Hartree–Fock versus quantum Monte Carlo study of persistent current in a one-dimensional ring with single scatterer

We calculate the persistent current of interacting spinless electrons in a one-dimensional ring containing a single δ barrier. We use the self-consistent Hartree–Fock method and the quantum Monte Carlo method which gives fully correlated solutions. Our Hartree–Fock method treats the non-local Fock term in a local approximation and also exactly (if the ring is not too large). Treating the Fock term exactly we attempt to support our previous Hartree–Fock result obtained in the local approximation, in particular the persistent current behaving like I∝L^-1-α, where L is the ring length and α>0 is the power depending only on the electron–electron interaction. Finally, we use the Hartree–Fock solutions as an input for our quantum Monte Carlo calculation. The Monte Carlo results exhibit only small quantitative differences from the Hartree–Fock results.     

Quantum n-Vector Anharmonic Crystal II: Displacement Fluctuations

Based on the 1/n-expansion derived in a previous paper, the displacement fluctuations are analyzed in a quantum n-vector model of anharmonic crystal in the large n regime. It is shown that in the ferroelectric phase the n limit of the local fluctuation field has faster large-distance correlation decay than its Hartree–Fock approximation. Also, the critical exponent of the global displacement fluctuation is strictly smaller there than the Hartree–Fock exponent. In particular, the displacement fluctuations may be normal in the ferroelectric phase in spite of the Hartree–Fock prediction.     

Lowering the Hartree–Fock Minimizer by Electron–Positron Pair Correlation

We prove by a simple computation that a suitable coupling to the positronic sector lowers the energy of the purely electronic minimizer of the electron–positron Hartree–Fock functional.     

Polaronic effects on laser dressed donor impurities in a quantum well

The effect of laser field on the binding energy in a GaAs/Ga1_1−xAl_xAs quantum well within the single band effective mass-approximation is investigated. Exciton binding energy is calculated as a function of well width with the renormalization of the semiconductor gap and conduction valence effective masses. The calculation includes the laser dressing effects on both the impurity Coulomb potential and the confinement potential. The valence-band anisotropy is included in our theoretical model. The 2D Hartree–Fock spatial dielectric function and the polaronic effects have been employed in our calculations. We investigate that reduction of binding energy in a doped quantum well due to screening effect and the intense laser field leads to semiconductor–metal transition.     

Effective pseudospin wave model for the coherent stripe phase in a bilayer system

Hartree–Fock theory predicts a stripe-like ground state for the two-dimensional electron gas in a bilayer quantum Hall system in a quantizing magnetic field at filling factor 4N+1 (with N>0). This stripe state contains quasi-1D linear coherent regions where electrons are delocalized across both wells and which support low-energy collective excitations in the form of phonons and pseudospin waves. We have recently computed the dispersion relation of these low-energy modes in the generalized random phase approximation. In this work, we propose an effective pseudospin model in which the stripe state is modeled as an array of coupled 1D anisotropic X–Y systems. The coupling constants and stiffness of our model are extracted from the density and pseudospin response functions computed in the GRPA.     

Oscillator strengths and lifetimes for the S V spectrum

The semi-empirical weighted oscillator strengths (gf) and the lifetimes presented in this work for all experimentally known electric dipole S V spectral lines and energy levels were carried out in a multiconfiguration Hartree–Fock relativistic (HFR) approach. In this calculation, the electrostatic parameters were optimized by a least-squares procedure, in order to improve the adjustment to experimental energy levels. This method produces lifetime values and gf values that are in agreement with intensity observations used for the interpretation of spectrograms of solar and laboratory plasmas.     

Effective action studies of quantum Hall skyrmions

We discuss effective action studies of quantum Hall spin textures both at edges and in the bulk. The effective action energy functional is minimized by numerically integrating the equations of motion. We compare the numerical results with analytical expressions valid for small and with results obtained from Hartree–Fock calculations. The Hartree–Fock energies are lower than the effective action energies, but for small the agreement is very good.     

