Showing papers on "Thomas–Fermi model published in 1999"
156 citations
95 citations
TL;DR: A density functional theory for the distribution of charged hard spheres (model for salt) around an infinite, rigid, and impenetrable charged cylinder was proposed in this article. But the theory is based on a weighted density approach where the hard-sphere contribution to the one-particle correlation function is evaluated nonperturbatively using a position dependent effective density, and the ionic part is obtained through a second-order functional Taylor expansion around a uniform fluid.
Abstract: A density functional theory is presented for the distribution of charged hard spheres (model for salt) around an infinite, rigid, and impenetrable charged cylinder (model for DNA or tobacco mosaic virus). The theory is based on a weighted density approach where the hard-sphere contribution to the one-particle correlation function is evaluated nonperturbatively using a position dependent effective density, and the ionic part is obtained through a second-order functional Taylor expansion around a uniform fluid. The theory is in good agreement with Monte Carlo simulations for the density distribution of monovalent, divalent, and mixed salts. For axial charge densities corresponding to DNA, the hypernetted chain integral equation theory is not as accurate as the density functional theory, but both liquid state approaches are superior to the Poisson−Boltzmann theory. For higher axial charge densities the density functional theory predicts interesting charge inversion effects that are absent in the nonlinear Po...
78 citations
TL;DR: In this paper, the phase space similarities between the uniformly mixed ensembles of eigenstates, and the quasiclassical Thomas-Fermi distribution, are exploited in order to generate a nearly optimal basis representation for an arbitrary quantum system.
Abstract: The quantitative phase space similarities between the uniformly mixed ensembles of eigenstates, and the quasiclassical Thomas–Fermi distribution, are exploited in order to generate a nearly optimal basis representation for an arbitrary quantum system. An exact quantum optimization functional is provided, and the minimum of the corresponding quasiclassical functional is proposed as an excellent approximation in the limit of large basis size. In particular, we derive a stationarity condition for the quasiclassical solution under the constraint of strong separability. The corresponding quantum result is the phase space optimized direct-product basis—customized with respect to the Hamiltonian itself, as well as the maximum energy of interest. For numerical implementations, an iterative, self-consistent-field-like algorithm based on optimal separable basis theory is suggested, typically requiring only a few reduced-dimensional integrals of the potential. Results are obtained for a coupled oscillator system, an...
75 citations
TL;DR: In this paper, the virial theorem for the exchange-correlation potential is shown to hold for time-dependent electronic systems and is illustrated by an exactly solved model: Hooke's atom with a timedependent force constant.
Abstract: The time dependence of the exchange-correlation energy in density functional theory is given in terms of the exchange-correlation potential. The virial theorem for the exchange-correlation potential is shown to hold for time-dependent electronic systems and is illustrated by an exactly solved model: Hooke’s atom with a time-dependent force constant. A relation between the coupling constant and functionals evaluated on scaled densities is derived. [S0031-9007(98)08169-1]
73 citations
TL;DR: In this paper, a new definition of the exchange-correlation charge is presented, which is related to the exchange correlation potential of density functional theory by the Poisson equation and can be evaluated numerically, thus providing direct input for the ongoing process of finding improved approximate density functionals.
Abstract: A new definition of the exchange-correlation charge is presented. This charge is related to the exchange-correlation potential of density functional theory by the Poisson equation. It is illustrated how, using the Zhao–Morrison–Parr method, this new exchange-correlation charge can be evaluated numerically, thus providing direct input for the ongoing process of finding improved approximate density functionals. Several properties of this new charge, including the sum rule and Coulombic-like behavior, are derived. Both atomic shell and subshell structures are observed. Exchange-correlation charges generated from various approximate functionals are calculated and compared with numerically accurate data for a few atoms.
45 citations
TL;DR: An analysis of the Colle-Salvetti (CS) wave function functional of the density as applied to the He atom shows: (i) it is not normalized; (ii) the corresponding Coulomb hole structure is inaccurate; (iii) the Coulombhole sum rule is violated; (iv) the ion correlation component of the Kohn-Sham (KS) correlation potential is erroneous; (v) the KS correlation potential was erroneous; and as mentioned in this paper.
