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1.
The renormalization of the relativistic self-consistent Hartree-Fock approximation is restudied. It is shown that the renormalization
procedure suggested by Bielajew and Serot can be greatly simplified and the renormalization achieved in a way no more complicated
than that of the relativistic self-consistent Fock approximation, if the parameters in the counterterms are allowed to be
density-dependent and the renormalization of the tadpole self-energy is treated appropriately. A transformation relation between
the four- and three-dimensional representation of the baryon self-energy is presented and a self-consistent Hartree-Fock scheme
different from that considered by Bielajew and Serot studied. The renormalized integral equations for the baryon self-energy
which includes effects from the Dirac sea are reformulated in a three-dimensional form. Explicit expressions are derived.
Received: 29 August 1997 / Revised version: 30 April 1998 相似文献
2.
Luc Lathouwers 《Annals of Physics》1976,102(2):347-370
The generator coordinate method for bound states is reformulated using the classical Fredholm theory of linear integral equations. A natural state formalism is developed to investigate the properties of the variational Hill-Wheeler equations. A generator coordinate representation of the one-dimensional harmonic oscillator is worked out analytically. 相似文献
3.
A.B. Utkin R. Vilar A.J. Smirnov 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2001,17(2):145-148
The consideration is carried out in its general formulation: the wave aberration function is represented in terms of classical
aberrations (the Zernike polynomials), the phase transfer function (argument of the complex optical transfer function) is
defined by a chain of transformations originating from the generalized pupil function. Quasi-analytical quadrature formulas
are derived that link the optical transfer function and the phase transfer function with the aberration terms. It is shown
that the phase transfer function contains information on the odd-order aberrations, which can be retrieved from coefficients
to the Taylor expansion of the derived quadrature relation.
Received 16 June 2001 相似文献
4.
Y. Duan H. Zhang 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》1999,5(1):47-51
We find that there exists an elementary topological current in Bose-Einstein condensation. Based on the -mapping topological current theory, the implicit function theorem and the Taylor expansion, the topological structure of
vortex lines is detailed in the neighborhoods of the bifurcation points of the condensate wave function.
Received: 9 April 1998 / Revised: 28 August 1998 / Accepted: 31 August 1998 相似文献
5.
A parameterized effective potential for molecules is developed in which the Coulomb and exchange parts of the Hartree-Fock potential are expressed in terms of the electron-nucleus interaction potential. Within the framework of the single-determinant approximation, equations for determining the parameters of the effective potential and of the finite basis set are obtained. In contrast to the equations of the Hartree-Fock method, the solution procedure for the equations for the parameterized effective potential does not require self-matching of the orbital expansion coefficients in terms of the basis set functions. Using the calculation of the ground state energy of diatomic hydrides as an example, the dependence of the effective potential parameters on the number of particles in the system is analyzed in detail. Based on this analysis, a simple two-parameter model is proposed. The results of calculations in terms of this model deviate from those obtained by the precision Hartree-Fock method by 0.02–0.06%. 相似文献
6.
M. Groß F. Spiegelmann 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》1998,4(2):219-224
We present a pseudopotential method to study the absorption spectroscopy of NO in an argon matrix modeled by a large albeit
finite cluster. The excited states of NO are described with the virtual orbitals of a NO+ Hartree-Fock calculation plus a core-polarization operator to account for the electron-NO+ correlation. The argon atoms of the matrix are replaced by pseudopotentials for the repulsive contributions and core-polarization
operators to account for matrix polarization and correlation with the excited electron. The model is shown to account for
the matrix-induced transition shifts and also for the cut-off of the Rydberg series for n >3 reported in absorption experiments from the ground state.
Received: 6 March 1998 / Revised: 1st June 1998 / Accepted: 16 June 1998 相似文献
7.
8.
We have formulated the Hartree-Fock equations for multielectron systems with two open shells (the Huzinaga method) in terms
of the density matrix in the LCAO approximation. In order to solve the Hartree-Fock equations, in the algebraic approximation
we have obtained expressions for the derivatives of the energy with respect to the density matrix elements and the nonlinear
atomic orbital parameters (the orbital exponents). We discuss the question of calculating the open shell parameters (the vector
coupling coefficients) in the configurations s1pN and s1dN within the Huzinaga method. We have calculated the energy for a series of atoms with two open shells in these configurations.
Using rather narrow basis sets of Slater-type atomic orbitals), we have obtained energy values close to the results of a numerical
solution of the Hartree-Fock equations with sufficiently high accuracy of the virial ratio.
__________
Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 2, pp. 145–152, March–April, 2007 相似文献
9.
H. Keiter M. Rosenberg 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,5(3):599-603
The scale of relaxation times in glasses has led to generalizations of the Drude model of the dielectric function in terms
of an integral, containing a Drude kernel and a probability distribution. This integral equation is solved by a Mellin or
a Stieltjes transform. Beyond known results, we obtain the probability distribution of the Havriliak-Negami dielectric function.
Even more general classes of dielectric models can be dealt with, using Mellin's transform. They may serve as checks for numerical
procedures applied to the underlying ill-posed problem, if experimental data for the dielectric function are used.
Received: 2 February 1998 / Accepted: 17 March 1998 相似文献
10.
M. Sellitto 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,4(2):135-138
We investigate by Monte-Carlo simulation the linear response function of three dimensional structural glass models defined
by short-range kinetic constraints and a trivial equilibrium Boltzmann-Gibbs measure. The breakdown of the fluctuation-dissipation
theorem in the glassy phase follows the prediction of mean field low temperature mode-coupling theory.
