Optimal control of strong-field ionization with time-dependent density-functional theory

We show that quantum optimal control theory (OCT) and time-dependent density-functional theory (TDDFT) can be combined to provide realistic femtosecond laser pulses for an enhanced ionization yield in many-electron systems. Using the H$_2$-molecule as a test case, the optimized laser pulse from the numerically exact scheme is compared to pulses obtained from OCT+TDDFT within the TD exact-exchange (TDEXX) and the TD local-density approximation (TDLDA). We find that the TDDFT-pulses produces an ionization yield of up to 50% when applied to the exact system. In comparison, pulses with a single frequency but the same fluence typically reach to yields around 5-15%, unless the frequency is carefully tuned into a Fano-type resonance that leads to $\sim 30$ yield. On the other hand, optimization within the exact system alone leads to yields higher than 80%, demonstrating that correlation effects beyond the TDEXX and TDLDA can give rise to even more efficient ionization mechanisms

Wigner molecules in polygonal quantum dots: A density functional study

We investigate the properties of many-electron systems in two-dimensional polygonal (triangle, square, pentagon, hexagon) potential wells by using the density functional theory. The development of the ground state electronic structure as a function of the dot size is of particular interest. First we show that in the case of two electrons, the Wigner molecule formation agrees with the previous exact diagonalization studies. Then we present in detail how the spin symmetry breaks in polygonal geometries as the spin density functional theory is applied. In several cases with more than two electrons, we find a transition to the crystallized state, yielding coincidence with the number of density maxima and the electron number. We show that this transition density, which agrees reasonably well with previous estimations, is rather insensitive to both the shape of the dot and the electron number.Comment: 8 pages, 11 figure

Quantitative modeling of spin relaxation in quantum dots

We use numerically exact diagonalization to calculate the spin-orbit and phonon-induced triplet-singlet relaxation rate in a two-electron quantum dot exposed to a tilted magnetic field. Our scheme includes a three-dimensional description of the quantum dot, the Rashba and the linear and cubic Dresselhaus spin-orbit coupling, the ellipticity of the quantum dot, and the full angular description of the magnetic field. We are able to find reasonable agreement with the experimental results of Meunier et al. [Phys. Rev. Lett. 98, 126601 (2007)] in terms of the singlet-triplet energy splitting and the spin relaxation rate, respectively. We analyze in detail the effects of the spin-orbit factors, magnetic-field angles, and the dimensionality, and discuss the origins of the remaining deviations from the experimental data

Construction of the B88 exchange-energy functional in two dimensions

We construct a generalized-gradient approximation for the exchange-energy density of finite two-dimensional systems. Guided by non-empirical principles, we include the proper small-gradient limit and the proper tail for the exchange-hole potential. The observed performance is superior to that of the two-dimensional local-density approximation, which underlines the usefulness of the approach in practical applications

The Hubble rate in averaged cosmology

The calculation of the averaged Hubble expansion rate in an averaged perturbed Friedmann-Lemaitre-Robertson-Walker cosmology leads to small corrections to the background value of the expansion rate, which could be important for measuring the Hubble constant from local observations. It also predicts an intrinsic variance associated with the finite scale of any measurement of H_0, the Hubble rate today. Both the mean Hubble rate and its variance depend on both the definition of the Hubble rate and the spatial surface on which the average is performed. We quantitatively study different definitions of the averaged Hubble rate encountered in the literature by consistently calculating the backreaction effect at second order in perturbation theory, and compare the results. We employ for the first time a recently developed gauge-invariant definition of an averaged scalar. We also discuss the variance of the Hubble rate for the different definitions.Comment: 12 pages, 25 figures, references added, clarity improved, frame switching subtlety fixed, results unchanged, v3 minor typos fixe

Light-cone averaging in cosmology: formalism and applications

We present a general gauge invariant formalism for defining cosmological averages that are relevant for observations based on light-like signals. Such averages involve either null hypersurfaces corresponding to a family of past light-cones or compact surfaces given by their intersection with timelike hypersurfaces. Generalized Buchert-Ehlers commutation rules for derivatives of these light-cone averages are given. After introducing some adapted "geodesic light-cone" coordinates, we give explicit expressions for averaging the redshift to luminosity-distance relation and the so-called "redshift drift" in a generic inhomogeneous Universe.Comment: 20 pages, 2 figures. Comments and references added, typos corrected. Version accepted for publication in JCA

A covariant and gauge invariant formulation of the cosmological "backreaction"

Using our recent proposal for defining gauge invariant averages we give a general-covariant formulation of the so-called cosmological "backreaction". Our effective covariant equations allow us to describe in explicitly gauge invariant form the way classical or quantum inhomogeneities affect the average evolution of our Universe.Comment: 12 pages, no figures. Typos corrected, matches version to appear in JCA