Showing papers on "Random phase approximation published in 1996"
TL;DR: In this paper, the authors report the implementation of time-dependent density functional response theory (TD-DFRT) for molecules using the timedependent local density approximation (TDLDA), which adds exchange and correlation response terms to their previous work which used the density functional theory (DFT) random phase approximation (RPA) [M. E. Casida, C. Jamorski, F. Bohr, J. Guan, and D. R. Salahub, in Theoretical and Computational Modeling of NLO and Electronic Materials, edited by S.
Abstract: We report the implementation of time‐dependent density‐functional response theory (TD‐DFRT) for molecules using the time‐dependent local density approximation (TDLDA). This adds exchange and correlation response terms to our previous work which used the density‐functional theory (DFT) random phase approximation (RPA) [M. E. Casida, C. Jamorski, F. Bohr, J. Guan, and D. R. Salahub, in Theoretical and Computational Modeling of NLO and Electronic Materials, edited by S. P. Karna and A. T. Yeates (ACS, Washington, D.C., in press)], and provides the first practical, molecular DFT code capable of treating frequency‐dependent response properties and electronic excitation spectra based on a formally rigorous approach. The essentials of the method are described, and results for the dynamic mean dipole polarizability and the first eight excitation energies of N2 are found to be in good agreement with experiment and with results from other ab initio methods.
856 citations
TL;DR: It is found that the inclusion of proton-neutron pairing influences the neutrinoless double beta decay rates significantly, in all cases allowing for larger values of the expectation value of light neutrino masses.
Abstract: We have investigated the role of proton-neutron pairing in the context of the quasiparticle random phase approximation formalism. This way the neutrinoless double beta decay matrix elements of the experimentally interesting A = 48, 76, 82, 96, 100, 116, 128, 130, and 136 systems have been calculated. We have found that the inclusion of proton-neutron pairing influences the neutrinoless double beta decay rates significantly, in all cases allowing for larger values of the expectation value of light neutrino masses. Using the best presently available experimental limits on the half lifetime of neutrinoless double beta decay we have extracted the limits on lepton number violating parameters. \textcopyright{} 1996 The American Physical Society.
155 citations
TL;DR: It is found that the final results are marginally affected by the broadening of the quasiparticles, and that their self-consistent energies are still close to their free-electron counterparts as they are in non-self-cons consistent calculations.
Abstract: With the aim of properly understanding the basis for and the utility of many-body perturbation theory as applied to extended metallic systems, we have calculated the electronic self-energy of the homogeneous electron gas within the GW approximation. The calculation has been carried out in a self-consistent way; i.e., the one-electron Green function obtained from Dyson’s equation is the same as that used to calculate the self-energy. The self-consistency is restricted in the sense that the screened interaction W is kept fixed and equal to that of the random-phase approximation for the gas. We have found that the final results are marginally affected by the broadening of the quasiparticles, and that their self-consistent energies are still close to their free-electron counterparts as they are in non-self-consistent calculations. The reduction in strength of the quasiparticles and the development of satellite structure (plasmons) gives, however, a markedly smaller dynamical self-energy leading to, e.g., a smaller reduction in the quasiparticle strength as compared to non-self-consistent results. The relatively bad description of plasmon structure within the non-self-consistent GW approximation is marginally improved. A first attempt at including W in the self-consistency cycle leads to an even broader and structureless satellite spectrum in disagreement with experiment. (Less)
106 citations
TL;DR: A self-contained theoretical analysis of the dynamical response of a one-dimensional electron system, as confined in a semiconductor quantum wire, within the random-phase approximation is provided.
Abstract: We provide a self-contained theoretical analysis of the dynamical response of a one-dimensional electron system, as confined in a semiconductor quantum wire, within the random-phase approximation. We carry out a detailed comparison with the corresponding two- and three-dimensional situations, and discuss the peculiarities arising in the one-dimensional linear response from the nonexistence of low energy single-particle excitations and from the linear nature of the long wavelength plasmon mode. We provide a critical discussion of the analytic properties of the complex dielectric function in the complex frequency plane. We investigate the zeros of the complex dielectric function, and calculate the plasmon dispersion, damping, and plasmon spectral weight in one dimension. We consider finite temperature and impurity scattering effects on one-dimensional plasmon dispersion and damping. \textcopyright{} 1996 The American Physical Society.
