Showing papers on "Random phase approximation published in 1992"
TL;DR: A quantitative analysis of carrier-carrier scattering and optical dephasing in semiconductors is presented and results are given for quasiequilibrium situations and for the relaxation of a kinetic hole in a quasithermal carrier distribution.
Abstract: A quantitative analysis of carrier-carrier scattering and optical dephasing in semiconductors is presented and results are given for quasiequilibrium situations and for the relaxation of a kinetic hole in a quasithermal carrier distribution. The calculations involve direct numerical integration of the Boltzmann equation for carrier-carrier scattering in the Born approximation. The screening of the Coulomb interaction is treated consistently in the fully dynamical random-phase approximation. Carrier relaxation rates are extracted from the Boltzmann-equation solution and a quantitative test of the relaxation-time approximation for situations near thermal quasiequilibrium is performed. The parametric dependence of carrier-collision rates and dephasing on plasma density, temperature, and electron and hole masses is discussed and analyzed in terms of phase-space blocking and screening.
154 citations
TL;DR: In this article, it was shown that the frequency dependence of a spherical shape is identical to that of a cubical boundary v = ( 3v F 4 ){1 + ( π 2 6 )( T e F ) 2 } is the average speed of a Fermi gas at temperature T.
141 citations
TL;DR: In this article, a new formalism has been developed to describe nuclear electromagnetic response within the continuum RPA theory, which can be extended in order to calculate cross sections for weak interactions in nuclei, in particular for inelastic neutrino scattering.
76 citations
TL;DR: The theoretical oscillator strength distribution is found to be very different for neutral and charged clusters, and Static polarizabilities of the clusters are calculated and compared with experimental values and with other calculations.
Abstract: Excitation energies and associated oscillator strengths for dipole-excited states of alkali-metal clusters — treated as jellium spheres — are calculated in the random-phase approximation (RPA). Closed-shell systems with 8, 20, 34, 40, 58, and 92 delocalized electrons are considered. The ground state is described in the Hartree-Fock(HF) approximation. The excitation spectrum is determined by solving the RPA equations. Exchange contributions are taken into account completely. The theoretical oscillator strength distribution is found to be very different for neutral and charged clusters. Static polarizabilities of the clusters are calculated and compared with experimental values and with other calculations.
71 citations
TL;DR: In this paper, the self-consistent random phase approximation (RPA) response function of infinite Fermi systems is derived from an effective interaction with velocity and density dependence, or equivalently from a local energy density functional.
62 citations
TL;DR: The band structure, the l-projected densities of states, the complex dielectric function, and the optical reflectivity were obtained in the energy range from 0 to 5 eV.
Abstract: The optical properties of ${\mathrm{CrSi}}_{2}$, both in polycrystalline and single-crystal form, were investigated between 0.01 and 5 eV. The dielectric functions were determined by different methods: Kramers-Kronig transformations of the near-normal reflectivity over the whole spectral range; direct measurement by spectroscopic ellipsometry from 1.4 to 5 eV; numerical inversion of the reflectance from two films with different thickness. The main difference between thin-film and single-crystal data is the presence, in the latter, of a strong free-carrier response, preventing the determination of the intrinsic absorption edge (interband optical gap). Moreover, the optical properties of ${\mathrm{CrSi}}_{2}$ were calculated within the local-density approximation using the semirelativistic linear-muffin-tin-orbital method. The band structure, the l-projected densities of states, the complex dielectric function, and the optical reflectivity were obtained in the energy range from 0 to 5 eV. The theoretical calculations are compared with the experimental data.
62 citations
TL;DR: A multiphonon diagram technique is developed to obtain vibration excitations, that are a mixture of phonons with polaronic plasmons and a critical temperature of the bipolaron formation is found.
Abstract: Dielectric response function of small polarons (SP's) is studied. The Debye radius is small, which reduces a short-range Coulomb repulsion to the magnitude of the order of the small-polaron (SP) bandwidth. Polaron-polaron attraction is enhanced by screening. A critical temperature of the bipolaron formation is found. The dielectric response becomes dynamic in a very low-frequency region. A multiphonon diagram technique is developed to obtain vibration excitations, that are a mixture of phonons with polaronic plasmons
53 citations
TL;DR: It is shown that the simple random-phase approximation provides an exact description for intrasubband plasmon dispersion in one-dimensional quantum wires, by establishing a general equivalence between the RPA and the strongly correlated Tomonaga-Luttinger model for the elementary-excitation spectra inOne-dimensional Fermi systems.
