Orbital Dependent Exchange-Only Methods for Periodic Systems

Various orbital-dependent exchange-only potentials are studied which exhibit correct long-range asymptotic behaviour. We present the first application of these potentials for polymers and by one of these potentials for molecules. Kohn-Sham type calculations have been carried out for polyethylene in order to make valuable comparison of these potentials with each other as well as with Hartree-Fock and exchange-only LDA methods. The Kohn-Sham band gap obtained with the optimized effective potetial method is corrected with the exchange contribution to the derivative discontinuity of the exchange-correlation potential. The corrected band gap obtained with the Slater's exchange potential is 9.7 eV close to the experiment.Comment: 11 pages, 2 figures. Phys. Rev. B60, 1999, in pres

Lattice density functional theory at finite temperature with strongly density-dependent exchange-correlation potentials

The derivative discontinuity of the exchange-correlation (xc) energy at integer particle number is a property of the exact, unknown xc functional of density functional theory (DFT) which is absent in many popular local and semilocal approximations. In lattice DFT, approximations exist which exhibit a discontinuity in the xc potential at half filling. However, due to convergence problems of the Kohn-Sham (KS) self-consistency cycle, the use of these functionals is mostly restricted to situations where the local density is away from half filling. Here a numerical scheme for the self-consistent solution of the lattice KS Hamiltonian with a local xc potential with rapid (or quasi-discontinuous) density dependence is suggested. The problem is formulated in terms of finite-temperature DFT where the discontinuity in the xc potential emerges naturally in the limit of zero temperature. A simple parametrization is suggested for the xc potential of the uniform 1D Hubbard model at finite temperature which is obtained from the solution of the thermodynamic Bethe ansatz. The feasibility of the numerical scheme is demonstrated by application to a model of fermionic atoms in a harmonic trap. The corresponding density profile exhibits a plateau of integer occupation at low temperatures which melts away for higher temperatures.Comment: 14 pages, 11 figure

The time-dependent exchange-correlation functional for a Hubbard dimer: quantifying non-adiabatic effect

We address and quantify the role of non-adiabaticity ("memory effects") in the exchange-correlation (xc) functional of time-dependent density functional theory (TDDFT) for describing non-linear dynamics of many-body systems. Time-dependent resonant processes are particularly challenging for available TDDFT approximations, due to their strong non-linear and non-adiabatic character. None of the known approximate density functionals are able to cope with this class of problems in a satisfactory manner. In this work we look at the prototypical example of the resonant processes by considering Rabi oscillations within the exactly soluble 2-site Hubbard model. We construct the exact adiabatic xc functional and show that (i) it does not reproduce correctly resonant Rabi dynamics, (ii) there is a sizable non-adiabatic contribution to the exact xc potential, which turns out to be small only at the beginning and at the end of the Rabi cycle when the ground state population is dominant. We then propose a "two-level" approximation for the time-dependent xc potential which can capture Rabi dynamics in the 2-site problem. It works well both for resonant and for detuned Rabi oscillations and becomes essentially exact in the linear response regime. This new, fully non-adiabatic and explicit density functional constitutes one of the main results of the present work.Comment: 8 pages, 5 figure

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

Highly anisotropic energy gap in superconducting Ba(Fe0.9_{0.9}Co0.1_{0.1})2_{2}As2_{2} from optical conductivity measurements

We have measured the complex dynamical conductivity, $\sigma = \sigma_{1} + i\sigma_{2}$, of superconducting Ba(Fe$_{0.9}$Co$_{0.1}$)$_{2}$As$_{2}$ ($T_{c} = 22$ K) at terahertz frequencies and temperatures 2 - 30 K. In the frequency dependence of $\sigma_{1}$ below $T_{c}$, we observe clear signatures of the superconducting energy gap opening. The temperature dependence of $\sigma_{1}$ demonstrates a pronounced coherence peak at frequencies below 15 cm$^{-1}$ (1.8 meV). The temperature dependence of the penetration depth, calculated from $\sigma_{2}$, shows power-law behavior at the lowest temperatures. Analysis of the conductivity data with a two-gap model, gives the smaller isotropic s-wave gap of $\Delta_{A} = 3$ meV, while the larger gap is highly anisotropic with possible nodes and its rms amplitude is $\Delta_{0} = 8$ meV. Overall, our results are consistent with a two-band superconductor with an $s_{\pm}$ gap symmetry.Comment: 6 pages, 4 figures, discussion on pair-barking scattering and possible lifting of the nodes is adde

Detection and Estimation Theory

Contains reports on two research projects.Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U.S. Air Force)under Contract DA 28-043-AMC-02536(E