92 citations
TL;DR: In this article, a general theoretical framework for the study of anisotropic composition fluctuations about an ordered block copolymer phase is developed based on the idea that, in order to study the effects of fluctuations around an ordered broken symmetry phase, the theory must be formulated as a self-consistent expansion around the mean-field solution of this ordered state.
Abstract: A general theoretical framework for the study of anisotropic composition fluctuations about an ordered block copolymer phase is developed The approach is based on the idea that, in order to study the effects of fluctuations around an ordered broken symmetry phase, the theory must be formulated as a self-consistent expansion around the mean-field solution of this ordered state A random phase approximation treatment of the theory leads to anisotropic correlation functions for the system It is shown that the calculation of the polymer correlation functions in an ordered phase is equivalent to the calculation of the energy bands and eigenfunctions for an electron in a periodic potential This general method is applied to the lamellar phase of block copolymers The calculated anisotropic scattering intensity captures the main features observed experimentally, including the secondary peaks due to fluctuations with hexagonal symmetry The origin of the anisotropic fluctuations can be traced to the formation o
81 citations
TL;DR: In this article, cubic response functions in the Random Phase Approximation for calculations of non-linear frequency-dependent properties of molecules were derived and implemented for nonlinear frequency dependent properties.
55 citations
TL;DR: The properties of both isoscalar and isovector monopole giant resonance (GR) are found to change drastically in nuclei around the neutron drip line.
Abstract: We study the effect of the unique shell structure as well as the very low particle threshold on collective modes in drip-line nuclei, first performing the Hartree-Fock (HF) calculation with Skyrme interactions and, then, using the random phase approximation solved in the coordinate space with the Green's function method. We examine also one-particle resonant states in the HF potential. The properties of both isoscalar and isovector monopole giant resonance (GR) are found to change drastically in nuclei around the neutron drip line. The characteristic feature of the isovector dipole modes as well as the isoscalar quadrupole modes in drip-line nuclei is also studied. \textcopyright{} 1996 The American Physical Society.
51 citations
TL;DR: In this paper, the authors presented a method which allows to treat correlations in finite Fermi systems in a more consistent way than the random-phase approximation (RPA), where the correlated ground state is always used.
Abstract: We present a method which allows us to treat correlations in finite Fermi systems in a more consistent way than the random-phase approximation (RPA). The quasiboson approximation (QBA), where expectation values in the ground state of the system are approximated by their values in the uncorrelated reference state, is avoided in our approach where the correlated ground state is always used. We derive a closed, nonlinear set of equations which determines the energies and wave functions of the excited states as well as the single-particle occupation numbers in the ground state. As an example we apply to metallic clusters a simplified version of the approach which represents, however, a significant improvement over previous attempts to go towards a self-consistent RPA. We show that our method allows one to correct for the inadequacy of standard RPA in cases where the use of QBA becomes questionable.
49 citations
TL;DR: In this article, the random phase approximation is reformulated to investigate the anisotropic fluctuations about an ordered polymer phase, which is applied to the lamellar phase of block copolymers.
Abstract: The random phase approximation is reformulated to investigate the anisotropic fluctuations about an ordered polymer phase. This very general method is applied to the lamellar phase of block copolymers. The calculated anisotropic scattering intensity captures the main features observed experimentally including the secondary peaks due to fluctuations with hexagonal symmetry. We also determined the limits of metastability of the lamellar phase as well as the bending and elastic moduli of the lamellae.
47 citations
TL;DR: In this article, the Debye function was used for Gaussian polymer coils using the interaction parameter, χ, and statistical segment length, b, as free parameters to estimate critical temperatures.
