Coherent potential approximation, averaged T-matrix approximation and Lloyd's model

It is shown how the single-site coherent potential approximation and the averaged T-matrix approximation become exact in the calculation of the averaged single-particle Green function of the electron in the Anderson model when the site energy is distributed randomly with lorentzian distribution. Using these approximations, Lloyd's exact result is reproduced.

A local 2-approximation algorithm for the vertex cover problem

We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (Δ + 1)2 synchronous communication rounds, where Δ is the maximum degree of the graph. For Δ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.

A simple local 3-approximation algorithm for vertex cover

We present a local algorithm (constant-time distributed algorithm) for finding a 3-approximate vertex cover in bounded-degree graphs. The algorithm is deterministic, and no auxiliary information besides port numbering is required. (c) 2009 Elsevier B.V. All rights reserved.

A local 2-approximation algorithm for the vertex cover problem

We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (Δ + 1)2 synchronous communication rounds, where Δ is the maximum degree of the graph. For Δ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.

Electron concentration dependence of exciton localization and freeze-out at local potential fluctuations in InN films

InN films with electron concentration ranging from n similar to 10(17) to 10(20) cm(-3) grown by metal-organic chemical vapor deposition (MOCVD) and molecular beam epitaxy (MBE) were investigated by variable-temperature photoluminescence and absorption measurements. The energy positions of absorption edge as well as photoluminescence peak of these InN samples with electron concentration above 10(18) cm(-3) show a distinct S-shape temperature dependence. With a model of potential fluctuations caused by electron-impurity interactions, the behavior can be quantitatively explained in terms of exciton freeze-out in local potential minima at sufficiently low temperatures, followed by thermal redistribution of the localized excitons when the band gap shrinks with increasing temperature. The exciton localization energy sigma (loc) is found to follow the n (5/12) power relation, which testifies to the observed strong localization effects in InN with high electron concentrations.

WMR navigation using local potential field corridors and narrow local occupancy grid perception

Path planning and control strategies applied to autonomous mobile robots should fulfil safety rules as well as achieve final goals. Trajectory planning applications should be fast and flexible to allow real time implementations as well as environment interactions. The methodology presented uses the on robot information as the meaningful data necessary to plan a narrow passage by using a corridor based on attraction potential fields that approaches the mobile robot to the final desired configuration. It employs local and dense occupancy grid perception to avoid collisions. The key goals of this research project are computational simplicity as well as the possibility of integrating this method with other methods reported by the research community. Another important aspect of this work consist in testing the proposed method by using a mobile robot with a perception system composed of a monocular camera and odometers placed on the two wheels of the differential driven motion system. Hence, visual data are used as a local horizon of perception in which trajectories without collisions are computed by satisfying final goal approaches and safety criteria

First-principles calculation of the AlAs/GaAs interface band structure using a self-energy-corrected local density approximation

We apply a self-energy-corrected local density approximation (LDA) to obtain corrected bulk band gaps and to study the band offsets of AlAs grown on GaAs (AlAs/GaAs). We also investigate the Al(x)Ga(1-x)As/GaAs alloy interface, commonly employed in band gap engineering. The calculations are fully ab initio, with no adjustable parameters or experimental input, and at a computational cost comparable to traditional LDA. Our results are in good agreement with experimental values and other theoretical studies. Copyright (C) EPLA, 2011

Hierarchical spherical model from a geometric point of view

A continuous version of the hierarchical spherical model at dimension d=4 is investigated. Two limit distributions of the block spin variable X(gamma), normalized with exponents gamma = d + 2 and gamma=d at and above the critical temperature, are established. These results are proven by solving certain evolution equations corresponding to the renormalization group (RG) transformation of the O(N) hierarchical spin model of block size L(d) in the limit L down arrow 1 and N ->infinity. Starting far away from the stationary Gaussian fixed point the trajectories of these dynamical system pass through two different regimes with distinguishable crossover behavior. An interpretation of this trajectories is given by the geometric theory of functions which describe precisely the motion of the Lee-Yang zeroes. The large-N limit of RG transformation with L(d) fixed equal to 2, at the criticality, has recently been investigated in both weak and strong (coupling) regimes by Watanabe (J. Stat. Phys. 115:1669-1713, 2004) . Although our analysis deals only with N = infinity case, it complements various aspects of that work.