Quantum Entanglement in Relativistic Three-Particle Systems

The relativistic three-particle systems are studied within the framework of Relativistic Schrödinger Theory (RST), with emphasis on the determination of the energy functional for the stationary bound states. The phenomenon of entanglement shows up here in form of the exchange energy which is a significant part of the relativistic field energy. The electromagnetic interactions become unified with the exchange interactions into a relativistic U(N) gauge theory, which has the Hartree–Fock equations as its non-relativistic limit. This yields a general framework for treating entangled states of relativistic many-particle systems, e.g., the N-electron atoms.     

Relativistic Schrödinger Theory and the Hartree–Fock Approach

Within the framework of Relativistic Schrödinger Theory (RST), the scalar two-particle systems with electromagnetic interactions are treated on the basis of a non-Abelian gauge group U(2) which is broken down to the Abelian subgroup U(1)×U(1). In order that the RST dynamics be consistent with the (non-Abelian) Maxwell equations, there arises a compatibility condition which yields cross relationships for the links between the field strengths and currents of both particles such that self-interactions are eliminated. In the non-relativistic limit, the RST dynamics becomes identical to the well-known Hartree–Fock equations (for spinless particles). Consequently the original RST field equations may be considered as the relativistic generalization of the Hartree–Fock equations, and the exchange interactions of the conventional theory (induced by the anti-symmetrization postulate) do reappear here as ordinary gauge interactions due to a broken symmetry.     

X-rays and matter – the basic interactions

In this introductory article we attempt to provide the theoretical basis for developing the interaction between X-rays and matter, so that one can unravel properties of matter by interpretation of X-ray experiments on samples. We emphasize that we are dealing with the basics, which means that we shall limit ourselves to a discussion of the interaction of an X-ray photon with an isolated atom, or rather with a single electron in a Hartree–Fock atom. Subsequent articles in this issue deal with more complicated – and interesting – forms of matter encompassing many atoms or molecules. To cite this article: J. Als-Nielsen, C. R. Physique 9 (2008).     

A Variational Wave Function for 2p2-Orbitals in Atomic Negative Ions

A variational wave function is used to describe the binding energy of atomic negative ions using a two-electron system in the 2p²-state. Each electron is described by a modified screened hydrogenic wave function involving two free screening parameters denoted by c and a. The model is applied to hydrogen, helium, lithium, and boron anions, where the optimum values of the screening parameters are deduced through fitting the optimized energy to available experimental and theoretical values. The behavior of the optimum wave function for each anion is also investigated as a function of electronic radial distance and compared with its counterpart in the screened hydrogenic model and the Hartree–Fock method.     

Calculations of the IR Intensities of Absorption Bands by the Hartree–Fock (ab initio) and Density-Functional Methods

Comparative calculations of the absolute intensities of bands in IR spectra were performed by the Hartree–Fock (ab initio) and density-functional methods for molecules containing different heteroatoms most cases, close coincidence between the curves calculated by these two methods is found, but there are also some unexpected disagreements in the results.     

Soliton–antisoliton interaction in a parametrically driven easy-plane magnetic wire

In the present work we study the soliton–antisoliton interaction in an anisotropic easy-plane magnetic wire forced by a transverse uniform and oscillatory magnetic field. This system is described in the continuous framework by the Landau–Lifshitz–Gilbert equation. We find numerically that the spatio-temporal magnetization field exhibits both annihilative and repulsive soliton–antisoliton interactions. We also describe this system with the aim of the associated Parametrically Driven and Damped Nonlinear Schrödinger amplitude equation and give an approximate analytical solution that roughly describes the repulsive interaction.     