Abstract: Neutron scattering experiments were performed on three molecular weight pairs of symmetric, isotopic blends of poly(dimethylsiloxane) (PDMS) of near-critical composition. Scattering data covering close to 3 decades in size were globally fit using the random phase approximation (RPA) and the Debye function for Gaussian polymer coils using the interaction parameter, χ, and statistical segment length, b, as free parameters. These wide q range fits differ from the standard, narrow q range RPA fits in that the power-law scaling regime and exponential decay regimes, related to b, are accounted for. Values for χ showed a well-behaved linear dependence on inverse temperature. Critical temperatures were estimated from these data. Direct observations of the miscibility limit, through neutron cloud points, were made in several cases which agree to some extent with the extrapolated critical points. Monotonic dependencies in temperature of the coil expansion factor, α, as calculated from the statistical segment length...
40 citations
TL;DR: In this paper, the two-neutrino mode of double beta decay of is investigated both theoretically and experimentally, using the quasiparticle random phase approximation approach, showing that for the detection of transitions to the two first excited states in the daughter nuclide will be possible in the very near future.
Abstract: The two-neutrino mode of double beta decay of is investigated both theoretically and experimentally. The calculations, using the quasiparticle random phase approximation approach, show that for the detection of transitions to the two first excited states in the daughter nuclide will be possible in the very near future. On the experimental side, new, most stringent limits on half-lives for the double beta decay of to excited states in have been obtained with a `well-type' germanium detector. They range between and years (90% CL).
TL;DR: In this article, a new formulation is given for the random phase approximation (RPA), which is based on the so-called algebraic-diagrammatic construction (ADC) used previously to derive higher-order approximations to the polarization and other propagators.
Abstract: With the aim of obtaining a practical approach to molecular photoionization continua, a new formulation is given for the random phase approximation (RPA). This development is based on the so-called algebraic-diagrammatic construction (ADC) used previously to derive higher-order approximations to the polarization and other propagators. In the ADC reformulation the RPA pseudo-eigenvalue equations split into two equivalent, generally Hermitian, secular problems of half dimension. Here the elements of the resulting ADC secular matrices are given in the form of `regular' perturbation expansions. Similar perturbation expansions result for the `effective' transition amplitudes required to calculate spectral intensities. Approximation schemes converging to the full RPA are obtained by truncating these perturbation expansions at successively higher-order n. For the lowest orders n = 1 and 2 the ADC(n)/RPA schemes are specified explicitly. In addition to the perturbation-theoretical approach, direct closed-form expressions are given for the ADC secular matrix and effective transition amplitudes relating these quantities to the RPA eigenvalues and eigenvectors. As shown by these relations, the ADC reformulation can be viewed as a specific form of quasi-degenerate perturbation theory (QDPT) applied to the RPA pseudo-eigenvalue problem. In the single-channel (SC) approximation the ADC secular equations reduce to a one-electron eigenvalue problem for an energy-independent non-local potential. A particularly useful method is the single-channel ADC(1) scheme combining the scattering solutions of the familiar frozen-core Hartree - Fock (FCHF) model with a simple first-order expression for the transition moments. Illustrative applications of the SC-ADC(1) method to the photoionization in and are reported. These calculations show that ground state correlation can quite substantially influence both the magnitude and the shape of the cross sections as a function of energy.
TL;DR: Both concepts, cluster decomposition and memory, are compared and it is found that they lead to the same quantum virial corrections of Beth-Uhlenbeck type in equilibrium, however, memory in the kinetic equation causes an additional renormalization of the effective energy transfer in nonequilibrium.