Abstract: We show---contrary to the viewpoint that the random-phase approximation (RPA) is progressively worse in lower dimensions---that the simple random-phase approximation provides an exact description for intrasubband plasmon dispersion in one-dimensional quantum wires, by establishing a general equivalence between the RPA and the strongly correlated Tomonaga-Luttinger model for the elementary-excitation spectra in one-dimensional Fermi systems. We also discuss the formal analogy between intrasubband and intersubband collective modes in quantum wires by showing that the one-dimensional intrasubband collective excitations can also be thought of as depolarization-shifted single-particle excitations. Our results explain why recent experimentally observed one-dimensional-plasmon dispersion in GaAs quantum wires can be quantitatively described by the RPA.
53 citations
TL;DR: The large number of active electrons in a C 60 cluster and the strong Coulomb interaction among them leads to a rich spectrum of collective states that compare very well with photoexcitation and electron-energy-loss-spectroscopy data on gas targets in the high-energy domain.
Abstract: The large number of active electrons in a C 60 cluster and the strong Coulomb interaction among them leads to a rich spectrum of collective states. States with total angular momentum up to L=8h have a strong collective character. The equivalent of both π and σ plasmons in graphite are predicted. In the low-energy region a strong dynamical screening is obtained, in good agreement with measured absorption spectra. The theoretical results compare very well with photoexcitation and electron-energy-loss-spectroscopy data on gas targets in the high-energy domain
34 citations
25 citations
TL;DR: Numerical calculations of the dynamical dielectric function in silicon are reported, using a continued-fraction expansion of the polarizability and a recently proposed representation of the inverse death function in terms of plasmonlike excitations, finding improved agreement with experiment compared to earlier calculations.
Abstract: We report on numerical calculations of the dynamical dielectric function in silicon, using a continued-fraction expansion of the polarizability and a recently proposed representation of the inverse dielectric function in terms of plasmonlike excitations A number of important technical refinements to further improve the computational efficiency of the method are introduced, making the ab initio calculation of the full energy dependence of the dielectric function comparable in cost to calculation of its static value Physical results include the observation of previously unresolved features in the random-phase approximated dielectric function and its inverse within the framework of density-functional theory in the local-density approximation, which may be accessible to experiment We discuss the dispersion of plasmon energies in silicon along the \ensuremath{\Lambda} and \ensuremath{\Delta} directions and find improved agreement with experiment compared to earlier calculations We also present quantitative evidence indicating the degree of violation of the Johnson f-sum rule for the dielectric function due to the nonlocality of the one-electron potential used in the underlying band-structure calculations
TL;DR: By use of a diagrammatic method, the density-density response functions in the random-phase approximation (RPA) and the collective-excitation spectrum for the extended Hubbard model with on-site attraction and arbitrary electron density, in the superconducting ground state are determined.
Abstract: By use of a diagrammatic method we determine the density-density response functions in the random-phase approximation (RPA) and the collective-excitation spectrum for the extended Hubbard model with on-site attraction and arbitrary electron density, in the superconducting ground state. The energy of the collective modes, given by the poles of these response functions, is found to be a linear function of the wave vector (for small k and short-range intersite interaction) with the velocity interpolating smoothly between the weak- (\ensuremath{\propto}2zt, \ensuremath{\Vert}U\ensuremath{\Vert}\ensuremath{\ll}2zt) and strong-coupling (\ensuremath{\propto}${\mathit{zt}}^{2}$/\ensuremath{\Vert}U\ensuremath{\Vert}, \ensuremath{\Vert}U\ensuremath{\Vert}\ensuremath{\gg}2zt) limits. The latter agrees with the results obtained from an effective pseudospin Hamiltonian valid in the strong-coupling limit. The numerical analysis for a two-dimensional (2D) square lattice shows the occurrence of a rotonlike minima near the zone boundary. In the weak-coupling regime we find that apart from a commensurate charge-density-wave (CDW) instability, an increase in the intersite Coulomb repulsion can give rise to a CDW incommensurate with the lattice period, away from half-filling. The resulting phase diagram for the 2D square lattice, including a singlet superconducting ground state, electronic-droplet formation, and CDW's, is determined. Finally, the effects of a long-range Coulomb interaction are analyzed briefly and it is shown that the energy of collective excitations evolves smoothly from the weak- to the strong-coupling limit for a 2D lattice.