Der Renormierungsgruppen-Fluß der konform-reduzierten Quantengravitation

Wir analysieren die Rolle von "Hintergrundunabhängigkeit" im Zugang der effektiven Mittelwertwirkung zur Quantengravitation. Wenn der nicht-störungstheoretische Renormierungsgruppen-(RG)-Fluß "hintergrundunabhängig" ist, muß die Vergröberung durch eine nicht spezifizierte, variable Metrik definiert werden. Die Forderung nach "Hintergrundunabhängigkeit" in der Quantengravitation führt dazu, daß die funktionale RG-Gleichung von zusätzlichen Feldern abhängt; dadurch unterscheidet sich der RG-Fluß in der Quantengravitation deutlich von dem RG-Fluß einer gewöhnlichen Quantentheorie, deren Moden-Cutoff von einer starren Metrik abhängt. Beispielsweise kann in der "hintergrundunabhängigen" Theorie ein Nicht-Gauß'scher Fixpunkt existieren, obwohl die entsprechende gewöhnliche Quantentheorie keinen solchen entwickelt. Wir untersuchen die Bedeutung dieses universellen, rein kinematischen Effektes, indem wir den RG-Fluß der Quanten-Einstein-Gravitation (QEG) in einem "konform-reduzierten" Zusammenhang untersuchen, in dem wir nur den konformen Faktor der Metrik quantisieren. Alle anderen Freiheitsgrade der Metrik werden vernachlässigt. Die konforme Reduktion der Einstein-Hilbert-Trunkierung zeigt exakt dieselben qualitativen Eigenschaften wie in der vollen Einstein-Hilbert-Trunkierung. Insbesondere besitzt sie einen Nicht-Gauß'schen Fixpunkt, der notwendig ist, damit die Gravitation asymptotisch sicher ist. Ohne diese zusätzlichen Feldabhängigkeiten ist der RG-Fluß dieser Trunkierung der einer gewöhnlichen $phi^4$-Theorie. Die lokale Potentialnäherung für den konformen Faktor verallgemeinert den RG-Fluß in der Quantengravitation auf einen unendlich-dimensionalen Theorienraum. Auch hier finden wir sowohl einen Gauß'schen als auch einen Nicht-Gauß'schen Fixpunkt, was weitere Hinweise dafür liefert, daß die Quantengravitation asymptotisch sicher ist. Das Analogon der Metrik-Invarianten, die proportional zur dritten Potenz der Krümmung ist und die die störungstheoretische Renormierbarkeit zerstört, ist unproblematisch für die asymptotische Sicherheit der konform-reduzierten Theorie. Wir berechnen die Skalenfelder und -imensionen der beiden Fixpunkte explizit und diskutieren mögliche Einflüsse auf die Vorhersagekraft der Theorie. Da der RG-Fluß von der Topologie der zugrundeliegenden Raumzeit abhängt, diskutieren wir sowohl den flachen Raum als auch die Sphäre. Wir lösen die Flußgleichung für das Potential numerisch und erhalten Beispiele für RG-Trajektorien, die innerhalb der Ultraviolett-kritischen Mannigfaltigkeit des Nicht-Gauß'schen Fixpunktes liegen. Die Quantentheorien, die durch einige solcher Trajektorien definiert sind, zeigen einen Phasenübergang von der bekannten (Niederenergie-) Phase der Gravitation mit spontan gebrochener Diffeomorphismus-Invarianz zu einer neuen Phase von ungebrochener Diffeomorphismus-Invarianz. Diese Hochenergie-Phase ist durch einen verschwindenden Metrik-Erwartungswert charakterisiert.