Abstract: The stopping power of dense nonideal plasmas is calculated in different approximations. The T-matrix approximation for binary collisions is compared with the random phase approximation for dielectric fluctuations. Within a microscopic model, the dynamical evolution of the velocity of the projectile is calculated. It reproduces well experimental values for the stopping of fast heavy ions. A comparison with molecular dynamical simulation is performed for the friction coefficient. It is found that the T matrix reproduces the simulation result with a charge dependence of ${\ensuremath{\xi}}^{1.4}$, where \ensuremath{\xi}=Z${\mathrm{\ensuremath{\Gamma}}}^{3/2}$. The connection to transport properties like conductivity is presented. In this way we extend former small \ensuremath{\Gamma} expansions to strongly coupled plasmas. Further improvements due to correlations are discussed. Both concepts, cluster decomposition and memory, are compared and it is found that they lead to the same quantum virial corrections of Beth-Uhlenbeck type in equilibrium. However, memory in the kinetic equation causes an additional renormalization of the effective energy transfer in nonequilibrium. \textcopyright{} 1996 The American Physical Society.
TL;DR: In this article, a first-principles calculation to determine the electronic properties of trans-polyacetylene using Hedin's first-order approximation for the self-energy is described.
Abstract: A first-principles calculation to determine the electronic properties of trans-polyacetylene using Hedin's $\mathrm{GW}$ approximation for the self-energy is described. To our knowledge this work is the first application of the $\mathrm{GW}$ method to a quasi-one-dimensional system. The zeroth-order approximation is used to initialize the calculation with the self-energy described by the Hartree-Fock exchange interaction. To include electron exchange and correlation beyond Hartree Fock, the first-order ($\mathrm{GW}$) approximation for the self-energy is adopted. Now the self-energy is energy dependent and is described by the single-particle Green's function ($G$) and the screened Coulomb interaction ($W$). For screening the Coulomb potential the complete wave number and frequency-dependent dielectric response tensor, within the random phase approximation, is employed. The $\mathrm{GW}$ calculation is carried to self-consistency. By implementing the $\mathrm{GWA}$, the Hartree-Fock minimum band gap is reduced by 68% and falls within the experimentally observed range. The optical reflectance and electron-energy-loss function, calculated with local field and lifetime effects, are presented and compared with experiment.
TL;DR: In this article, the dispersion of the Nd spin wave excitations in Nd2CuO4 was analyzed with the help of a random phase approximation model calculation, and the results indicated that the interaction of the nd spins is opposed to the ordering enforced by the exchange.
Abstract: We performed inelastic-neutron-scattering experiments to determine the dispersion of the Nd spin wave excitations in Nd2CuO4. The results were analysed with the help of a random phase approximation model calculation. We were able to find a set of exchange interactions that describes both the observed energies and the intensities of the excitations. Our result indicates that the interaction of the Nd spins is opposed to the ordering enforced by the Nd-Cu exchange. We argue that this will lead to an instability of the Nd ordering in the Ce-doped systems which might be important for the onset of high γ-values.
TL;DR: A random matrix ensemble for bulk type-II superconductors in the mixed state is introduced and the single-particle excitation spectrum is determined using random matrix theory.
Abstract: We introduce a random matrix ensemble for bulk type-II superconductors in the mixed state and determine the single-particle excitation spectrum using random matrix theory. The results are compared with planar tunnel junction experiments in PbBi thin films. More low energy states appear than in the Abrikosov-Gor'kov-Maki or Ginzburg-Landau descriptions, consistent with observations.
TL;DR: In this article, the band-gap renormalization (BGR) in semiconductor quantum wires is studied. And the results for the BGR are compared with the recent experimental measurements and other theoretical calculations.
Abstract: We study the band-gap renormalization (BGR) in semiconductor quantum wires. Assuming an electron - hole system in quasi-equilibrium, we employ the random-phase approximation (RPA) and beyond (e.g., local-field corrections) to calculate the electron and the hole self-energies. The plasmon-pole approximation to the static dielectric function agrees well with the RPA result. Our results for the BGR are compared with the recent experimental measurements and other theoretical calculations.
TL;DR: In this article, a method for calculation of NMR spin-spin coupling constants is implemented at the random phase approximation (RPA) using the semi-empirical AM1 approach with localized molecular orbitals.
TL;DR: The very low-energy transition strength unique in neutron drip line neclei is studied, taking an example of $8}^{28}\mathrm{O}_{20}$ and performing the Hartree-Fock plus RPA calculation with Skyrme interaction.
