Reverse engineering in many-body quantum physics: Correspondence between many-body systems and effective single-particle equations

The mapping, exact or approximate, of a many-body problem onto an effective single-body problem is one of the most widely used conceptual and computational tools of physics. Here, we propose and investigate the inverse map of effective approximate single-particle equations onto the corresponding many-particle system. This approach allows us to understand which interacting system a given single-particle approximation is actually describing, and how far this is from the original physical many-body system. We illustrate the resulting reverse engineering process by means of the Kohn-Sham equations of density-functional theory. In this application, our procedure sheds light on the nonlocality of the density-potential mapping of density-functional theory, and on the self-interaction error inherent in approximate density functionals.

Physical signatures of discontinuities of the time-dependent exchange-correlation potential

The exact exchange-correlation (XC) potential in time-dependent density-functional theory (TDDFT) is known to develop steps and discontinuities upon change of the particle number in spatially confined regions or isolated subsystems. We demonstrate that the self-interaction corrected adiabatic local-density approximation for the XC potential has this property, using the example of electron loss of a model quantum well system. We then study the influence of the XC potential discontinuity in a real-time simulation of a dissociation process of an asymmetric double quantum well system, and show that it dramatically affects the population of the resulting isolated single quantum wells. This indicates the importance of a proper account of the discontinuities in TDDFT descriptions of ionization, dissociation or charge transfer processes.

Density-functional description of superconducting and magnetic proximity effects across a tunneling barrier

A density-functional formalism for superconductivity and magnetism is presented. The resulting relations unify previously derived Kohn-Sham equations for superconductors and for noncollinear magnetism. The formalism, which discriminates Cooper-pair singlets from triplets, is applied to two quantum liquids coupled by tunneling through a barrier. An exact expression is derived, relating the eigenstates and eigenvalues of the Kohn-Sham equations, unperturbed by tunneling, on one side of the barrier to the proximity-induced ordering potential on the other.

Density functional theory investigation of 3d, 4d, and 5d 13-atom metal clusters

The knowledge of the atomic structure of clusters composed by few atoms is a basic prerequisite to obtain insights into the mechanisms that determine their chemical and physical properties as a function of diameter, shape, surface termination, as well as to understand the mechanism of bulk formation. Due to the wide use of metal systems in our modern life, the accurate determination of the properties of 3d, 4d, and 5d metal clusters poses a huge problem for nanoscience. In this work, we report a density functional theory study of the atomic structure, binding energies, effective coordination numbers, average bond lengths, and magnetic properties of the 3d, 4d, and 5d metal (30 elements) clusters containing 13 atoms, M(13). First, a set of lowest-energy local minimum structures (as supported by vibrational analysis) were obtained by combining high-temperature first- principles molecular-dynamics simulation, structure crossover, and the selection of five well-known M(13) structures. Several new lower energy configurations were identified, e. g., Pd(13), W(13), Pt(13), etc., and previous known structures were confirmed by our calculations. Furthermore, the following trends were identified: (i) compact icosahedral-like forms at the beginning of each metal series, more opened structures such as hexagonal bilayerlike and double simple-cubic layers at the middle of each metal series, and structures with an increasing effective coordination number occur for large d states occupation. (ii) For Au(13), we found that spin-orbit coupling favors the three-dimensional (3D) structures, i.e., a 3D structure is about 0.10 eV lower in energy than the lowest energy known two-dimensional configuration. (iii) The magnetic exchange interactions play an important role for particular systems such as Fe, Cr, and Mn. (iv) The analysis of the binding energy and average bond lengths show a paraboliclike shape as a function of the occupation of the d states and hence, most of the properties can be explained by the chemistry picture of occupation of the bonding and antibonding states.

