Two-dimensional limit of exchange-correlation energy functional approximations in density functional theory

We investigate the behavior of three-dimensional (3D) exchange-correlation energy functional approximations of density functional theory in anisotropic systems with two-dimensional (2D) character. Using two simple models, quasi-2D electron gas and two-electron quantum dot, we show a {\it fundamental limitation} of the local density approximation (LDA), and its semi-local extensions, generalized gradient approximation (GGA) and meta-GGA (MGGA), the most widely used forms of which are worse than the LDA in the strong 2D limit. The origin of these shortcomings is in the inability of the local (LDA) and semi-local (GGA/MGGA) approximations to describe systems with 2D character in which the nature of the exchange-correlation hole is very nonlocal. Nonlocal functionals provide an alternative approach, and explicitly the average density approximation (ADA) is shown to be remarkably accurate for the quasi-2D electron gas system. Our study is not only relevant for understanding of the functionals but also practical applications to semiconductor quantum structures and materials such as graphite and metal surfaces. We also comment on the implication of our findings to the practical device simulations based on the (semi-)local density functional method.Comment: 21 pages including 9 figures, to be published in Phys. Rev.

Nonrenormalization of Flux Superpotentials in String Theory

Recent progress in understanding modulus stabilization in string theory relies on the existence of a non-renormalization theorem for the 4D compactifications of Type IIB supergravity which preserve N=1 supersymmetry. We provide a simple proof of this non-renormalization theorem for a broad class of Type IIB vacua using the known symmetries of these compactifications, thereby putting them on a similar footing as the better-known non-renormalization theorems of heterotic vacua without fluxes. The explicit dependence of the tree-level flux superpotential on the dilaton field makes the proof more subtle than in the absence of fluxes.Comment: 16 pages, no figures. Final version, to appear in JHEP. Arguments for validity of R-symmetry made more explicit. Minor extra comments and references adde

New Solution of D=11 Supergravity on S^7 from D=4

A new static partially twisted solution of N=4, SO(4) gauged supergravity in D=11 is obtained in this work using Cveti\^c et al embedding of four dimensional into eleven dimensional supergravities. In four dimensions we get two solutions: an asymptotic one corresponding to $AdS_4$ and a near horizon fixed point solution of the form $AdS_2\times H_2$. Hence, while the former solution has 32 supercharges the latter turns out to have only 4 conserved. Moreover, we managed to find an exact interpolating solution, thus connecting the above two. Aiming at a future study of $AdS/CFT$ duality for the theory at hand we derived the Penrose limit of the four dimensional solutions. Interestingly the pp-wave limit of the near horizon solution suggests itself as being of the supernumerary supersymmetric type. In D=11 we exhibit the uplift of the four dimensional solutions: one associated to $AdS_4\times S^7$ and the other to a foliation of $AdS_2\times H_2 \times S^7$, as well as their pp-wave limits.Comment: 14 pages, LaTe

Uplifting and Inflation with D3 Branes

Back-reaction effects can modify the dynamics of mobile D3 branes moving within type IIB vacua, in a way which has recently become calculable. We identify some of the ways these effects can alter inflationary scenarios, with the following three results: (1) By examining how the forces on the brane due to moduli-stabilizing interactions modify the angular motion of D3 branes moving in Klebanov-Strassler type throats, we show how previous slow-roll analyses can remain unchanged for some brane trajectories, while being modified for other trajectories. These forces cause the D3 brane to sink to the bottom of the throat except in a narrow region close to the D7 brane, and do not ameliorate the \eta-problem of slow roll inflation in these throats; (2) We argue that a recently-proposed back-reaction on the dilaton field can be used to provide an alternative way of uplifting these compactifications to Minkowski or De Sitter vacua, without the need for a supersymmetry-breaking anti-D3 brane; and (3) by including also the D-term forces which arise when supersymmetry-breaking fluxes are included on D7 branes we identify the 4D supergravity interactions which capture the dynamics of D3 motion in D3/D7 inflationary scenarios. The form of these potentials sheds some light on recent discussions of how symmetries constrain D term interactions in the low-energy theory.Comment: JHEP.cls, 35 pages, 3 .eps figure

Killing spectroscopy of closed timelike curves

We analyse the existence of closed timelike curves in spacetimes which possess an isometry. In particular we check which discrete quotients of such spaces lead to closed timelike curves. As a by-product of our analysis, we prove that the notion of existence or non-existence of closed timelike curves is a T-duality invariant notion, whenever the direction along which we apply such transformations is everywhere spacelike. Our formalism is straightforwardly applied to supersymmetric theories. We provide some new examples in the context of D-branes and generalized pp-waves.Comment: 1+35 pages, no figures; v2, new references added. Final version to appear in JHE

Frustrated two-dimensional Josephson junction array near incommensurability

To study the properties of frustrated two-dimensional Josephson junction arrays near incommensurability, we examine the current-voltage characteristics of a square proximity-coupled Josephson junction array at a sequence of frustrations f=3/8, 8/21, 0.382 $(\approx (3-\sqrt{5})/2)$, 2/5, and 5/12. Detailed scaling analyses of the current-voltage characteristics reveal approximately universal scaling behaviors for f=3/8, 8/21, 0.382, and 2/5. The approximately universal scaling behaviors and high superconducting transition temperatures indicate that both the nature of the superconducting transition and the vortex configuration near the transition at the high-order rational frustrations f=3/8, 8/21, and 0.382 are similar to those at the nearby simple frustration f=2/5. This finding suggests that the behaviors of Josephson junction arrays in the wide range of frustrations might be understood from those of a few simple rational frustrations.Comment: RevTex4, 4 pages, 4 eps figures, to appear in Phys. Rev.