Abstract: The very low-energy transition strength unique in neutron drip line neclei is studied, taking an example of $_{8}^{28}\mathrm{O}_{20}$ and performing the Hartree-Fock plus RPA calculation with Skyrme interaction. The most dramatic example is monopole modes, however, an appreciable amount of isovector dipole strength may appear also in the very low excitation energy. Unperturbed response functions are carefully studied, which contain all basic information on the exotic behavior of the RPA strength function. The low-energy transition strength is induced by the excitations of neutrons, which have smaller binding energies and smaller angular momenta. The neutrons with a few MeV binding energies are sufficient for obtaining this strength, and the phenomena are differentiated from the so-called soft multipole excitations in halo nuclei.
TL;DR: In this article, the authors present experimental and theoretical results for the broadening of the 0.5 eV charge carrier plasmon in (A = K, Rb) compounds.
Abstract: We present experimental and theoretical results for the broadening of the 0.5 eV charge carrier plasmon in (A = K, Rb) compounds. The experimental width (0.5 eV) is very large and comparable to the plasmon energy. We have performed RPA calculations for a three-band model of orientationally disordered molecules. We show that it is unlikely that the width can be caused by the disorder or by a decay in single electron - hole pair excitations. Instead we have studied the decay in an electron - hole pair dressed by phonon excitations. We have calculated the response function, using Green's functions dressed by the self-energy due to the electron - phonon interaction. Vertex corrections are included to satisfy the Ward identity. We show that this leads to a width of the plasmon which is comparable to its energy, in agreement with experiment.
TL;DR: In this article, the energy spectrum of atoms is constructed by introducing the hopping to atoms in their own harmonic potential, and the pair distribution function is determined by the Ward-Takahashi relations associated with the spatially translational and rotational invariance.
Abstract: Atom and phonon Green functions are determined by the Ward-Takahashi relations associated with the spatially translational and rotational invariance. In the random phase approximation, the energy spectrum of atoms is constructed by introducing the hopping to atoms in their own harmonic potential. Phonon dispersion curves and their width are completely described by two parameters: the eigenfrequency of the harmonic potential of an atom and the magnitude of the hopping energy of atoms, and the pair distribution function. The phonon life time appears when the phonon frequency merges into the continuum of the particle-hole excitation; the particle-hole excitation appears above the band gap of atoms.
TL;DR: In this paper, the effect of ground state correlations into the QRPA equation of motion for the two-neutrino double beta (ββ 2ν) decay is carefully analyzed and the resulting model, called renormalized QRPA (RQRPA), does not collapse near the physical value of the nuclear force strength in the particle-particle channel, as happens with the ordinary QRPA.
TL;DR: In this article, the dielectric function of a spherical two-dimensional electron gas (2DEG) is calculated in the framework of the random phase approximation, along with the electron energy loss function.
TL;DR: In this article, a spin-one Ising model with biquadratic exchange interaction is investigated within a functional integration approach, and the phase diagram is analyzed by means of Landau's free energy expansion.
Abstract: A spin-one Ising model with biquadratic exchange interaction is investigated within a functional integration approach. The phase diagram is analyzed by means of Landau's free energy expansion. The dependence of the features of the system on the ratio of bilinear to biquadratic exchange interaction constants is discussed. In the random phase approximation, expressions for phase transition temperatures and the tricritical point for the ferromagnetic transition are obtained.
TL;DR: In this article, the one-dimensional Fermi gas with attractive δ-delta interaction is treated in the quasiparticle random-phase approximation at zero temperature, and the collective modes are evaluated numerically in the high density (weak-coupling) and in the low density (strongcoupled) case.
Abstract: The one-dimensional Fermi gas with attractive \ensuremath{\delta} interaction is treated in the quasiparticle random-phase approximation at zero temperature. The collective modes are evaluated numerically in the high-density (weak-coupling) and in the low-density (strong-coupling) case. Whereas in the weak-coupling limit the ordinary (particle-hole) random-phase approximation is approached for low momenta, the collective mode in the strong-coupling limit reproduces the Bogoliubov mode for the weakly interacting gas of particle-particle pairs (bosons). We find a smooth evolution of the collective modes from weak to strong coupling. Analytical approximations for the dispersion relation in the long-wavelength limit are derived for both weak and strong coupling. \textcopyright{} 1996 The American Physical Society.
