Beyond time-dependent exact-exchange: the need for long-range correlation

In the description of the interaction between electrons beyond the classical Hartree picture, bare exchange often yields a leading contribution. Here we discuss its effect on optical spectra of solids, comparing three different frameworks: time-dependent Hartree-Fock, a recently introduced combined density-functional and Green's functions approach applied to the bare exchange self-energy, and time-dependent exact-exchange within time-dependent density-functional theory (TD-EXX). We show that these three approximations give rise to identical excitonic effects in solids; these effects are drastically overestimated for semiconductors. They are partially compensated by the usual overestimation of the quasiparticle band gap within Hartree-Fock. The physics that lacks in these approaches can be formulated as screening. We show that the introduction of screening in TD-EXX indeed leads to a formulation that is equivalent to previously proposed functionals derived from Many-Body Perturbation Theory. It can be simulated by reducing the long-range part of the Coulomb interaction: this produces absorption spectra of semiconductors in good agreement with experiment.Comment: 12 pages, 3 figures, 1 tabl

Approximating the coefficients in semilinear stochastic partial differential equations

We investigate, in the setting of UMD Banach spaces E, the continuous dependence on the data A, F, G and X_0 of mild solutions of semilinear stochastic evolution equations with multiplicative noise of the form dX(t) = [AX(t) + F(t,X(t))]dt + G(t,X(t))dW_H(t), X(0)=X_0, where W_H is a cylindrical Brownian motion on a Hilbert space H. We prove continuous dependence of the compensated solutions X(t)-e^{tA}X_0 in the norms L^p(\Omega;C^\lambda([0,T];E)) assuming that the approximating operators A_n are uniformly sectorial and converge to A in the strong resolvent sense, and that the approximating nonlinearities F_n and G_n are uniformly Lipschitz continuous in suitable norms and converge to F and G pointwise. Our results are applied to a class of semilinear parabolic SPDEs with finite-dimensional multiplicative noise.Comment: Referee's comments have been incorporate

Ab initio study of reflectance anisotropy spectra of a sub-monolayer oxidized Si(100) surface

The effects of oxygen adsorption on the reflectance anisotropy spectrum (RAS) of reconstructed Si(100):O surfaces at sub-monolayer coverage (first stages of oxidation) have been studied by an ab initio DFT-LDA scheme within a plane-wave, norm-conserving pseudopotential approach. Dangling bonds and the main features of the characteristic RAS of the clean Si(100) surface are mostly preserved after oxidation of 50% of the surface dimers, with some visible changes: a small red shift of the first peak, and the appearance of a distinct spectral structure at about 1.5 eV. The electronic transitions involved in the latter have been analyzed through state-by-state and layer-by-layer decompositions of the RAS. We suggest that new interplay between present theoretical results and reflectance anisotropy spectroscopy experiments could lead to further clarification of structural and kinetic details of the Si(100) oxidation process in the sub-monolayer range.Comment: 21 pages, 8 figures. To be published in Physical Rev.

An empirical study of unfair terms in online auction contracts in the UK: Evidence for the need for better enforcement mechanisms

This paper studies the terms of 28 online auction sites. It uncovers that, in this industry, unfair terms are common. The paper focusses on a small number of clauses but conclusively shows that enforcement in the UK is insufficient. The reasons for this insufficiency are explored and solutions proposed

On the density of systems of non-linear spatially homogeneous SPDEs

In this paper, we consider a system of $k$ second order non-linear stochastic partial differential equations with spatial dimension $d \geq 1$, driven by a $q$-dimensional Gaussian noise, which is white in time and with some spatially homogeneous covariance. The case of a single equation and a one-dimensional noise, has largely been studied in the literature. The first aim of this paper is to give a survey of some of the existing results. We will start with the existence, uniqueness and H\"older's continuity of the solution. For this, the extension of Walsh's stochastic integral to cover some measure-valued integrands will be recalled. We will then recall the results concerning the existence and smoothness of the density, as well as its strict positivity, which are obtained using techniques of Malliavin calculus. The second aim of this paper is to show how these results extend to our system of SPDEs. In particular, we give sufficient conditions in order to have existence and smoothness of the density on the set where the columns of the diffusion matrix span $\R^k$. We then prove that the density is strictly positive in a point if the connected component of the set where the columns of the diffusion matrix span $\R^k$ which contains this point has a non void intersection with the support of the law of the solution. We will finally check how all these results apply to the case of the stochastic heat equation in any space dimension and the stochastic wave equation in dimension $d\in \{1,2,3\}$

Random-field Solutions to Linear Hyperbolic Stochastic Partial Differential Equations with Variable Coefficients

In this article we show the existence of a random-field solution to linear stochastic partial differential equations whose partial differential operator is hyperbolic and has variable coefficients that may depend on the temporal and spatial argument. The main tools for this, pseudo-differential and Fourier integral operators, come from microlocal analysis. The equations that we treat are second-order and higher-order strictly hyperbolic, and second-order weakly hyperbolic with uniformly bounded coefficients in space. For the latter one we show that a stronger assumption on the correlation measure of the random noise might be needed. Moreover, we show that the well-known case of the stochastic wave equation can be embedded into the theory presented in this article.Comment: 40 pages, final version, Stochastic Processes and their Applications (2017

Simultaneous description of four positive and four negative parity bands

The extended coherent state model is further extended in order to describe two dipole bands of different parities. The formalism provides a consistent description of eight rotational bands. A unified description for spherical, transitional and deformed nuclei is possible. Projecting out the angular momentum and parity from a sole state, the $K^{\pi}=1^+$ band acquires a magnetic character, while the electric properties prevail for the other band. Signatures for a static octupole deformation in some states of the dipole bands are pointed out. Some properties which distinguish between the dipole band states and states of the same parity but belonging to other bands are mentioned. Interesting features concerning the decay properties of the two bands are found. Numerical applications are made for $^{158}$Gd, $^{172}$Yb, $^{228,232}$Th, $^{226}$Ra, $^{238}$U and $^{238}$Pu, and the results are compared with the available data.Comment: 36 pages, 13 figures, 12 table