Abstract: An analysis of the Colle-Salvetti (CS) wave-function functional of the density as applied to the He atom shows: (i) it is not normalized; (ii) the corresponding Coulomb hole structure is inaccurate; (iii) the Coulomb hole sum rule is violated; (iv) the Coulomb component of the Kohn-Sham (KS) correlation potential is inaccurate; (v) the KS correlation potential is erroneous; (vi) the Coulomb correlation and correlation--kinetic-energy components of the KS correlation energy are in error. Thus, the description by this wave function of the physics of electron correlation is inaccurate. As such the results obtained via the CS wave function and those based on it are not well founded.
42 citations
TL;DR: In this paper, a self-gravitating massive fermion system is studied in the framework of the general-relativisticThomas-Fermi model and the properties of the free energy functional and its relation to Einstein's Fleld equations are investigated.
Abstract: A system of self-gravitating massive fermions isstudied in the framework of the general-relativisticThomas-Fermi model. We study the properties of the freeenergy functional and its relation to Einstein's fleld equations. We then describe aself-gravitating fermion gas by a set of Thomas-Fermitype self-consistency equations.
38 citations
TL;DR: In this article, a simple weighted density functional approach is developed for inhomogeneous ionic fluids and applied to the structure of the electric double layer using the restricted primitive model where the ions are considered to be charged hard spheres of equal diameter.
Abstract: A simple weighted density functional approach is developed for inhomogeneous ionic fluids and applied to the structure of the electric double layer using the restricted primitive model where the ions are considered to be charged hard spheres of equal diameter. The formalism is nonperturbative with both hard-sphere and electrical contributions to the one-particle correlation function evaluated through a suitably averaged weighted density, the only input being the second-order direct correlation functions of the corresponding uniform system. The approach is designed in such a way, that the calculation of the weight function is decoupled from the weighted density. Numerical results on the ionic density profile and the mean electrostatic potential near a hard wall at several surface charge densities are shown to compare well with available simulation results. The corresponding results for the nonprimitive molecular solvent model provide insight into the layering effect and the charge inversion phenomena.
33 citations
TL;DR: In this article, a density functional theory within the generalized gradient approximation was used to predict ferromagnetism on the Fermi surface of the Sr2RuO4.
Abstract: Ab initio electronic structure calculations on Sr2RuO4, based on density functional theory within the generalized gradient approximation are reported. Contrary to calculations within the local density approximation, ferromagnetism is predicted. The results could have consequences for the interpretation of experiments which probe the Fermi surface and for the understanding of the unconventional superconductivity in Sr2RuO4.
27 citations
TL;DR: In this article, the effects of the photon field for the model are discussed under the Thomas-Fermi approximation, and possible other mechanisms and other systems for the photo-induced superconductivity are also examined theoretically.
Abstract: Expressions of the transition temperature for various anomalous phases are first derived in the framework of the two-band model for copper oxides. The effects of the photon field for the model are discussed under the Thomas–Fermi approximation. Possible other mechanisms and other systems for the photo-induced superconductivity are also examined theoretically. We also point out the possibilities of the photo-induced superconductivity in a Little model. Possible model systems of the tunable superconductivity by external fields are proposed as an example of dynamic controls of electronic, magnetic, and optical properties of materials. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75, 549–561, 1999
TL;DR: In this paper, the authors proposed an electron density in atoms and ions, which has the Thomas-Fermi-Dirac form in the intermediate region of r, satisfies the Kato condition for small r, and has the correct asymptotic behavior at large values of r where r is the distance from the nucleus.
TL;DR: In this article, the properties of warm symmetric and asymmetric nuclear matter are investigated in the frame of the Thomas-Fermi approximation using a recent modern parametrization of the effective nucleon-nucleon � ×
Abstract: The properties of warm symmetric and asymmetric nuclear matter are investigated in the frame of the Thomas-Fermi approximation using a recent modern parametrization of the effective nucleon-nucleon � ×
TL;DR: In this paper, a one-dimensional time-dependent Thomas-Fermi model of atoms, molecules, and small clusters exposed to an intense sub-picosecond laser field is developed.