Collider and Dark Matter Phenomenology of Models with Mirage Unification

We examine supersymmetric models with mixed modulus-anomaly mediated SUSY breaking (MM-AMSB) soft terms which get comparable contributions to SUSY breaking from moduli-mediation and anomaly-mediation. The apparent (mirage) unification of soft SUSY breaking terms at Q=mu_mir not associated with any physical threshold is the hallmark of this scenario. The MM-AMSB structure of soft terms arises in models of string compactification with fluxes, where the addition of an anti-brane leads to an uplifting potential and a de Sitter universe, as first constructed by Kachru {\it et al.}. The phenomenology mainly depends on the relative strength of moduli- and anomaly-mediated SUSY breaking contributions, and on the Higgs and matter field modular weights, which are determined by the location of these fields in the extra dimensions. We delineate the allowed parameter space for a low and high value of tan(beta), for a wide range of modular weight choices. We calculate the neutralino relic density and display the WMAP-allowed regions. We show the reach of the CERN LHC and of the International Linear Collider. We discuss aspects of MM-AMSB models for Tevatron, LHC and ILC searches, muon g-2 and b->s \gamma branching fraction. We also calculate direct and indirect dark matter detection rates, and show that almost all WMAP-allowed models should be accessible to a ton-scale noble gas detector. Finally, we comment on the potential of colliders to measure the mirage unification scale and modular weights in the difficult case where mu_mir>>M_GUT.Comment: 34 pages plus 42 EPS figures; version with high resolution figures is at http://www.hep.fsu.edu/~bae

Phonon-mediated anisotropic superconductivity in the Y and Lu nickel borocarbides

We present scanning tunneling spectroscopy and microscopy measurements at low temperatures in the borocarbide materials RNi2B2C (R=Y, Lu). The characteristic strong coupling structure due to the pairing interaction is unambiguously resolved in the superconducting density of states. It is located at the superconducting gap plus the energy corresponding to a phonon mode identified in previous neutron scattering experiments. These measurements also show that this mode is coupled to the electrons through a highly anisotropic electron-phonon interaction originated by a nesting feature of the Fermi surface. Our experiments, from which we can extract a large electron-phonon coupling parameter lambda (between 0.5 and 0.8), demonstrate that this anisotropic electron-phonon coupling has an essential contribution to the pairing interaction. The tunneling spectra show an anisotropic s-wave superconducting gap function.Comment: 5 pages, 3 figure

Group theoretical analysis of symmetry breaking in two-dimensional quantum dots

We present a group theoretical study of the symmetry-broken unrestricted Hartree-Fock orbitals and electron densities in the case of a two-dimensional N-electron single quantum dot (with and without an external magnetic field). The breaking of rotational symmetry results in canonical orbitals that (1) are associated with the eigenvectors of a Hueckel hamiltonian having sites at the positions determined by the equilibrium molecular configuration of the classical N-electron problem, and (2) transform according to the irreducible representations of the point group specified by the discrete symmetries of this classical molecular configuration. Through restoration of the total-spin and rotational symmetries via projection techniques, we show that the point-group discrete symmetry of the unrestricted Hartree-Fock wave function underlies the appearance of magic angular momenta (familiar from exact-diagonalization studies) in the excitation spectra of the quantum dot. Furthermore, this two-step symmetry-breaking/symmetry-restoration method accurately describes the energy spectra associated with the magic angular momenta.Comment: A section VI.B entitled "Quantitative description of the lowest rotational band" has been added. 16 pages. Revtex with 10 EPS figures. A version of the manuscript with high quality figures is available at http://calcite.physics.gatech.edu/~costas/uhf_group.html For related papers, see http://www.prism.gatech.edu/~ph274c

Observational evidence confirms modelling of the long-term integrity of CO2-reservoir caprocks

Storage of anthropogenic CO2 in geological formations relies on a caprock as the primary seal preventing buoyant super-critical CO2 escaping. Although natural CO2 reservoirs demonstrate that CO2 may be stored safely for millions of years, uncertainty remains in predicting how caprocks will react with CO2-bearing brines. This uncertainty poses a significant challenge to the risk assessment of geological carbon storage. Here we describe mineral reaction fronts in a CO2 reservoir-caprock system exposed to CO2 over a timescale comparable with that needed for geological carbon storage. The propagation of the reaction front is retarded by redox-sensitive mineral dissolution reactions and carbonate precipitation, which reduces its penetration into the caprock to ∼7 cm in ∼105 years. This distance is an order-of-magnitude smaller than previous predictions. The results attest to the significance of transport-limited reactions to the long-term integrity of sealing behaviour in caprocks exposed to CO2.Funding was provided by NERC to the CRIUS consortium (NE/F004699/1), Shell Global Solutions, for GR as part of the Center for Nanoscale Controls on Geologic CO₂ (NCGC), an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award # DE-AC02-05CH11231, and DECC, which provided a CCS Innovation grant for completion of this work