Transition-metal 13-atom clusters assessed with solid and surface-biased functionals

First-principles density-functional theory studies have reported open structures based on the formation of double simple-cubic (DSC) arrangements for Ru(13), Rh(13), Os(13), and Ir(13), which can be considered an unexpected result as those elements crystallize in compact bulk structures such as the face-centered cubic and hexagonal close-packed lattices. In this work, we investigated with the projected augmented wave method the dependence of the lowest-energy structure on the local and semilocal exchange-correlation (xc) energy functionals employed in density-functional theory. We found that the local-density approximation (LDA) and generalized-gradient formulations with different treatment of the electronic inhomogeneities (PBE, PBEsol, and AM05) confirm the DSC configuration as the lowest-energy structure for the studied TM(13) clusters. A good agreement in the relative total energies are obtained even for structures with small energy differences, e. g., 0.10 eV. The employed xc functionals yield the same total magnetic moment for a given structure, i.e., the differences in the bond lengths do not affect the moments, which can be attributed to the atomic character of those clusters. Thus, at least for those systems, the differences among the LDA, PBE, PBEsol, and AM05 functionals are not large enough to yield qualitatively different results. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3577999]

Effective coordination concept applied for phase change (GeTe)(m)(Sb(2)Te(3))(n) compounds

In this work, we employed the effective coordination concept to study the local environments of the Ge, Sb, and Te atoms in the Ge(m)Sb(2n)Te(m+3n) compounds. From our calculations and analysis, we found an average effective coordination number (ECN) reduction of 1.59, 1.42, and 1.37, for the Ge, Sb, Te atoms in the phase transition from crystalline, ECN=5.55 (Ge), 5.73 (Sb), 4.37 (Te), to the amorphous phase, ECN=3.96 (Ge), 4.31 (Sb), 3.09 (Te), for the Ge(2)Sb(2)Te(5) composition. Similar changes are observed for other compositions. Thus, our results indicate that the coordination changes from the crystalline to amorphous phase are not large as previously assumed in the literature, i.e., from sixfold to fourfold for Ge, which can contribute to obtain a better understanding of the crystalline to amorphous phase transition. (C) 2011 American Institute of Physics. [doi:10.1063/1.3533422]

The role of electron localization in the atomic structure of transition-metal 13-atom clusters: the example of Co(13), Rh(13), and Hf(13)

The crystalline structure of transition-metals (TM) has been widely known for several decades, however, our knowledge on the atomic structure of TM clusters is still far from satisfactory, which compromises an atomistic understanding of the reactivity of TM clusters. For example, almost all density functional theory (DFT) calculations for TM clusters have been based on local (local density approximation-LDA) and semilocal (generalized gradient approximation-GGA) exchange-correlation functionals, however, it is well known that plain DFT fails to correct the self-interaction error, which affects the properties of several systems. To improve our basic understanding of the atomic and electronic properties of TM clusters, we report a DFT study within two nonlocal functionals, namely, the hybrid HSE (Heyd, Scuseria, and Ernzerhof) and GGA + U functionals, of the structural and electronic properties of the Co(13), Rh(13), and Hf(13) clusters. For Co(13) and Rh(13), we found that improved exchange-correlation functionals decrease the stability of open structures such as the hexagonal bilayer (HBL) and double simple-cubic (DSC) compared with the compact icosahedron (ICO) structure, however, DFT-GGA, DFT-GGA + U, and DFT-HSE yield very similar results for Hf(13). Thus, our results suggest that the DSC structure obtained by several plain DFT calculations for Rh(13) can be improved by the use of improved functionals. Using the sd hybridization analysis, we found that a strong hybridization favors compact structures, and hence, a correct description of the sd hybridization is crucial for the relative energy stability. For example, the sd hybridization decreases for HBL and DSC and increases for ICO in the case of Co(13) and Rh(13), while for Hf(13), the sd hybridization decreases for all configurations, and hence, it does not affect the relative stability among open and compact configurations.

On the k-restricted structure ratio in planar and outerplanar graphs

A planar k-restricted structure is a simple graph whose blocks are planar and each has at most k vertices. Planar k-restricted structures are used by approximation algorithms for Maximum Weight Planar Subgraph, which motivates this work. The planar k-restricted ratio is the infimum, over simple planar graphs H, of the ratio of the number of edges in a maximum k-restricted structure subgraph of H to the number edges of H. We prove that, as k tends to infinity, the planar k-restricted ratio tends to 1/2. The same result holds for the weighted version. Our results are based on analyzing the analogous ratios for outerplanar and weighted outerplanar graphs. Here both ratios tend to 1 as k goes to infinity, and we provide good estimates of the rates of convergence, showing that they differ in the weighted from the unweighted case.