Abstract: We have developed a one-dimensional time-dependent Thomas-Fermi model of atoms, molecules, and small clusters exposed to an intense subpicosecond laser field. In this model, the dynamics of an electronic cloud is governed by the hydrodynamic equations of motion, whereas the nuclei move in accordance with the Newton equations. The quantum mechanics enters in this approach only through the constitutive relation between the pressure and the density, which is derived from the application of Fermi-Dirac statistics to a noninteracting $T=0$ temperature electron gas. The time-independent version of the model, formulated in terms of the integral equation for the electric potential, is also discussed. We present numerical results for diatomic molecules and small clusters irradiated by the strong laser pulses. In the case of molecules, we observe the multielectron ionization accompanied by dissociation. The kinetic energy defect, understood as a reduction of the energy of resulting ions in comparison with a simple Coulomb explosion picture, is explained in terms of a screening effect of escaping fragments by the ejected electrons. For small clusters we find that the explosion of the cluster has a stepwise character; the consecutive layers of atoms are stripped off one by one. We observe the highly energetic (as compared with diatomic systems) atomic fragments even for relatively low laser intensities and a few atoms clusters. Also, the model predicts the nonuniform energy distribution among the same charge state ions and supports the idea of hot electrons generated in the cluster via a mechanism of inverse bremsstrahlung.
TL;DR: In this paper, a common link can be found between finite temperature mean field theory and the statistical fragmentation model and the latter naturally arises in the spinodal region, and although the exact statistical model is a canonical model and uses temperature, microcanonical results which use constant energy rather than constant temperature can also be obtained from the canonical model using saddle point approximation.
Abstract: We deal with two different aspects of an exactly soluble statistical model of fragmentation. First we show, using zero range force and finite temperature Thomas-Fermi theory, that a common link can be found between finite temperature mean field theory and the statistical fragmentation model. We show the latter naturally arises in the spinodal region. Next we show that although the exact statistical model is a canonical model and uses temperature, microcanonical results which use constant energy rather than constant temperature can also be obtained from the canonical model using saddle-point approximation. The methodology is extremely simple to implement and at least in all the examples studied in this work is very accurate.
TL;DR: In the mean field approximation, a trapped Bose-Einstein condensate at zero temperature is described by the Gross-Pitaevskii equation for the condensates or, equivalently, by the hydrodynamic equations for the number density and current density.
Abstract: In the mean-field approximation, a trapped Bose-Einstein condensate at zero temperature is described by the Gross-Pitaevskii equation for the condensate or, equivalently, by the hydrodynamic equations for the number density and current density. These equations receive corrections from quantum field fluctuations around the mean field. We calculate the semiclassical corrections to these equations for a general time-independent state of the condensate, extending previous work to include vortex states as well as the ground state. In the Thomas-Fermi limit, the semiclassical corrections can be taken into account by adding a local correction term to the Gross-Pitaevskii equation. At second order in the Thomas-Fermi expansion, the semiclassical corrections can be taken into account by adding local correction terms to the hydrodynamic equations. [copyright] [ital 1999] [ital The American Physical Society]
TL;DR: In this article, a two-dimensional model of gauged fermions with quartic couplings in the large-N$ limit is analyzed. But the coupling constants of both theories are arbitrary.
Abstract: We analyze a two-dimensional model of gauged fermions with quartic couplings in the large-$N$ limit. This combines the 't Hooft model and the Gross-Neveu model where the coupling constants of both theories are arbitrary. Analytic equations describing the meson states of the theory are derived and are solved systematically using various methods. The physics of the model is investigated.
TL;DR: In this paper, the Hartree-Fock potential is added to the diagonal elements of the Hamiltonian matrix to calculate the electronic spectrum of Si δ-doped quantum wells in GaAs taking into account exchange and correlation effects.
Abstract: We express the exchange and correlation potential analytically in terms of the Hartree potential in the Thomas-Fermi approximation. This result permits the inclusion of the exchange and correlation effects in a semi-empirical tight binding model considering the Hartree-Fock potential as an external one. We simply add this potential to the diagonal elements of the Hamiltonian matrix. As an example, we calculate the electronic spectrum of Si δ-doped quantum wells in GaAs taking into account the exchange and correlation effects. Our results agree quite well with the self-consistent calculations published previously and with the experimental results available for this system.
