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

Can superhorizon perturbations drive the acceleration of the Universe?

It has recently been suggested that the acceleration of the Universe can be explained as the backreaction effect of superhorizon perturbations using second order perturbation theory. If this mechanism is correct, it should also apply to a hypothetical, gedanken universe in which the subhorizon perturbations are absent. In such a gedanken universe it is possible to compute the deceleration parameter $q_0$ measured by comoving observers using local covariant Taylor expansions rather than using second order perturbation theory. The result indicates that second order corrections to $q_0$ are present, but shows that if $q_0$ is negative then its magnitude is constrained to be less than or of the order of the square of the peculiar velocity on Hubble scales today. We argue that since this quantity is constrained by observations to be small compared to unity, superhorizon perturbations cannot be responsible for the acceleration of the Universe.Comment: revtex, 4 pages, no figures; final published versio

Exchange and correlation energy functionals for two-dimensional open-shell systems

We consider density functionals for exchange and correlation energies in two-dimensional systems. The functionals are constructed by making use of exact constraints for the angular averages of the corresponding exchange and correlation holes, respectively, and assuming proportionality between their characteristic sizes. The electron current and spin are explicitly taken into account, so that the resulting functionals are suitable to deal with systems exhibiting orbital currents and/or spin polarization. Our numerical results show that in finite systems the proposed functionals outperform the standard two-dimensional local spin-density approximation, still performing well also in the important limit of the homogeneous two-dimensional electron gas

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

On the lower bound on the exchange-correlation energy in two dimensions

We study the properties of the lower bound on the exchange-correlation energy in two dimensions. First we review the derivation of the bound and show how it can be written in a simple density-functional form. This form allows an explicit determination of the prefactor of the bound and testing its tightness. Next we focus on finite two-dimensional systems and examine how their distance from the bound depends on the system geometry. The results for the high-density limit suggest that a finite system that comes as close as possible to the ultimate bound on the exchange-correlation energy has circular geometry and a weak confining potential with a negative curvature

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

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

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