Exchange potential from the common energy denominator approximation for the Kohn-Sham Green's function: Application to (hyper)polarizabilities of molecular chains

An approximate Kohn-Sham (KS) exchange potential v(xsigma)(CEDA) is developed, based on the common energy denominator approximation (CEDA) for the static orbital Green's function, which preserves the essential structure of the density response function. v(xsigma)(CEDA) is an explicit functional of the occupied KS orbitals, which has the Slater v(Ssigma) and response v(respsigma)(CEDA) potentials as its components. The latter exhibits the characteristic step structure with "diagonal" contributions from the orbital densities \psi(isigma)\(2), as well as "off-diagonal" ones from the occupied-occupied orbital products psi(isigma)psi(j(not equal1)sigma). Comparison of the results of atomic and molecular ground-state CEDA calculations with those of the Krieger-Li-Iafrate (KLI), exact exchange (EXX), and Hartree-Fock (HF) methods show, that both KLI and CEDA potentials can be considered as very good analytical "closure approximations" to the exact KS exchange potential. The total CEDA and KLI energies nearly coincide with the EXX ones and the corresponding orbital energies epsilon(isigma) are rather close to each other for the light atoms and small molecules considered. The CEDA, KLI, EXX-epsilon(isigma) values provide the qualitatively correct order of ionizations and they give an estimate of VIPs comparable to that of the HF Koopmans' theorem. However, the additional off-diagonal orbital structure of v(xsigma)(CEDA) appears to be essential for the calculated response properties of molecular chains. KLI already considerably improves the calculated (hyper)polarizabilities of the prototype hydrogen chains H-n over local density approximation (LDA) and standard generalized gradient approximations (GGAs), while the CEDA results are definitely an improvement over the KLI ones. The reasons of this success are the specific orbital structures of the CEDA and KLI response potentials, which produce in an external field an ultranonlocal field-counteracting exchange potential. (C) 2002 American Institute of Physics.

Exchange-correlation energy and potential as approximate functionals of occupied and virtual Kohn-Sham orbitals: Application to dissociating H-2

The standard local density approximation and generalized gradient approximations fail to properly describe the dissociation of an electron pair bond, yielding large errors (on the order of 50 kcal/mol) at long bond distances. To remedy this failure, a self-consistent Kohn-Sham (KS) method is proposed with the exchange-correlation (xc) energy and potential depending on both occupied and virtual KS orbitals. The xc energy functional of Buijse and Baerends [Mol. Phys. 100, 401 (2002); Phys. Rev. Lett. 87, 133004 (2001)] is employed, which, based on an ansatz for the xc-hole amplitude, is able to reproduce the important dynamical and nondynamical effects of Coulomb correlation through the efficient use of virtual orbitals. Self-consistent calculations require the corresponding xc potential to be obtained, to which end the optimized effective potential (OEP) method is used within the common energy denominator approximation for the static orbital Green's function. The problem of the asymptotic divergence of the xc potential of the OEP when a finite number of virtual orbitals is used is addressed. The self-consistent calculations reproduce very well the entire H-2 potential curve, describing correctly the gradual buildup of strong left-right correlation in stretched H-2. (C) 2003 American Institute of Physics.

The effect of additional Si and SiGe layers on the confinement potential of GeMn diluted ferromagnetic semiconductor

In this work we analyze the spin-polarized charge density distribution in the GeMn diluted ferromagnetic semiconductors (DFS). The calculations are performed within a self-consistent k.p method, in which the exchange correlation effects in the local density approximation, as well as the strain effects due to the lattice mismatch, are taken into account. Our findings show that the extra confinement potential provided by the barriers and the variation of the Mn content in the DFS are responsible for a separation between the different spin charge densities, giving rise to higher mobility spin-polarized currents or high ferromagnetism transition temperatures systems. (c) 2008 Elsevier B.V. All rights reserved.

Theory of strongly correlated electron systems. I. Intersite coulomb interaction and the approximation of renormalized fermions in total energy calculations