TL;DR: In this article, the equilibrium properties of coupled quantum-dot structures are studied in the semi-classical two-dimensional Thomas-Fermi approximation and the results of the self-consistent numerical solution of this equation are obtained.
Abstract: The equilibrium properties of coupled quantum-dot structures are studied in the semi-classical two-dimensional Thomas-Fermi approximation. We show that the simple analytical procedure for the solution of the relevant Thomas-Fermi equation based on the well known parabolic ansatz reproduces accurately the results of the self-consistent numerical solution of this equation. In this way we calculate the electronic configurations inherent in such structures both numerically and analytically. In particular, we demonstrate the possibility of electrostatic tuning of the many-electron dot until it is completely erased due to the interaction with the neighbouring dot. We use our analytical results also for calculations of the charging energy and tunnelling integral, i.e. the parameters which are relevant for nanodevices containing arrays of quantum-dot cells.
TL;DR: In this article, a differential equation relating an unknown, but local, function of ground-state electron density ρ, say S(ρ), is shown to have an analytical solution in terms of ρ(r) for spherically symmetric systems.
Abstract: A differential equation relating an unknown, but local, function of ground-state electron density ρ, say S(ρ), is shown first to have an analytical solution for S(r) in terms of ρ(r) for spherically symmetric systems. For closed shell atoms Kr and Xe, S(r) and S(ρ) over the density range 0<ρ<ρ(r = 0) are plotted and examined. S(r) has a roughly monotonically decreasing behaviour with small additional features reflecting electronic shell structure. the general shape of S(ρ) is also found to be the same for these atoms, use of which is made to present an approach to the non-relativisitic limit of large numbers of electrons via these closed shell atoms. Relaxing spherical symmetry, it is proposed that the resulting partial differential equation should be powerful enough to describe the ground-state electron density in neutral homonuclear molecules and clusters for large number of electrons.
TL;DR: In this paper, the eigenmode spectrum for collective multipole vibrations of the electrons of alkali clusters including coupling between surface and volume plasmons was calculated starting from the hydrodynamic approximation.
Abstract: We calculate the eigenmode spectrum for collective multipole vibrations of the electrons of alkali clusters including coupling between surface and volume plasmons. We formulate the equations of motion for the collective variables (density and velocity potential) starting from the hydrodynamic approximation. We investigate the effect of the diffusibility of the valence electrons on their collective modes, considering an equilibrium density of the valence electrons with a smooth surface profile. This effect was not considered in previous work carried out by the first author, who assumed the equilibrium density of the valence electrons to be a constant that has the bulk value. The results indicate that, within the hydrodynamic model, surface spill-out effects lead to a tendency for a red-shift from the Mie frequency and a mixing of resonance modes when the size of the cluster decreases. The eigenmodes fulfil the linear energy-weighted sum rule, the inverse energy-weighted sum rule and orthogonality relations.
TL;DR: In this article, a Thomas-Fermi model of a spherical shell of positive charge is investigated under various boundary conditions, and the electron distribution and the ionization charge are given particular attention.
Abstract: A Thomas-Fermi model of a spherical shell of positive charge is investigated, under various boundary conditions. The electron distribution and the ionization charge are given particular attention.
TL;DR: The Schwinger quantum correction to the classic Thomas-Fermi atom was directly derived by solving for the latter without recourse to a modeling after the harmonicoscillator potential and without solving for particle density as discussed by the authors.
Abstract: The Schwinger quantum correction to the classicThomas-Fermi atom is directly derived by solving for thelatter without recourse to a modeling after the harmonicoscillator potential and without solving for theparticle density.
TL;DR: In this paper, a self-gravitating fermion gas is described by a set of Thomas-Fermi type self-consistency equations, and the properties of the free energy functional and its relation to Einstein's field equations are studied.
Abstract: A system of self-gravitating massive fermions is studied in the framework of the general-relativistic Thomas-Fermi model. We study the properties of the free energy functional and its relation to Einstein's field equations. A self-gravitating fermion gas we then describe by a set of Thomas-Fermi type self-consistency equations.