TL;DR: A method based on a real-space random-phase approximation to study the phonon spectra of doped and undoped halogen-bridged transition-metal-chain complexes finds that each type of defect has specific signatures in both infrared and Raman spectra, which can help to identify different types of defects experimentally.
Abstract: We have developed a method based on a real-space random-phase approximation (RPA) to study the phonon spectra of doped and undoped halogen-bridged transition-metal-chain complexes. The method is very convenient in cases of spatially inhomogeneous mean-field structures. Thus, we are able to find the usual extended phonon modes as well as local modes associated with polaron, bipolaron, kink, exciton, or impurity structures in intrinsically or extrinsically doped systems. The corresponding infrared absorption spectra and Raman spectra (as a function of the excitation energy) are calculated. We demonstrate the method for a homogeneous charge-density-wave system, and for electron and hole polarons. We find that each type of defect has specific signatures in both infrared and Raman spectra, which can help to identify different types of defects experimentally.
TL;DR: In this article, a new formalism to electronic polarizability of dense, partially ionized plasmas is proposed, based upon the density functional theory for the electronic equilibrium, the random phase approximation for the density response of electrons, and the cluster expansion in the averaging over ionic configurations.
Abstract: We propose a new formalism to electronic polarizability of dense, partially ionized plasmas. This formalism is based upon the density functional theory for the electronic equilibrium, the random phase approximation for the density response of electrons, and the cluster expansion in the averaging over ionic configurations. The first term in the final cluster expansion for the imaginary part of electron polarizability corresponds to the Lindhard dielectric function formula. The second term contains the electronic states of the average atom. The additional effects that result from this theory are: channel mixing (screening), “inverse Bremstrahlung” corrections, and free-bound electronic transitions. Our approach allows the plasma (collective) and atomic physics phenomena to be treated in the frame of one formalism. The theory can be applied for stopping power and opacity calculations.
TL;DR: In this paper, the Coulomb pseudo-potential µ* was shown to be smaller than µ~0.4 in C60 in random phase approximation, where N(0) is the density of states per spin and molecule.
Abstract: We study the screening for C60 in the random phase approximation. For a free molecule we find a substantial reduction of the interaction between close atoms but an “antiscreening” of the interaction between distant atoms. For a C60 solid there is an efficient screening of the intraband Coulomb interaction (U~0.05 eV), leading to µ=UN(0)~0.4, where N(0) is the density of states per spin and molecule. We then study the renormalization of the Coulomb pseudo-potential µ* due to higher subbands in a simple two-band model. We find that the renormalization is small, although a traditional approach, summing ladder diagrams in the screened interaction, predicts a large renormalization. This suggests that µ* may not be much smaller than µ~0.4 in C60. To obtain reasonable transition temperatures, Tc, this value of μ* (~0.4) requires values of the electron-phonon coupling constant λ, which are not very much larger than what has been calculated.
TL;DR: A description of the fractional-statistics gas based on the complete summation of Hartree, Fock, ladder and bubble diagrams is presented, and the superfluid properties identified previously in the random-phase-approximation (RPA) calculation are substantially confirmed.
Abstract: A description of the fractional-statistics gas based on the complete summation of Hartree, Fock, ladder and bubble diagrams is presented. The superfluid properties identified previously in the random-phase-approximation (RPA) calculation are substantially confirmed. The discrepancy between the RPA sound speed and the Hartree-Fock bulk modulus is found to be eliminated. The unusual Hall-effect behavior is found to vanish for the Bose gas test case but not for the fractional-statistics gas, implying that it is physically correct
TL;DR: Strong Coulomb interactions are indicated and imply an inadequacy of linear screening theory, the Born approximation, and the Boltzmann equation for electron-impurity scattering applied to the electron-gas model for doped silicon at low temperature, despite apparently good agreement with experiment.
