1,542 research outputs found
Performance of one-body reduced density matrix functionals for the homogeneous electron gas
The subject of this study is the exchange-correlation-energy functional of
reduced density matrix functional theory. Approximations of this functional are
tested by applying them to the homogeneous electron gas. We find that two
approximations recently proposed by Gritsenko, Pernal, and Baerends, J. Chem.
Phys., {\bf 122}, 204102 (2005), yield considerably better correlation energies
and momentum distributions than previously known functionals. We introduce
modifications to these functionals which, by construction, reproduce the exact
correlation energy of the homogeneous electron gas
Discontinuity of the chemical potential in reduced-density-matrix-functional theory
We present a novel method for calculating the fundamental gap. To this end,
reduced-density-matrix-functional theory is generalized to fractional particle
number. For each fixed particle number, , the total energy is minimized with
respect to the natural orbitals and their occupation numbers. This leads to a
function, , whose derivative with respect to the particle
number has a discontinuity identical to the gap. In contrast to density
functional theory, the energy minimum is generally not a stationary point of
the total-energy functional. Numerical results, presented for alkali atoms, the
LiH molecule, the periodic one-dimensional LiH chain, and solid Ne, are in
excellent agreement with CI calculations and/or experimental data.Comment: 9 pages, 3 figures, version as publishe
Open shells in reduced-density-matrix-functional theory
Reduced-density-matrix-functional theory is applied to open-shell systems. We
introduce a spin-restricted formulation by appropriately expressing approximate
correlation-energy functionals in terms of spin-dependent occupation numbers
and spin-independent natural orbitals. We demonstrate that the additional
constraint of total-spin conservation is indispensable for the proper treatment
of open-shell systems. The formalism is applied to the first-row open-shell
atoms. The obtained ground-state energies are in very good agreement with the
exact values as well as other state of the art quantum chemistry calculationsComment: 4 pages, 2 figures, corrected typo
Exchange-energy functionals for finite two-dimensional systems
Implicit and explicit density functionals for the exchange energy in finite
two-dimensional systems are developed following the approach of Becke and
Roussel [Phys. Rev. A 39, 3761 (1989)]. Excellent agreement for the
exchange-hole potentials and exchange energies is found when compared with the
exact-exchange reference data for the two-dimensional uniform electron gas and
few-electron quantum dots, respectively. Thereby, this work significantly
improves the availability of approximate density functionals for dealing with
electrons in quasi-two-dimensional structures, which have various applications
in semiconductor nanotechnology.Comment: 5 pages, 3 figure
Optimized Effective Potential Method in Current-Spin Density Functional Theory
Current-spin density functional theory (CSDFT) provides a framework to
describe interacting many-electron systems in a magnetic field which couples to
both spin- and orbital-degrees of freedom. Unlike in usual (spin-) density
functional theory, approximations to the exchange-correlation energy based on
the model of the uniform electron gas face problems in practical applications.
In this work, explicitly orbital-dependent functionals are used and a
generalization of the Optimized Effective Potential (OEP) method to the CSDFT
framework is presented. A simplifying approximation to the resulting integral
equations for the exchange-correlation potentials is suggested. A detailed
analysis of these equations is carried out for the case of open-shell atoms and
numerical results are given using the exact-exchange energy functional. For
zero external magnetic field, a small systematic lowering of the total energy
for current-carrying states is observed due to the inclusion of the current in
the Kohn-Sham scheme. For states without current, CSDFT results coincide with
those of spin density functional theory.Comment: 11 pages, 3 figure
Exchange-correlation orbital functionals in current-density-functional theory: Application to a quantum dot in magnetic fields
The description of interacting many-electron systems in external magnetic
fields is considered in the framework of the optimized effective potential
method extended to current-spin-density functional theory. As a case study, a
two-dimensional quantum dot in external magnetic fields is investigated.
