7,545 research outputs found
Fluctuating parts of nuclear ground state correlation energies
Background: Heavy atomic nuclei are often described using the
Hartree-Fock-Bogoliubov (HFB) method. In principle, this approach takes into
account Pauli effects and pairing correlations while other correlation effects
are mimicked through the use of effective density-dependent interactions.
Purpose: Investigate the influence of higher order correlation effects on
nuclear binding energies using Skyrme's effective interaction.
Methods: A cut-off in relative momenta is introduced in order to remove
ultraviolet divergences caused by the zero-range character of the interaction.
Corrections to binding energies are then calculated using the
quasiparticle-random-phase approximation (QRPA) and second order many-body
perturbation theory (MBPT2).
Result: Contributions to the correlation energies are evaluated for several
isotopic chains and an attempt is made to disentangle which parts give rise to
fluctuations that may be difficult to incorporate on the HFB level. The
dependence of the results on the cut-off is also investigated.
Conclusions: The improved interaction allows explicit summations of
perturbation series which is useful for the description of some nuclear
observables. However, refits of the interaction parameters are needed to obtain
more quantitative results
Current and vorticity auto correlation functions in open microwave billiards
Using the equivalence between the quantum-mechanical probability density in a
quantum billiard and the Poynting vector in the corresponding microwave system,
current distributions were studied in a quantum dot like cavity, as well as in
a Robnik billiard with lambda=0.4, and an introduced ferrite cylinder. Spatial
auto correlation functions for currents and vorticity were studied and compared
with predictions from the random-superposition-of-plane-waves hypothesis. In
addition different types of vortex neighbour spacing distributions were
determined and compared with theory.Comment: PTP-LaTeX, 10 pages with 6 figures submitted to Progress of
Theoretical Physics Supplemen
Calculations of Hubbard U from first-principles
The Hubbard \emph{U} of the \emph{3d} transition metal series as well as
SrVO, YTiO, Ce and Gd has been estimated using a recently proposed
scheme based on the random-phase approximation. The values obtained are
generally in good accord with the values often used in model calculations but
for some cases the estimated values are somewhat smaller than those used in the
literature. We have also calculated the frequency-dependent \emph{U} for some
of the materials. The strong frequency dependence of \emph{U} in some of the
cases considered in this paper suggests that the static value of \emph{U} may
not be the most appropriate one to use in model calculations. We have also made
comparison with the constrained LDA method and found some discrepancies in a
number of cases. We emphasize that our scheme and the constrained LDA method
theoretically ought to give similar results and the discrepancies may be
attributed to technical difficulties in performing calculations based on
currently implemented constrained LDA schemes.Comment: 24 pages, 13 figures; Submitted to Phys. Rev.
The correlation potential in density functional theory at the GW-level: spherical atoms
As part of a project to obtain better optical response functions for nano
materials and other systems with strong excitonic effects we here calculate the
exchange-correlation (XC) potential of density-functional theory (DFT) at a
level of approximation which corresponds to the dynamically- screened-exchange
or GW approximation. In this process we have designed a new numerical method
based on cubic splines which appears to be superior to other techniques
previously applied to the "inverse engineering problem" of DFT, i.e., the
problem of finding an XC potential from a known particle density. The
potentials we obtain do not suffer from unphysical ripple and have, to within a
reasonable accuracy, the correct asymptotic tails outside localized systems.
The XC potential is an important ingredient in finding the particle-conserving
excitation energies in atoms and molecules and our potentials perform better in
this regard as compared to the LDA potential, potentials from GGA:s, and a DFT
potential based on MP2 theory.Comment: 13 pages, 9 figure
A simple, efficient, and general treatment of the singularities in Hartree-Fock and exact-exchange Kohn-Sham methods for solids
We present a general scheme for treating the integrable singular terms within
exact exchange (EXX) Kohn-Sham or Hartree-Fock (HF) methods for periodic
solids. We show that the singularity corrections for treating these
divergencies depend only on the total number and the positions of k-points and
on the lattice vectors, in particular the unit cell volume, but not on the
particular positions of atoms within the unit cell. The method proposed here to
treat the singularities constitutes a stable, simple to implement, and general
scheme that can be applied to systems with arbitrary lattice parameters within
either the EXX Kohn-Sham or the HF formalism. We apply the singularity
correction to a typical symmetric structure, diamond, and to a more general
structure, trans-polyacetylene. We consider the effect of the singularity
corrections on volume optimisations and k-point convergence. While the
singularity corrections clearly depends on the total number of k-points, it
exhibits a remarkably small dependence upon the choice of the specific
arrangement of the k-points.Comment: 24 pages, 5 Figures, re-submitted to Phys. Rev. B after revision
Electric field response of strongly correlated one-dimensional metals: a Bethe-Ansatz density functional theory study
We present a theoretical study on the response properties to an external
electric field of strongly correlated one-dimensional metals. Our investigation
is based on the recently developed Bethe-Ansatz local density approximation
(BALDA) to the density functional theory formulation of the Hubbard model. This
is capable of describing both Luttinger liquid and Mott-insulator correlations.
The BALDA calculated values for the static linear polarizability are compared
with those obtained by numerically accurate methods, such as exact (Lanczos)
diagonalization and the density matrix renormalization group, over a broad
range of parameters. In general BALDA linear polarizabilities are in good
agreement with the exact results. The response of the exact exchange and
correlation potential is found to point in the same direction of the perturbing
potential. This is well reproduced by the BALDA approach, although the fine
details depend on the specific parameterization for the local approximation.
Finally we provide a numerical proof for the non-locality of the exact exchange
and correlation functional.Comment: 8 pages and 8 figure
GW band structure of InAs and GaAs in the wurtzite phase
We report the first quasiparticle calculations of the newly observed wurtzite
polymorph of InAs and GaAs. The calculations are performed in the GW
approximation using plane waves and pseudopotentials. For comparison we also
report the study of the zinc-blende phase within the same approximations. In
the InAs compound the In 4d electrons play a very important role: whether they
are frozen in the core or not, leads either to a correct or a wrong band
ordering (negative gap) within the Local Density Appproximation (LDA). We have
calculated the GW band structure in both cases. In the first approach, we have
estimated the correction to the pd repulsion calculated within the LDA and
included this effect in the calculation of the GW corrections to the LDA
spectrum. In the second case, we circumvent the negative gap problem by first
using the screened exchange approximation and then calculating the GW
corrections starting from the so obtained eigenvalues and eigenfunctions. This
approach leads to a more realistic band-structure and was also used for GaAs.
For both InAs and GaAs in the wurtzite phase we predict an increase of the
quasiparticle gap with respect to the zinc-blende polytype.Comment: 9 pages, 6 figures, 3 table
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