The generator coordinate method in time-dependent density-functional theory: memory made simple

The generator coordinate (GC) method is a variational approach to the quantum many-body problem in which interacting many-body wave functions are constructed as superpositions of (generally nonorthogonal) eigenstates of auxiliary Hamiltonians containing a deformation parameter. This paper presents a time-dependent extension of the GC method as a new approach to improve existing approximations of the exchange-correlation (XC) potential in time-dependent density-functional theory (TDDFT). The time-dependent GC method is shown to be a conceptually and computationally simple tool to build memory effects into any existing adiabatic XC potential. As an illustration, the method is applied to driven parametric oscillations of two interacting electrons in a harmonic potential (Hooke's atom). It is demonstrated that a proper choice of time-dependent generator coordinates in conjunction with the adiabatic local-density approximation reproduces the exact linear and nonlinear two-electron dynamics quite accurately, including features associated with double excitations that cannot be captured by TDDFT in the adiabatic approximation.Comment: 10 pages, 13 figure

Degenerate ground states and nonunique potentials: breakdown and restoration of density functionals

The Hohenberg-Kohn (HK) theorem is one of the most fundamental theorems of quantum mechanics, and constitutes the basis for the very successful density-functional approach to inhomogeneous interacting many-particle systems. Here we show that in formulations of density-functional theory (DFT) that employ more than one density variable, applied to systems with a degenerate ground state, there is a subtle loophole in the HK theorem, as all mappings between densities, wave functions and potentials can break down. Two weaker theorems which we prove here, the joint-degeneracy theorem and the internal-energy theorem, restore the internal, total and exchange-correlation energy functionals to the extent needed in applications of DFT to atomic, molecular and solid-state physics and quantum chemistry. The joint-degeneracy theorem constrains the nature of possible degeneracies in general many-body systems

Spin gaps and spin-flip energies in density-functional theory

Energy gaps are crucial aspects of the electronic structure of finite and extended systems. Whereas much is known about how to define and calculate charge gaps in density-functional theory (DFT), and about the relation between these gaps and derivative discontinuities of the exchange-correlation functional, much less is know about spin gaps. In this paper we give density-functional definitions of spin-conserving gaps, spin-flip gaps and the spin stiffness in terms of many-body energies and in terms of single-particle (Kohn-Sham) energies. Our definitions are as analogous as possible to those commonly made in the charge case, but important differences between spin and charge gaps emerge already on the single-particle level because unlike the fundamental charge gap spin gaps involve excited-state energies. Kohn-Sham and many-body spin gaps are predicted to differ, and the difference is related to derivative discontinuities that are similar to, but distinct from, those usually considered in the case of charge gaps. Both ensemble DFT and time-dependent DFT (TDDFT) can be used to calculate these spin discontinuities from a suitable functional. We illustrate our findings by evaluating our definitions for the Lithium atom, for which we calculate spin gaps and spin discontinuities by making use of near-exact Kohn-Sham eigenvalues and, independently, from the single-pole approximation to TDDFT. The many-body corrections to the Kohn-Sham spin gaps are found to be negative, i.e., single particle calculations tend to overestimate spin gaps while they underestimate charge gaps.Comment: 11 pages, 1 figure, 3 table

Andreev reflection and Klein tunneling in graphene

This is a colloquium-style introduction to two electronic processes in a carbon monolayer (graphene), each having an analogue in relativistic quantum mechanics. Both processes couple electron-like and hole-like states, through the action of either a superconducting pair potential or an electrostatic potential. The first process, Andreev reflection, is the electron-to-hole conversion at the interface with a superconductor. The second process, Klein tunneling, is the tunneling through a p-n junction. Existing and proposed experiments on Josephson junctions and bipolar junctions in graphene are discussed from a unified perspective. CONTENTS: I. INTRODUCTION II. BASIC PHYSICS OF GRAPHENE (Dirac equation; Time reversal symmetry; Boundary conditions; Pseudo-diffusive dynamics) III. ANDREEV REFLECTION (Electron-hole conversion; Retro-reflection vs. specular reflection; Dirac-Bogoliubov-de Gennes equation; Josephson junctions; Further reading) IV. KLEIN TUNNELING (Absence of backscattering; Bipolar junctions; Magnetic field effects; Further reading) V. ANALOGIES (Mapping between NS and p-n junction; Retro-reflection vs. negative refraction; Valley-isospin dependent quantum Hall effect; Pseudo-superconductivity)Comment: 20 pages, 28 figures; "Colloquium" for Reviews of Modern Physic