Excellent agreement with quantum Monte Carlo results is obtained when
self-interaction corrected correlation energies from the standard local
spin-density approximation are added to exact-exchange results. Full
self-consistency within the complete current-spin-density-functional framework
is found to be of minor importance.Comment: 5 pages, 2 figures, submitted to PR
Constraining Dark Matter with the Long-Term Variability of Quasars
By comparing the results of numerical microlensing simulations to the
observed long-term variability of quasars, strong upper limits on the
cosmological density of compact objects in the mass range 0.01 to 0.0001 solar
masses may be imposed. Using recently developed methods to better approximate
the amplification of large sources, we investigate in what way the constraints
are affected by assumptions concerning the size of the optical
continuum-emitting region of quasars in the currently favored (Omega_M=0.3,
Omega_Lambda=0.7) cosmology.Comment: 3 pages, 2 figures, to appear in the proceedings from the conference
"Lighthouses of the Universe: The Most Luminous Celestial Objects and Their
Use for Cosmology", Garching, August 2001 (Springer-Verlag
Gravitational lensing statistics with extragalactic surveys. II. Analysis of the Jodrell Bank-VLA Astrometric Survey
We present constraints on the cosmological constant from
gravitational lensing statistics of the Jodrell Bank-VLA Astrometric Survey
(JVAS). Although this is the largest gravitational lens survey which has been
analysed, cosmological constraints are only comparable to those from optical
surveys. This is due to the fact that the median source redshifts of JVAS are
lower, which leads to both relatively fewer lenses in the survey and a weaker
dependence on the cosmological parameters. Although more approximations have to
be made than is the case for optical surveys, the consistency of the results
with those from optical gravitational lens surveys and other cosmological tests
indicate that this is not a major source of uncertainty in the results.
However, joint constraints from a combination of radio and optical data are
much tighter. Thus, a similar analysis of the much larger Cosmic Lens All-Sky
Survey should provide even tighter constraints on the cosmological constant,
especially when combined with data from optical lens surveys.
At 95% confidence, our lower and upper limits on ,
using the JVAS lensing statistics information alone, are respectively -2.69 and
0.68. For a flat universe, these correspond to lower and upper limits on
\lambda_{0} of respectively -0.85 and 0.84. Using the combination of JVAS
lensing statistics and lensing statistics from the literature as discussed in
Quast & Helbig (Paper I) the corresponding values are
-1.78 and 0.27. For a flat universe, these correspond to lower and upper limits
on of respectively -0.39 and 0.64.Comment: LaTeX, 9 pages, 18 PostScript files in 6 figures. Paper version
available on request. Data available from
http://gladia.astro.rug.nl:8000/ceres/data_from_papers/papers.htm
Lensing galaxies: light or dark?
In a recent paper, Hawkins (1997) argues on the basis of statistical studies
of double-image gravitational lenses and lens candidates that a large
population of dark lenses exists and that these outnumber galaxies with more
normal mass-to-light ratios by a factor of 3:1. If correct, this is a very
important result for many areas of astronomy including galaxy formation and
cosmology. In this paper we discuss our new radio-selected gravitational lens
sample, JVAS/CLASS, in order to test and constrain this proposition. We have
obtained ground-based and HST images of all multiple-image lens systems in our
sample and in 12 cases out of 12 we find the lensing galaxies in the optical
and/or near infrared. Our success in finding lensing galaxies creates problems
for the dark lens hypothesis. If it is to survive, ad hoc modifications seem to
be necessary: only very massive galaxies (more than about one trillion solar
masses) can be dark, and the cutoff in mass must be sharp. Our finding of lens
galaxies in all the JVAS/CLASS systems is complementary evidence which supports
the conclusion of Kochanek et al. (1997) that many of the wide-separation
optically-selected pairs are physically distinct quasars rather than
gravitational lens systems.Comment: 4 pages, 2 included figures, accepted for publication in Astronomy
and Astrophysics. Paper version available on request. This replacement amends
the text to allow more discussion of the overlap with astro-ph/971016
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