Abstract: The dielectric function for semidegenerate [ital n]-type silicon is calculated in both the random-phase approximation (RPA) and the Singwi-Tosi-Land-Sjoelander (STLS) approximation in a study of linear screening theory and electron mobility. Using a spherical effective-mass model for the six conduction-band valleys, the Boltzmann equation is solved exactly for phonon plus impurity scattering and the resulting mobility is compared with experiment. Significant differences are found in doped silicon at nonzero temperatures between Boltzmann equation solutions in the RPA Born approximation and the less accurate force-force correlation function formula for the electrical resistivity due to electron-impurity scattering. Phonon scattering has only secondary importance and is treated by standard deformation-potential models. The problem of scattering by linearly screened ionized impurities is treated with exact phase-shift scattering theory. RPA phase-shift calculated electron mobilities in [ital n]-type silicon at 300 and 77 K agree more closely with experiment than the Born approximation or Thomas-Fermi calculations. The local field correction to RPA screening of impurity potentials is not significant in scattering cross sections when the electron-electron vertex function is included. However, assuming full ionization, the STLS dielectric function yields negative electronic compressibilities at 77 K in a concentration region centered approximately where the metal-insulator transition takesmore » place at [ital T]=0, and coinciding with strong violations of the Friedel sum rule by linearly screened potentials. Strong Coulomb interactions are indicated and imply an inadequacy of linear screening theory, the Born approximation, and the Boltzmann equation for electron-impurity scattering applied to the electron-gas model for doped silicon at low temperature, despite apparently good agreement with experiment.« less
TL;DR: Momentum transfer between two quasi-one-dimensional electron gases, mediated by the Coulomb interaction, is considered in the presence of a magnetic field normal to the plane of the gases and exhibits Shubnikov\char21{}de Haas oscillations.
Abstract: Momentum transfer between two quasi-one-dimensional electron gases, mediated by the Coulomb interaction, is considered in the presence of a magnetic field normal to the plane of the gases. The lateral confinement is assumed to be parabolic. Impurity scattering (screened) and electron-electron interaction are treated self-consistently within the random-phase approximation. The current response is evaluated from the derived momentum-balance equations, which involve the nonequilibrium electron polarizability, in conjunction with a drifted-temperature model for the polarizability. An applied current driven through either of the gases, whose centers are separated by a distance a, induces a contactless current in the other gas about ${10}^{5}$ times smaller and in direct analogy with the zero-magnetic-field observations of Solomon et al. Both the applied and the induced current exhibit Shubnikov\char21{}de Haas oscillations. The applied current increases slightly with a and saturates at a finite value. In contrast, the induced current decreases approximately as ${\mathit{a}}^{\mathrm{\ensuremath{-}}2}$ for a much larger than the wire width.
TL;DR: In this paper, a charge-density-wave instability for electrons in quasi-one-dimensional structures due to Coulomb interaction effects is discussed. And the effect of a finite local field correction on the stability of double-quantum-wire structures is discussed, and it is shown that for a fixed wire distance and wire radius the energy of the ω− plasmon vanishes if the particle density is smaller than a critical value.
Abstract: We discuss a charge-density-wave instability for electrons in quasi-one-dimensional structures due to Coulomb interaction effects. The two plasmon modes (ω+, ω−) of a double-quantum-wire structure are studied. The effect of a finite local-field correction is discussed. For small wavenumbers, it is shown that for a fixed wire distance and wire radius the energy of the ω− plasmon vanishes if the particle density is smaller than a critical value. The disappearance of the ω− mode corresponds to a singularity in the static susceptibility of the system.
TL;DR: In this article, a graph representation of the electron-magnon and electron-electron interactions in the Hubbard model with infinite on-site Coulomb interaction U is obtained for a wide range of electron concentration n. All of them are expressed through the unique system of four-point and three-point vertex parts.