Received: 24 April 1998 / Received in final form: 8 May 1998 / Accepted: 11 May 1998 相似文献
11.
12.
13.
P. Grangier J.-P. Poizat 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》1999,7(1):99-105
By generalizing recently obtained results we calculate the excess noise factor (Petermann factor) for a laser system with
non-orthogonal eigenmodes. The quantum consistency of the calculation is shown through the explicit conservation of input-output
commutation rules. As a result of the calculation, the excess noise in the lasing mode is shown to depend on the laser gain
below threshold, and on the noise analysis frequency below and above threshold.
Received: 27 October 1998 / Received in final form: 11 March 1999 相似文献
14.
The generator coordinate method (GCM) wave function is used as a trial function in a Kohn type variational principle for scattering phase shifts. It is shown that a GCM trial function is a solution of the variational equations if the Hill-Wheeler integral equation is satisfied subject to an appropriate boundary condition. A new method for introducing the scattering boundary condition is presented. There is a uniqueness theorem for the phase shift. 相似文献
15.
Fangzong Wang Xiaobing Liao & Xiong Xie 《advances in applied mathematics and mechanics.》2016,8(1):128-144
The differential quadrature method has been widely used in scientific and
engineering computation. However, for the basic characteristics of time domain differential
quadrature method, such as numerical stability and calculation accuracy or
order, it is still lack of systematic analysis conclusions. In this paper, according to the
principle of differential quadrature method, it has been derived and proved that the
weighting coefficients matrix of differential quadrature method meets the importantV-transformation feature. Through the equivalence of the differential quadrature
method and the implicit Runge-Kutta method, it has been proved that the differential
quadrature method is A-stable and $s$-stage $s$-order method. On this basis, in order
to further improve the accuracy of the time domain differential quadrature method,
a class of improved differential quadrature method of $s$-stage $2s$-order has been proposed
by using undetermined coefficients method and Padéapproximations. The numerical results show that the proposed differential quadrature method is more precise
than the traditional differential quadrature method. 相似文献
16.
17.
We present and discuss various Hartree-Fock iteration techniques which are all derived from the simple gradient iteration step where one proceeds along the slope of steepest descent of the energy functional. Particular attention is paid to modern numerical applications where the single-particle wave functions are represented in a coordinate or momentum space grid. A quantitative, comparison is given using a one-dimensional model space. As an example the optimum method thus found is applied in a realistic three-dimensional calculation of 16O. 相似文献
18.
F. Calvo P. Labastie 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》1998,3(3):229-236
A new scheme for estimating densities of states at non zero angular momentum is proposed, using the Monte-Carlo (MC) and multiple
histogram methods. It is based on a rigorous expression of the classical density of states for a rotating system. Two features
appear: the centrifugal energy ( angular momentum and I the instantaneous inertia tensor in the center of mass reference frame) is added to the potential
energy and the configurational densities of states is weighted by . Comparing the MC results for the 13-atom Lennard-Jones cluster and a calculation based on molecular dynamics (MD) shows
that this weight is important if the rotation induces a structural change at a finite temperature. The MC algorithm proves
to be much more efficient than MD, even at finite .
Received: 27 January 1998 / Received in final form: 15 June 1998 / Accepted: 18 June 1998 相似文献
19.
J.E. Amaro M.B. Barbaro J.A. Caballero T.W. Donnelly A. Molinari 《The European Physical Journal A - Hadrons and Nuclei》2002,15(4):421-427
The impact of Hartree-Fock correlations on the nuclear momentum distribution is studied in a fully relativistic one-boson-exchange
model. Hartree-Fock equations are exactly solved to first order in the coupling constants. The renormalization of the Dirac
spinors in the medium is shown to affect the momentum distribution, as opposed to what happens in the non-relativistic case.
The unitarity of the model is shown to be preserved by the present renormalization procedure.
Received: 7 June 2002 / Accepted: 24 September 2002 / Published online: 10 December 2002
RID="a"
ID="a"e-mail: juan@nucle.us.es
Communicated by G. Orlandini 相似文献
20.
V. Meden W. Metzner U. Schollwöck O. Schneider T. Stauber K. Schönhammer 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,16(4):631-646
We present a study of the one-particle spectral properties for a variety of models of Luttinger liquids with open boundaries.
We first consider the Tomonaga-Luttinger model using bosonization. For weak interactions the boundary exponent of the power-law
suppression of the spectral weight close to the chemical potential is dominated by a term linear in the interaction. This
motivates us to study the spectral properties also within the Hartree-Fock approximation. It already gives power-law behavior
and qualitative agreement with the exact spectral function. For the lattice model of spinless fermions and the Hubbard model
we present numerically exact results obtained using the density-matrix renormalization-group algorithm. We show that many
aspects of the behavior of the spectral function close to the boundary can again be understood within the Hartree-Fock approximation.
For the repulsive Hubbard model with interaction U the spectral weight is enhanced in a large energy range around the chemical potential. At smaller energies a power-law suppression,
as predicted by bosonization, sets in. We present an analytical discussion of the crossover and show that for small U it occurs at energies exponentially (in -1/U) close to the chemical potential, i.e. that bosonization only holds on exponentially small energy scales. We show that such a crossover can also be found in other
models.
Received 8 February 2000 and Received in final form 25 April 2000 相似文献