TL;DR: A continuum random phase approximation (RPA) method for evaluating the structure function of nuclear matter is developed, where exchange terms for any particle-hole interaction are explicitly included.
Abstract: A continuum random phase approximation (RPA) method for evaluating the structure function of nuclear matter is developed, where exchange terms for any particle-hole interaction are explicitly included. The method is applied to the inclusive transverse quasielastic electron scattering response at momentum transfer ranging from q=300 to 550 MeV/c. The interaction employed is a ${\mathit{g}}^{\ensuremath{'}}$ Landau-Migdal constant plus a (\ensuremath{\pi}+\ensuremath{\rho})-meson exchange interaction. A comparison with the standard ring series is made showing that the inclusion of finite range effects in the exchange terms is necessary. \textcopyright{} 1996 The American Physical Society.
TL;DR: In this paper, a thermal renormalized random phase approximation (TRRPA) is proposed to study collective excitations in hot nuclei, taking account of a deviation of state occupation numbers from the thermal RPA prescriptions.
Abstract: A method taking account of a deviation of state occupation numbers from the thermal RPA prescriptions is elaborated to study collective excitations in hot nuclei. This thermal renormalized random phase approximation (TRRPA) is from Ken-Ji Hara and D.J. Rowe. In developing the TRRPA, a formalism of the thermofield dynamics (TFD) is used. Some numerical results are given for the SU(2) model.
TL;DR: In this article, the authors analyzed the screened electron-electron interaction in a multi-band electron system with two nonoverlapping bands in the long wavelength limit and showed that the corresponding dielectric matrix reduces to a $2\times2$ form.
Abstract: The screened electron-electron interaction in a multi-band electron system is calculated within the random phase approximation and in the tight-binding representation. The obtained dielectric matrix contains, beside the usual site-site correlations, also the site-bond and bond-bond correlations, and thus includes all physically relevant polarization processes. The arguments are given that the bond contributions are negligible in the long wavelength limit. We analyse the system with two non-overlapping bands in this limit, and show that the corresponding dielectric matrix reduces to a $2\times2$ form. The intra-band and inter-band contributions are represented by diagonal matrix elements, while the off-diagonal elements contain the mixing between them. The latter is absent in insulators but may be finite in conductors. Performing the multipole expansion of the bare long-range interaction, we show that this mixing is directly related to the symmetry of the atomic orbitals participating in the tight-binding electronic states. In systems with forbidden atomic dipolar transitions, the intra-band and inter-band polarizations are separated. However, when the dipolar transitions are allowed, the off-diagonal elements of the dielectric matrix are of the same order as diagonal ones, due to a finite monopole-dipole interaction between the intra-band and inter-band charge fluctuations.
TL;DR: In this article, a graphical derivative technique is introduced to obtain the contributions to the interparticle interactions from different channels, and it is shown that the interaction in the particle-hole channel can induce the metal-insulator phase transition when the Fermi momentum is comparable with the inverse interlayer spacing, leading to the linear temperature dependence of the quasiparticle damping.
Abstract: By means of the Fermi-liquid approach, the effects of exchange and correlations are considered in a layered two-dimensional electron gas. A graphical derivative technique is introduced to obtain the contributions to the interparticle interactions from different channels. It is shown that the interaction in the particle - hole channel can induce the metal - insulator phase transition when the Fermi momentum is comparable with the inverse interlayer spacing, . It is also shown that the Cooper-like scattering processes give rise to the scaling of the Fermi liquid response as Im , which leads to the linear temperature dependence of the quasiparticle damping. The possibility of superconductivity in the region between the insulator and normal metal phases, accounting for the particle - hole excitations, is discussed. The effect of the spin fluctuations on the superconductivity due to the particle - hole excitations is also considered.