The diagrammatic strong-coupling perturbation theory (SCPT) for correlated electron systems is developed for intersite Coulomb interaction and for a nonorthogonal basis set. The construction is based on iterations of exact closed equations for many - electron Green functions (GFs) for Hubbard operators in terms of functional derivatives with respect to external sources. The graphs, which do not contain the contributions from the fluctuations of the local population numbers of the ion states, play a special role: a one-to-one correspondence is found between the subset of such graphs for the many - electron GFs and the complete set of Feynman graphs of weak-coupling perturbation theory (WCPT) for single-electron GFs. This fact is used for formulation of the approximation of renormalized Fermions (ARF) in which the many-electron quasi-particles behave analogously to normal Fermions. Then, by analyzing: (a) Sham's equation, which connects the self-energy and the exchange- correlation potential in density functional theory (DFT); and (b) the Galitskii and Migdal expressions for the total energy, written within WCPT and within ARF SCPT, a way we suggest a method to improve the description of the systems with correlated electrons within the local density approximation (LDA) to DFT. The formulation, in terms of renormalized Fermions LIDA (RF LDA), is obtained by introducing the spectral weights of the many electron GFs into the definitions of the charge density, the overlap matrices, effective mixing and hopping matrix elements, into existing electronic structure codes, whereas the weights themselves have to be found from an additional set of equations. Compared with LDA+U and self-interaction correction (SIC) methods, RF LDA has the advantage of taking into account the transfer of spectral weights, and, when formulated in terms of GFs, also allows for consideration of excitations and nonzero temperature. Going beyond the ARF SCPT, as well as RF LIDA, and taking into account the fluctuations of ion population numbers would require writing completely new codes for ab initio calculations. The application of RF LDA for ab initio band structure calculations for rare earth metals is presented in part 11 of this study (this issue). (c) 2005 Wiley Periodicals, Inc.

Trapped fermions in a synthetic non-Abelian gauge field

On increasing the coupling strength (lambda) of a non-Abelian gauge field that induces a generalized Rashba spin-orbit interaction, the topology of the Fermi surface of a homogeneous gas of noninteracting fermions of density rho similar to k(F)(3) undergoes a change at a critical value, lambda(T) approximate to k(F) [Phys. Rev. B 84, 014512 ( 2011)]. In this paper we analyze how this phenomenon affects the size and shape of a cloud of spin-1/2 fermions trapped in a harmonic potential such as those used in cold atom experiments. We develop an adiabatic formulation, including the concomitant Pancharatnam-Berry phase effects, for the one-particle states in the presence of a trapping potential and the gauge field, obtaining approximate analytical formulas for the energy levels for some high symmetry gauge field configurations of interest. An analysis based on the local density approximation reveals that, for a given number of particles, the cloud shrinks in a characteristic fashion with increasing.. We explain the physical origins of this effect by a study of the stress tensor of the system. For an isotropic harmonic trap, the local density approximation predicts a spherical cloud even for anisotropic gauge field configurations. We show, via a calculation of the cloud shape using exact eigenstates, that for certain gauge field configurations there is a systematic and observable anisotropy in the cloud shape that increases with increasing gauge coupling lambda. The reasons for this anisotropy are explained using the analytical energy levels obtained via the adiabatic approximation. These results should be useful in the design of cold atom experiments with fermions in non-Abelian gauge fields. An important spin-off of our adiabatic formulation is that it reveals exciting possibilities for the cold-atom realization of interesting condensed matter Hamiltonians by using a non-Abelian gauge field in conjunction with another potential. In particular, we show that the use of a spherical non-Abelian gauge field with a harmonic trapping potential produces a monopole field giving rise to a spherical geometry quantum Hall-like Hamiltonian in the momentum representation.

Simulation of inhomogeneous distributions of ultracold atoms in an optical lattice via a massively parallel implementation of nonequilibrium strong-coupling perturbation theory

We present a nonequilibrium strong-coupling approach to inhomogeneous systems of ultracold atoms in optical lattices. We demonstrate its application to the Mott-insulating phase of a two-dimensional Fermi-Hubbard model in the presence of a trap potential. Since the theory is formulated self-consistently, the numerical implementation relies on a massively parallel evaluation of the self-energy and the Green's function at each lattice site, employing thousands of CPUs. While the computation of the self-energy is straightforward to parallelize, the evaluation of the Green's function requires the inversion of a large sparse 10(d) x 10(d) matrix, with d > 6. As a crucial ingredient, our solution heavily relies on the smallness of the hopping as compared to the interaction strength and yields a widely scalable realization of a rapidly converging iterative algorithm which evaluates all elements of the Green's function. Results are validated by comparing with the homogeneous case via the local-density approximation. These calculations also show that the local-density approximation is valid in nonequilibrium setups without mass transport.