1,641 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
Gaussian approximations for the exchange-energy functional of current-carrying states: Applications to two-dimensional systems
Electronic structure calculations are routinely carried out within the
framework of density-functional theory, often with great success. For electrons
in reduced dimensions, however, there is still a need for better approximations
to the exchange-correlation energy functional. Furthermore, the need for
properly describing current-carrying states represents an additional challenge
for the development of approximate functionals. In order to make progress along
these directions, we show that simple and efficient expressions for the
exchange energy can be obtained by considering the short-range behavior of the
one-body spin-density matrix. Applications to several two-dimensional systems
confirm the excellent performance of the derived approximations, and verify the
gauge-invariance requirement to be of great importance for dealing with
current-carrying states
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
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
Effective inhomogeneous inflation: curvature inhomogeneities of the Einstein vacuum
We consider spatially averaged inhomogeneous universe models and argue that,
already in the absence of sources, an effective scalar field arises through
foliating and spatially averaging inhomogeneous geometrical curvature
invariants of the Einstein vacuum. This scalar field (the `morphon') acts as an
inflaton, if we prescribe a potential of some generic form. We show that, for
any initially negative average spatial curvature, the morphon is driven through
an inflationary phase and leads - on average - to a spatially flat, homogeneous
and isotropic universe model, providing initial conditions for pre-heating and,
by the same mechanism, a possibly natural self-exit.Comment: 9 pages, 2 figures, to appear in Class. Quant. Grav. as Fast Track
Communicatio
- …