1,425 research outputs found
Cosmological acceleration from structure formation
We discuss the Buchert equations, which describe the average expansion of an
inhomogeneous dust universe. In the limit of small perturbations, they reduce
to the Friedmann-Robertson-Walker equations. However, when the universe is very
inhomogeneous, the behaviour can be qualitatively different from the FRW case.
In particular, the average expansion rate can accelerate even though the local
expansion rate decelerates everywhere. We clarify the physical meaning of this
paradoxical feature with a simple toy model, and demonstrate how acceleration
is intimately connected with gravitational collapse. This provides a link to
structure formation, which in turn has a preferred time around the era when
acceleration has been observed to start.Comment: 6 pages, awarded honorable mention in the 2006 Gravity Research
Foundation essay competitio
THE EFFECT OF THE STRAIN RATE ON THE SHORT TERM SHEAR RESPONSE OF ARTICULAR CARTILAGE
The shear stress relaxation of cylindrical, osteochondra1 plugs was measured by means of ramp displacements at strain rates ranging approximately from 0.06 s-1 to 13 S-1. The plugs were prepared from patellar grooves of fresh bovine femora. For each specimen separately, the data was fitted t o a five-parameter quasi- linear viscoelastic model. The different loading rates were pooled together to obtain a solution that would conform as well as possible to all time-dependent force functions measured with a particular specimen. This method makes it possible to analyze stress functions caused by arbitrary strain histories. From strain rate 10 3-1 to rate 0.1 s-1 the shear modulus dropped in average by a factor of 1 . 5 2 and the relaxation was roughly logarithmic. At rate 10 s-1, the average ,shear modulus was 4 . 8 5 MPa. All the moduli were assessed a t a fixed, 4% strain to avoid errors due to nonlinearity of the material. The measured stresses were well within human physiological limits, and the strain rates used in the experiment correspond to the time-scale of human knee joint loading during walking or running
Local correlation functional for electrons in two dimensions
We derive a local approximation for the correlation energy in two-dimensional
electronic systems. In the derivation we follow the scheme originally developed
by Colle and Salvetti for three dimensions, and consider a Gaussian
approximation for the pair density. Then, we introduce an ad-hoc modification
which better accounts for both the long-range correlation, and the
kinetic-energy contribution to the correlation energy. The resulting functional
is local, and depends parametrically on the number of electrons in the system.
We apply this functional to the homogeneous electron gas and to a set of
two-dimensional quantum dots covering a wide range of electron densities and
thus various amounts of correlation. In all test cases we find an excellent
agreement between our results and the exact correlation energies. Our
correlation functional has a form that is simple and straightforward to
implement, but broadly outperforms the commonly used local-density
approximation
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
Optimal Control of Quantum Rings by Terahertz Laser Pulses
Complete control of single-electron states in a two-dimensional semiconductor
quantum-ring model is established, opening a path into coherent laser-driven
single-gate qubits. The control scheme is developed in the framework of optimal
control theory for laser pulses of two-component polarization. In terms of
pulse lengths and target-state occupations, the scheme is shown to be superior
to conventional control methods that exploit Rabi oscillations generated by
uniform circularly polarized pulses. Current-carrying states in a quantum ring
can be used to manipulate a two-level subsystem at the ring center. Combining
our results, we propose a realistic approach to construct a laser-driven
single-gate qubit that has switching times in the terahertz regime.Comment: Phys. Rev. Lett. (in print) (2007
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
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
Relativistic cosmological perturbation scheme on a general background: scalar perturbations for irrotational dust
In standard perturbation approaches and N-body simulations, inhomogeneities
are described to evolve on a predefined background cosmology, commonly taken as
the homogeneous-isotropic solutions of Einstein's field equations
(Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmologies). In order to make
physical sense, this background cosmology must provide a reasonable description
of the effective, i.e. spatially averaged, evolution of structure
inhomogeneities also in the nonlinear regime. Guided by the insights that (i)
the average over an inhomogeneous distribution of matter and geometry is in
general not given by a homogeneous solution of general relativity, and that
(ii) the class of FLRW cosmologies is not only locally but also globally
gravitationally unstable in relevant cases, we here develop a perturbation
approach that describes the evolution of inhomogeneities on a general
background being defined by the spatially averaged evolution equations. This
physical background interacts with the formation of structures. We derive and
discuss the resulting perturbation scheme for the matter model `irrotational
dust' in the Lagrangian picture, restricting our attention to scalar
perturbations.Comment: 18 pages. Matches published version in CQ
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.
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