In-plane magnetic field-induced anisotropy and orientation energy of stripe phases at half-filled high Landau levels

We report on detailed Hartree–Fock calculations of the unidirectional charge density wave orientation energy induced by a tilted magnetic field. We find that for current experimental samples stripes are oriented perpendicular to the in-plane field, consistent with experiment. For wider two-dimensional electron systems we predict tilt-induced stripe states with variable anisotropy energy sign.     

Plasma excitations in the superconducting state of two-band layered superconductors

We investigate the low-frequency plasma modes polarized in the c-direction in two-band layered superconductors. The dynamic dielectric function (ω,q) is derived at T=0, using the generalized random-phase-approximation which is consistent with the Hartree–Fock single-particle states. It is shown that the dielectric function has two zero-points which correspond to the longitudinal plasma modes in two-band layered superconductors.     

Microscopic modeling of intersubband resonances in InAs/AlSb quantum wells

Linear absorption spectra from intersubband resonance in InAs/AlSb quantum wells are analyzed theoretically using the intersubband semiconductor Bloch equation approach. Our model goes beyond the Hartree–Fock approximation and treats particle–particle correlations under the second Born approximation. Electron–electron and longitudinal optical phonon scatterings from such a treatment describe intrinsic line broadening to the intersubband resonance. Electron subbands are determined self-consistently with a spurious-state-free 8-band k·p Hamiltonian under the envelope function approximation. To compare with experimental measurements, we also included line broadening due to electron-interface roughness scattering. Excellent agreement was achieved for temperature-dependent absorption spectra in the mid-infrared frequency range, after taking into careful account the interplay of material parameters, nonparabolicity in bandstructure, and many-body effects.     

Single-electron charging spectra: from natural to artificial atoms

We present a theoretical study of the charging spectra in natural and artificial atoms. We apply a model electrostatic potential created by a homogenously charged sphere. This model potential allows for a continuous passage from the Coulomb potential of the nucleus to parabolic confinement potential of quantum dots. We consider electron systems with N=1,…,10 electrons with the use of the Hartree–Fock method. We discuss the qualitative similarities and differences between the chemical potential spectrum of electron systems bound to nucleus and confined in quantum dots.     

Commutator Green's functions for a spin Hamiltonian

All the commutator Green's functions are calculated for the Heisenberg spin Hamiltonian in the Hartree-Fock approximation. It is shown further that the Tyablikov transverse commutator Green's function corresponds to the Hartree—Fock approximation only for the longitudinal part of the Heisenberg spin Hamiltonian, and to obtain the longitudinal part of the commutator Green's function to the same accuracy as the Tyablikov transverse commutator Green's function it is necessary to go over to the Hartree—Fock approximation only with respect to the transverse part of the Heisenberg spin Hamiltonian.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 62–65, December, 1980.     

Exchange-enhanced spin-splitting in a two-dimensional electron gas in the presence of the Rashba spin–orbit interaction

We present a theoretical study on how many-body effects can affect the spin-splitting of a two-dimensional electron gas in the presence of the Rashba spin–orbit interaction. The standard Hartree–Fock approximation and Green's function approach are employed to calculate the energy spectrum and density of states of a spin-split two-dimensional electron gas (2DEG). We find that the presence of the exchange interaction can enhance significantly the spin-splitting of a 2DEG on top of the Rashba effect. The physical reasons behind this important phenomenon are discussed.     

Experimental and theoretical investigations into the electronic structure of CF2Br2 by electron momentum spectroscopy

The binding energy spectra and electron momentum density distributions for the valence orbitals of CF₂Br₂ have been obtained by using electron momentum spectroscopy (EMS) at an impact energy of 1200 eV plus binding energy. The measured electron momentum profiles are compared with Hartree–Fock (HF) and density functional theory (DFT) calculations with different-sized basis sets. In general, the DFT-B3LYP calculation using the large basis sets of 6-311++G** and aug-cc-pVTZ fairly describe the experimental results. Moreover, the controversial orderings of the outer valence orbitals have been reassigned. The pole strength of the main ionization transition from the inner valence orbital of 1b₂ is determined.