metal and a heavy fermion superconductor in the Fulde–Ferrell (FF) type of the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state. We assume s-wave symmetry of the superconducting gap. The parameters of the superconductor: the gap magnitude, the chemical potential, and the Cooper pair center-of-mass-momentum Q, are all determined self-consistently within a mean-field (BCS) scheme. The Cooper pair momentum Q is chosen as perpendicular to the junction interface. We calculate the junction conductance for a series of barrier strengths. In the case of incoming electron with spin σ = ↑ only for magnetic fields close to the upper critical field H_c2, we obtain the so-called Andreev window, i.e. the energy interval in which the reflection probability is maximal, which in turn is indicated by a peak in the conductance. The last result differs with other non-self-consistent calculations existing in the literature.     

Note on the calculation of electrostatic lattice potentials

We reconsider the problem of calculating electrostatic lattice potentials, or in fact potentials of the type |r|^βφ_l(r), where φ_l(r) is the lth derivative of the l/|r|^p potential. According to Ewald, and generalized by Nijboer and de Wette, the slowly converging potential can be expressed in two screened potentials, one on the original lattice and the other on the reciprocal lattice, which are rapidly converging. In general these screenings are related by a type of Hankel transform. The request of (asymptotic) symmetry between the screenings then leads to the well-known screenings as the best possible. Detailed formula needed for calculations are given.     

Magnetic Bloch states and Hall conductivity of a two-dimensional electron gas in a periodic potential without inversion center

Quantum states of 2D electrons are studied in a periodic potential without inversion center in the presence of a magnetic field. It is shown that the energy spectrum in magnetic subbands is not symmetric about the center of magnetic Brillouin zone E(k)≠E(?k). Singularities (phase branching points) of the electron wave function, which determine the quantization law of Hall conductivity σ_xy, are studied in the k space. It is found that a sharp change takes place in the number of points in the magnetic Brillouin zone and in the corresponding values of topological invariants determining the Hall conductivity of filled subbands. It is noted that the longitudinal conductivity of a lattice without inversion center placed in a magnetic field is not invariant with respect to a change in sign of the electric field, and a photovoltaic effect must arise in an ac electromagnetic field.     

Calculation of high-order rotational centrifugal-distortion matrix elements for a Hund's case (a) basis set

The derivation of explicit expressions for the Hund's case (a) matrix elements of R^2k is discussed, where R is the mechanical rotational angular momentum operator of the molecule. A recursion relation is developed that permits matrix elements of R^2k to be expressed in terms of those of R^2(k?1), thus affording a straightforward means of calculating the case (a) matrix elements of rotational centrifugal-distortion constants D_v, H_v, L_v, M_v, etc., to an arbitrarily high order. The explicit matrix elements of L_v are listed.     

Field of linear frames as a fundamental self-interacting system

We present some philosophical and physical arguments supporting the hypothesis that the most fundamental self-interacting field in an amorphous space-time is the field of linear frames, i.e. the quadruple of vector bosons. We construct a wide class of Lagrangian dynamical models invariant under the total group of diffeomorphisms and under the natural action of the proper linear group GL⁺ (4, R) on the tetrad field. There exist some links between these models and the Hamiltonian dynamical systems on GL⁺ (3, R) (the mechanics of affinely-rigid bodies [23] [27]). We present the general form of field equations, conservation laws and Bianchi identities. There exist some formal similarities between our Lagrangians and those used in non-linear electrodynamics, in particular in the Born–Infeld theory [21]. We also give a few rough remarks concerning models invariant under natural subgroups of GL⁺ (4, R), i.e. under SL(4, R) and SO(1, 3; R) (special linear group and Lorentz group). The latter class includes the conventional Einstein relativity and the more general metrical-parallelism models. It turns out that there are GL⁺ (4, R)-invariant Lagrangians which are structurally alike the conventional Einstein Lagrangian.We have not derived as yet either mathematical or physical consequences of the presented model. Nevertheless, it seems to follow from our discussion that, a priori, the GL⁺ (4, R)-invariant tetrad models could be competitive with the Einstein theory. The next thing to be done would be a careful mathematical analysis of these models and attempts to compare their consequences with those of the Einstein relativity and of other field theories.     

The dynamic structure of <Emphasis Type="Italic">cis</Emphasis> and <Emphasis Type="Italic">trans</Emphasis> conformers of substituted phosphinous acids

The potential energy surfaces of bis-(trifluoromethyl)-phosphinous (III), diemthylphosphinous (IV), and bis-(pentafluorophenyl)-phosphinous (V) acids, the geometric parameters of the cis and trans conformers of these acids, and their P-O and O-H stretching vibration frequencies were calculated by the density functional theory method (PBE, 4Z). The potential energy surface sections corresponding to internal rotations about the P-O bonds were constructed, and dynamic problems for such a motion of the proton in a cyclic potential were solved by the Ritz method using a basis set of 100 trigonometric functions. According to calculations, the energy differences between the cis and trans conformers of acids III–V were of 4–7 kJ/mol, and the heights of potential barriers separating these conformers were of from 11 to 16 kJ/mol. In acids III and V, the cis, and, in IV, the trans conformer was stabler. At 298 K, only the ground vibrational states were populated for both rotamers of IV and V and the cis conformer of III. The special features of the potential of III were such that, at 298 K, the first excited vibrational level of its trans conformer was also noticeably populated.     

Mobility of an electron in a Guassian random potential

The mobility of an electron in a Gaussian random potential is evaluated. It is shown that the relaxation time of the electron is found to be proportional to $\text{L}{}^2\text{|}\text{p}\text{|}$ for large and small correlation lengths L where |p| is the electron momentum.     

Macroscopic behaviour of a charged Boltzmann gas

We consider a classical charged gas (with self-consistent Coulomb interaction) described by a solvable linearized Boltzmann equation with thermalization on uniformly distributed scatterers. It is shown that if one scales the time t, the reciprocal space coordinate k and the Debye length l as λ²t, (1/λ)k, λl, respectively, in the λ → ∞ limit the charge density is equal to the solution of the corresponding diffusion-conduction (macroscopic) equation.     

Nonlocal density functional calculation of the electron affinity of atoms

The weighted-density approximation (WDA) to the exchange-correlation potential V_xc (r) is used to compute electron affinities of atoms within the context of density functional theory. Good results are obtained for the affinities of H, O and F, but it is critical that the WDA must be applied in such a way as to preserve the correct asymptotic behaviour of V_xc (r).     

Effect of the geometrical phase shift on the spin and orbital angular momenta of light traveling in a coiled optical fiber with optical activity

The intrinsic spin and extrinsic orbital angular momenta (S and L) and their torque densities are derived and formulated using the plane waves for light propagating in coiled optically active fiber cores which have homogeneity and inhomogeneity of refractive index n. The effect of the geometrical phase shift χ on S, L, their densities (per unit volume) and their torque densities of the right and left circularly polarized plane waves split in such a fiber is analyzed using the locally inertial coordinate frame for a fiber core with homogeneity of n and the non-inertial coordinate frame for a fiber core with inhomogeneity of n.     

Specific features of the thermal electromotive force in Bi quantum wires in transverse magnetic and electric fields

The thermal electromotive force (emf) in Bi quantum wires has been calculated in the model of potential in the form of a paraboloid of revolution in a uniform magnetic field H, which is normal to the axis of the studied nanostructure, and in a direct-current (dc) electric field E ‖ H. It has been shown that, with an increase in E, the thermal emf α _xx is described by a nonmonotonic function at different values of H. A physical interpretation of this behavior of α _xx as a function of E is proposed with account for the interaction between carriers and the rough surface of the nanowire.