Abstract: On the basis of a regular perturbation theory in the form of diagrammatic technique with X-operators, a ferromagnetic state in the Hubbard model with infinite on-site Coulomb interaction U is studied for a wide range of electron concentration n. Treating the kinetic energy of electrons as perturbation, we get the exact graphic representations for three Green’s functions and for electrons with spin ↑ and ↓ (spontaneous magnetic moment is in ↑ direction) and for spin waves. All of them are expressed through the unique system of four-point and three-point vertex parts for effective electron-magnon and electron-electron interactions. These vertex parts are calculated in two approximations: a low-density approximation for n≪1 or nh=1–n≫1, and the generalized random-phase approximation (GRPA), which was suggested earlier by us for the description of paramagnetic phase in this model. An important result in both cases is the understanding of essential difference of electron states with spin ↑ and ↓. The state for ↑ has coherent character in all region of electron concentration (n>nc) where a ferromagnetic state exists, while the state for spin ↓ has mixed characters including both coherent and incoherent contribution. For the saturated ferromagnetism (n>ns) when nh≪1, is an entirely incoherent (nonquasiparticle) state. Appearance of incoherent state is probably a general property of strongly correlated systems distinguishing its behavior from the Fermi liquid. We show also that the Hubbard-I approximation has no region of applicability for the electron with spin ↓ in a ferromagnet and we found a new factor describing the correlation-narrowing of ↓ spin electron band. Green’s function calculated in two different limits n≪1 and nh≪1, are jointed together to allow us to calculate ns which lies in the intermediate concentration regime. For simple cubic lattice we found ns=0.87. In the limit nh≪1 our results reduce to the earlier known ones, including Nagaoka’s result for the spin wave energy. We point out the way to construct a rigorous theory for ferromagnetic state in the intermediate range of electron concentration. In the conclusion several important problems are discussed in connection to the continuation of the present work.
TL;DR: In this article, the RPA correlations for small, closed shell Na clusters up to Na 92 and compare it with the correlations described by energy-density functionals in the local-density approximation.
TL;DR: In this article, the authors derived the polarization tensor for a system of charged spin-one bosons and antibosons in the case of no external magnetic field using the self-consistent random-phase approximation (RP A) method.
Abstract: We derive the polarization tensor for a system of charged spin-one bosons and antibosons in the case of no external magnetic field. This requires a thorough exposition of relativistic spin-one quantum mechanics, and thus we initially focus upon the Sakata-Taketani equation and its free-field solutions. We employ these results to evaluate the matrix elements required for the calculation of the polarization tensor, which itself is derived via the self-consistent random-phase approximation (RP A) method. It is from this tensor that we obtain the longitudinal and transverse dielectric response functions for this plasma. We evaluate these response functions at zero temperature, and exhibit the characteristic modes of oscillation. Finally, we discuss possible generalizations of this work, in particular to a finite-temperature plasma, and to one with an external magnetic field. In this paper, we present a study of the relativistic spin-one particle-antiparticle plasma, in the presence of no external magnetic field. The course of the investigation begins with a review of single particle theories of spin-one (vector) bosons, which we present in § 2 of this work. In § 3 of the paper, we present a detailed treatment of the six-component formalism for spin-one bosons, first developed by Sakata and Taketani/) which we then employ in our linear response theory calculations for the plasma. To our knowledge, this particular formalism is under-represented in the literature pertinent to spin-one bosons, and hence our exposition is an attempt to clarify its general features, and underscore its particular utility in work of the nature we have undertaken. The latter part of the paper (§§ 4 and 5) contains the linear response calculations proper. We set about deriving the polarization four-tensor, employing a method first· proposed by Harris,z) this being the self-consistent random-phase approximation (RPA) method. We then obtain the characteristic modes of oscillation of the plasma. At present, we concern ourselves solely with the plasma properties of the polari zation tensor, leaving a complete study of the vacuum modes of oscillation and their renormalization to a later paper, in which we also propose to introduce the presence of an external magnetic field. Employing our plane-wave solutions of the Sakata Taketani equation for the case of no external fields, we proceed to calculate the longitudinal and transverse dielectric response functions, which are obtained via the employment of the relationship between the covariant polarization four-tensor and the dielectric three-tensor. In the case of the longitudinal response function, we present the formal result which is valid for all temperatures, and we then evaluate the longitudinal and transverse response functions at zero temperature, from which we obtain the modes of oscillation. Our work follows on from that of Kowalenko, Frankel and Hines (KFH),3) who studied the spin-zero pair plasma by employing a self-consistent field method to find
TL;DR: In this paper, single beta decay transitions in 114-120 Pd are calculated in the framework of the quasiparticle random phase approximation (QRPA) and the effective two-body interaction is constructed from the Bonn one-boson exchange potential (OBEP).
