1,087 research outputs found
Interaction-Induced Spin Polarization in Quantum Dots
The electronic states of lateral many electron quantum dots in high magnetic
fields are analyzed in terms of energy and spin. In a regime with two Landau
levels in the dot, several Coulomb blockade peaks are measured. A zig-zag
pattern is found as it is known from the Fock-Darwin spectrum. However, only
data from Landau level 0 show the typical spin-induced bimodality, whereas
features from Landau level 1 cannot be explained with the Fock-Darwin picture.
Instead, by including the interaction effects within spin-density-functional
theory a good agreement between experiment and theory is obtained. The absence
of bimodality on Landau level 1 is found to be due to strong spin polarization.Comment: 4 pages, 5 figure
Rectangular quantum dots in high magnetic fields
We use density-functional methods to study the effects of an external
magnetic field on two-dimensional quantum dots with a rectangular hard-wall
confining potential. The increasing magnetic field leads to spin polarization
and formation of a highly inhomogeneous maximum-density droplet at the
predicted magnetic field strength. At higher fields, we find an oscillating
behavior in the electron density and in the magnetization of the dot. We
identify a rich variety of phenomena behind the periodicity and analyze the
complicated many-electron dynamics, which is shown to be highly dependent on
the shape of the quantum dot.Comment: 6 pages, 6 figures, submitted to Phys. Rev.
BACK-REACTION IN RELATIVISTIC COSMOLOGY
We introduce the concept of back-reaction in relativistic cosmological modeling. Roughly speaking, this can be thought of as the difference between the large-scale behavior of an inhomogeneous cosmological solution of Einstein’s equations, and a homogeneous and isotropic solution that is a best-fit to either the average of observables or dynamics in the inhomogeneous solution. This is sometimes paraphrased as “the effect that structure has of the large-scale evolution of the universe.” Various different approaches have been taken in the literature in order to try and understand back-reaction in cosmology. We provide a brief and critical summary of some of them, highlighting recent progress that has been made in each case
Geometric and impurity effects on quantum rings in magnetic fields
We investigate the effects of impurities and changing ring geometry on the
energetics of quantum rings under different magnetic field strengths. We show
that as the magnetic field and/or the electron number are/is increased, both
the quasiperiodic Aharonov-Bohm oscillations and various magnetic phases become
insensitive to whether the ring is circular or square in shape. This is in
qualitative agreement with experiments. However, we also find that the
Aharonov-Bohm oscillation can be greatly phase-shifted by only a few impurities
and can be completely obliterated by a high level of impurity density. In the
many-electron calculations we use a recently developed fourth-order imaginary
time projection algorithm that can exactly compute the density matrix of a
free-electron in a uniform magnetic field.Comment: 8 pages, 7 figures, to appear in PR
The Spatial Averaging Limit of Covariant Macroscopic Gravity - Scalar Corrections to the Cosmological Equations
It is known that any explicit averaging scheme of the type essential for
describing the large scale behaviour of the Universe, must necessarily yield
corrections to the Einstein equations applied in the Cosmological setting. The
question of whether or not the resulting corrections to the Einstein equations
are significant, is still a subject of debate, partly due to possible
ambiguities in the averaging schemes available. In particular, it has been
argued in the literature that the effects of averaging could be gauge
artifacts. We apply the formalism of Zalaletdinov's Macroscopic Gravity (MG)
which is a fully covariant and nonperturbative averaging scheme, in an attempt
to construct gauge independent corrections to the standard
Friedmann-Lemaitre-Robertson-Walker (FLRW) equations. We find that whereas one
cannot escape the problem of dependence on \emph{one} gauge choice -- which is
inherent in the assumption of large scale homogeneity and isotropy -- it is
however possible to construct \emph{spacetime scalar} corrections to the
standard FLRW equations. This partially addresses the criticism concerning the
corrections being gauge artifacts. For a particular initial choice of gauge
which simplifies the formalism, we explicitly construct these scalars in terms
of the underlying inhomogeneous geometry, and incidentally demonstrate that the
formal structure of the corrections with this gauge choice is identical to that
of analogous corrections derived by Buchert in the context of spatial averaging
of scalars.Comment: 18 pages, no figures, revtex4; v2 - minor clarifications added; v3 -
minor changes in presentation to improve clarity, reference added, to appear
in Phys. Rev.
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
Scale dependence of cosmological backreaction
Due to the non-commutation of spatial averaging and temporal evolution,
inhomogeneities and anisotropies (cosmic structures) influence the evolution of
the averaged Universe via the cosmological backreaction mechanism. We study the
backreaction effect as a function of averaging scale in a perturbative approach
up to higher orders. We calculate the hierarchy of the critical scales, at
which 10% effects show up from averaging at different orders. The dominant
contribution comes from the averaged spatial curvature, observable up to scales
of 200 Mpc. The cosmic variance of the local Hubble rate is 10% (5%) for
spherical regions of radius 40 (60) Mpc. We compare our result to the one from
Newtonian cosmology and Hubble Space Telescope Key Project data.Comment: 6 pages, 2 figures; v3: substantial modifications, new figure
On the relation between the isotropy of the CMB and the geometry of the universe
The near-isotropy of the cosmic microwave background (CMB) is considered to
be the strongest indication for the homogeneity and isotropy of the universe, a
cornerstone of most cosmological analysis. We derive new theorems which extend
the Ehlers-Geren-Sachs result that an isotropic CMB implies that the universe
is either stationary or homogeneous and isotropic, and its generalisation to
the almost isotropic case. We discuss why the theorems do not apply to the real
universe, and why the CMB observations do not imply that the universe would be
nearly homogeneous and isotropic.Comment: 5 pages. v2: Corrected an error in the proof, added references and
clarification
Broken Symmetry in Density-Functional Theory: Analysis and Cure
We present a detailed analysis of the broken-symmetry mean-field solutions
using a four-electron rectangular quantum dot as a model system. Comparisons of
the density-functional theory predictions with the exact ones show that the
symmetry breaking results from the single-configuration wave function used in
the mean-field approach. As a general cure we present a scheme that
systematically incorporates several configurations into the density-functional
theory and restores the symmetry. This cure is easily applicable to any
density-functional approach.Comment: 4 pages, 4 figures, submitted to PR
On the violation of a local form of the Lieb-Oxford bound
In the framework of density-functional theory, several popular density
functionals for exchange and correlation have been constructed to satisfy a
local form of the Lieb-Oxford bound. In its original global expression, the
bound represents a rigorous lower limit for the indirect Coulomb interaction
energy. Here we employ exact-exchange calculations for the G2 test set to show
that the local form of the bound is violated in an extensive range of both the
dimensionless gradient and the average electron density. Hence, the results
demonstrate the severity in the usage of the local form of the bound in
functional development. On the other hand, our results suggest alternative ways
to construct accurate density functionals for the exchange energy.Comment: (Submitted on 27 April 2012
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