A Nation Deceived: How Schools Hold Back America's Brightest Students, Volume II

Provides a comprehensive review of research on the academic acceleration of gifted students

On the "Causality Paradox" of Time-Dependent Density Functional Theory

I show that the so-called causality paradox of time-dependent density functional theory arises from an incorrect formulation of the variational principle for the time evolution of the density. The correct formulation not only resolves the paradox in real time, but also leads to a new expression for the causal exchange-correlation kernel in terms of Berry curvature. Furthermore, I show that all the results that were previously derived from symmetries of the action functional remain valid in the present formulation. Finally, I develop a model functional theory which explicitly demonstrates the workings of the new formulation.Comment: 21 page

A time-dependent approach to electron pumping in open quantum systems

We propose a time-dependent approach to investigate the motion of electrons in quantum pump device configurations. The occupied one-particle states are propagated in real time and used to calculate the local electron density and current. An advantage of the present computational scheme is that the same computational effort is required to simulate monochromatic, polychromatic and nonperiodic drivings. Furthermore, initial state dependence and history effects are naturally accounted for. This approach can also be embedded in the framework of time-dependent density functional theory to include electron-electron interactions. In the special case of periodic drivings we combine the Floquet theory with nonequilibrium Green's functions and obtain a general expression for the pumped current in terms of inelastic transmission probabilities. This latter result is used for benchmarking our propagation scheme in the long-time limit. Finally, we discuss the limitations of Floquet-based schemes and suggest our approach as a possible way to go beyond them.Comment: 14 pages, 8 figure

Non-adiabatic electron dynamics in time-dependent density-functional theory

Time-dependent density-functional theory (TDDFT) treats dynamical exchange and correlation (xc) via a single-particle potential, Vxc(r,t), defined as a nonlocal functional of the density n(r',t'). The popular adiabatic local-density approximation (ALDA) for Vxc(r,t) uses only densities at the same space-time point (r,t). To go beyond the ALDA, two local approximations have been proposed based on quantum hydrodynamics and elasticity theory: (a) using the current as basic variable (C-TDDFT) [G. Vignale, C. A. Ullrich, and S. Conti, Phys. Rev. Lett. 79, 4878 (1997)], (b) working in a co-moving Lagrangian reference frame (L-TDDFT) [I. V. Tokatly, Phys. Rev. B 71, 165105 (2005)]. This paper illustrates, compares, and analyzes both non-adiabatic theories for simple time-dependent model densities in the linear and nonlinear regime, for a broad range of time and frequency scales. C- and L-TDDFT are identical in certain limits, but in general exhibit qualitative and quantitative differences in their respective treatment of elastic and dissipative electron dynamics. In situations where the electronic density rapidly undergoes large deformations, it is found that non-adiabatic effects can become significant, causing the ALDA to break down.Comment: 15 pages, 15 figure

Non-collinear spin-spiral phase for the uniform electron gas within Reduced-Density-Matrix-Functional Theory

The non-collinear spin-spiral density wave of the uniform electron gas is studied in the framework of Reduced-Density-Matrix-Functional Theory. For the Hartree-Fock approximation, which can be obtained as a limiting case of Reduced-Density-Matrix-Functional Theory, Overhauser showed a long time ago that the paramagnetic state of the electron gas is unstable with respect to the formation of charge or spin density waves. Here we not only present a detailed numerical investigation of the spin-spiral density wave in the Hartree-Fock approximation but also investigate the effects of correlations on the spin-spiral density wave instability by means of a recently proposed density-matrix functional.Comment: 9 pages, 10 figure

Electronic, dynamical and superconducting properties of CaBeSi

We report first-principles calculations on the normal and superconducting state of CaBe(x)Si(2-x) (x=1), in the framework of density functional theory for superconductors (SCDFT). CaBeSi is isostructural and isoelectronic to MgB2 and this makes possible a direct comparison of the electronic and vibrational properties and the electron-phonon interaction of the two materials. Despite the many similarities with MgB2 (e.g. sigma bands at the Fermi level and a larger Fermi surface nesting), according to our calculations CaBeSi has a very low critical temperature (Tc ~ 0.4 K, consistent with the experiment). CaBeSi exhibits a complex gap structure, with three gaps at Fermi level: besides the two sigma and pi gaps, present also in MgB2, the appearance of a third gap is related to the anisotropy of the Coulomb repulsion, acting in different way on the bonding and antibonding electronic pi states.Comment: 6 pages, 5 figure