TL;DR: In this paper, a theory of many-body phenomena in a strongly coupled electron-phonon system is developed, taking into account the polaron collapse of the electron band and the instability of the phonon vacuum.
Abstract: A new theory of many-body phenomena in a strongly coupled electron-phonon system is developed, taking into account the polaron collapse of the electron band and the instability of the phonon vacuum. A “λ −1 ” expansion and multi-phonon diagram technique are developed to obtain the dielectric response function and new vibrational excitations. Static and dynamic responses show unusual temperature, q and ω dependences. Phonons mix with polaronic plasmons thus forming new excitations - “plas-phons”. A microscopic model of the anomalous extra modes, observed in neutron scattering experiments in metal oxides is proposed. The relevance of the polaron theory of high- T c superconductivity to high- T c oxides is discussed in view of some recent experimental results. The charged Bose-liquid ground state (small bipolarons) is claimed to be relevant to describe some normal and superconducting state properties of metal oxides.
TL;DR: In this article, the Tamm-Dancoff method was applied to a hydrogen fluoride chain to calculate the exciton energies in the random-phase approximation for polymers with helical symmetry.
Abstract: Ab initio Hartree–Fock crystal orbital results were used as input for the calculation of exciton energies in the Tamm–Dancoff and random-phase approximation for polymers with helical symmetry. The calculations were applied to a hydrogen fluoride chain. We show that the Tamm–Dancoff method is a good approximation to the random-phase theory. Furthermore, the influence of the band–band interaction in the exciton calculation has been investigated.
TL;DR: In this paper, the evolution of the optical absorption spectra of alkali microclusters as a function of the total charge was studied using the random phase approximation upon a jellium background, while treating the Coulomb force in the local density approximation.
TL;DR: In this article, the authors investigate multipole excitations of an electron gas constrained to a spherical surface and explore the size dependence of the energy, the energy loss intensity and the character of each excitation mode.
TL;DR: It is shown that for very large particle numbers, the static-path approximation is an excellent approximation, while for small particleNumbers, the random-phase-approximation corrections should be taken into account, especially for particle numbers small enough to cause the normal- to superconducting-phase transition.
Abstract: The fluctuations properties of the BCS Hamiltonian which are induced in finite systems are explored. It is shown that for very large particle numbers, the static-path approximation is an excellent approximation, while for small particle numbers, the random-phase-approximation corrections should be taken into account, especially for particle numbers small enough to cause the normal- to superconducting-phase transition. A correlated mean field containing quantal fluctuations is introduced and compared with the Hartree-Bogoliubov mean field.
TL;DR: In this article, the generalized random-phase approximation (GRPA) is formulated as an approximation taking into account electron loop-type diagrams, and both the dynamic magnetic and dielectric susceptibilities are calculated for a wide interval of electron concentrations, 0
Abstract: The Hubbard model in the limit of strong Coulomb interaction (the (t-J) model) is studied by the diagram technique for Hubbard operators. The generalized random-phase approximation (GRPA) is formulated as an approximation taking into account electron loop-type diagrams. Within the framework of this approximation, both the dynamic magnetic and dielectric susceptibilities are calculated for a wide interval of electron concentrations, 0
TL;DR: Within the random-phase approximation (RPA), the average surface-plasmon energy of voids and bubbles in nearly-free-electron metals is obtained using energy-weighted moments of the electronic response to operators of type r -(L+1) Y L0.
Abstract: Within the random-phase approximation (RPA), we have obtained the average surface-plasmon energy of voids and bubbles in nearly-free-electron metals using energy-weighted moments of the electronic response to operators of type r -(L+1) Y L0 . We have used a local-density approximation of Slater and Wigner type for the exchange and correlation energies, respectively, and the jellium model for the positive ionic background. Compact expressions for the plasmon average energies are given, which allow one to discuss clearly the role played by the kinetic- and Coulomb energy contributions to the restoring force of the L modes