Exchange-correlation vector potentials and vorticity-dependent exchange-correlation energy densities in two-dimensional systems

We present a new approach how to calculate the scalar exchange-correlation potentials and the vector exchange-correlation potentials from current-carrying ground states of two-dimensional quantum dots. From these exchange-correlation potentials we derive exchange-correlation energy densities and examine their vorticity (or current) dependence. Compared with parameterizations of current-induced effects in literature we find an increased significance of corrections due to paramagnetic current densities.Comment: 5 figures, submitted to PR

Contribution of IASI to the observation of dust aerosol emissions (morning and nighttime) over the Sahara desert

Observing the planet at global scale, twice a day, and measuring the whole infrared atmospheric spectrum (8,461 channels at 0.50 cm−1 resolution), Infrared Atmospheric Sounder Interferometer (IASI)/METOP can concurrently detect clouds, determine the 3‐D atmospheric structure (temperature, water vapor, ozone, etc.), surface properties (emissivity and temperature), as well as dust aerosol AOD and altitude. Observing morning (0930 hr) and nighttime (2130 hr), IASI is in relatively good phase with the most frequent times of occurrence of the main Saharan dust uplift mechanisms reported in the literature. Here we classify IASI dust observations according to both the dust loading (AOD) and the dust layer height, providing a more comprehensive picture of dust characteristics. This classification is analyzed at daily scale and its capability to detect dust uplift events is evaluated through comparisons with results from the particularly well documented June 2011 Fennec campaign. Then, a Dust Emission Index (DEI), specific to IASI, is constructed by selecting AOD‐altitude bins with largest AODs and smallest altitudes likely indicative of freshly emitted dust. Applying this to the 12‐year 2007–2018 period, we determine climatological DEI maps and comparisons are made with other equivalent existing results derived from ground‐based or other satellite observations. Results of these comparisons demonstrate the capability of IASI to document the dust distribution over the whole Earth desert areas over a long period of time. The present approach is also suitable to the processing of the at least hourly observations of the coming Infrared Sounder instrument (IRS), planned on board Meteosat Third Generation (2021)

Spin currents and spin dynamics in time-dependent density-functional theory

We derive and analyse the equation of motion for the spin degrees of freedom within time-dependent spin-density-functional theory (TD-SDFT). Results are (i) a prescription for obtaining many-body corrections to the single-particle spin currents from the Kohn-Sham equation of TD-SDFT, (ii) the existence of an exchange-correlation (xc) torque within TD-SDFT, (iii) a prescription for calculating, from TD-SDFT, the torque exerted by spin currents on the spin magnetization, (iv) a novel exact constraint on approximate xc functionals, and (v) the discovery of serious deficiencies of popular approximations to TD-SDFT when applied to spin dynamics.Comment: now includes discussion of OEP and GGA; to appear in Phys. Rev. Let

The spin angular gradient approximation in the density functional theory

A spin angular gradient approximation for the exchange correlation magnetic field in the density functional formalism is proposed. The usage of such corrections leads to a consistent spin dynamical approach beyond the local approximation. The proposed technique does not contain any approximations for the form of potential and can be used in modern full potential band structure methods. The obtained results indicate that the direct 'potential' exchange in 3d magnets is rather small compared to the indirect 'kinetic' exchange, thus justifies the dynamical aspect of the local density approximation in 3d metals

Exchange-correlation energy densities for two-dimensional systems from quantum dot ground-states

In this paper we present a new approach how to extract polarization-dependent exchange-correlation energy densities for two-dimensional systems from reference densities and energies of quantum dots provided by exact diagonalization. Compared with results from literature we find systematic corrections for all polarizations in the regime of high densities.Comment: 7 figures. submitted to Phys. Rev.