Survival time of random walk in random environment among soft obstacles

We consider a Random Walk in Random Environment (RWRE) moving in an i.i.d. random field of obstacles. When the particle hits an obstacle, it disappears with a positive probability. We obtain quenched and annealed bounds on the tails of the survival time in the general d-dimensional case. We then consider a simplified one-dimensional model (where transition probabilities and obstacles are independent and the RWRE only moves to neighbour sites), and obtain finer results for the tail of the survival time. In addition, we study also the ""mixed"" probability measures (quenched with respect to the obstacles and annealed with respect to the transition probabilities and vice-versa) and give results for tails of the survival time with respect to these probability measures. Further, we apply the same methods to obtain bounds for the tails of hitting times of Branching Random Walks in Random Environment (BRWRE).

Hitting and returning to rare events for all alpha-mixing processes

We prove that for any a-mixing stationary process the hitting time of any n-string A(n) converges, when suitably normalized, to an exponential law. We identify the normalization constant lambda(A(n)). A similar statement holds also for the return time. To establish this result we prove two other results of independent interest. First, we show a relation between the rescaled hitting time and the rescaled return time, generalizing a theorem of Haydn, Lacroix and Vaienti. Second, we show that for positive entropy systems, the probability of observing any n-string in n consecutive observations goes to zero as n goes to infinity. (c) 2010 Elsevier B.V. All rights reserved.

A Component of the Xanthomonadaceae Type IV Secretion System Combines a VirB7 Motif with a N0 Domain Found in Outer Membrane Transport Proteins

Type IV secretion systems (T4SS) are used by Gram-negative bacteria to translocate protein and DNA substrates across the cell envelope and into target cells. Translocation across the outer membrane is achieved via a ringed tetradecameric outer membrane complex made up of a small VirB7 lipoprotein (normally 30 to 45 residues in the mature form) and the C-terminal domains of the VirB9 and VirB10 subunits. Several species from the genera of Xanthomonas phytopathogens possess an uncharacterized type IV secretion system with some distinguishing features, one of which is an unusually large VirB7 subunit (118 residues in the mature form). Here, we report the NMR and 1.0 angstrom X-ray structures of the VirB7 subunit from Xanthomonas citri subsp. citri (VirB7(XAC2622)) and its interaction with VirB9. NMR solution studies show that residues 27-41 of the disordered flexible N-terminal region of VirB7(XAC2622) interact specifically with the VirB9 C-terminal domain, resulting in a significant reduction in the conformational freedom of both regions. VirB7(XAC2622) has a unique C-terminal domain whose topology is strikingly similar to that of N0 domains found in proteins from different systems involved in transport across the bacterial outer membrane. We show that VirB7(XAC2622) oligomerizes through interactions involving conserved residues in the N0 domain and residues 42-49 within the flexible N-terminal region and that these homotropic interactions can persist in the presence of heterotropic interactions with VirB9. Finally, we propose that VirB(7XAC2622) oligomerization is compatible with the core complex structure in a manner such that the N0 domains form an extra layer on the perimeter of the tetradecameric ring.

Structure, stability, depolarized light scattering, and vibrational spectra of fullerenols from all-electron density-functional-theory calculations

We have investigated the stability, electronic properties, Rayleigh (elastic), and Raman (inelastic) depolarization ratios, infrared and Raman absorption vibrational spectra of fullerenols [C(60)(OH)(n)] with different degrees of hydroxylation by using all-electron density-functional-theory (DFT) methods. Stable arrangements of these molecules were found by means of full geometry optimizations using Becke's three-parameter exchange functional with the Lee, Yang, and Parr correlation functional. This DFT level has been combined with the 6-31G(d,p) Gaussian-type basis set, as a compromise between accuracy and capability to treat highly hydroxylated fullerenes, e.g., C(60)(OH)(36). Thus, the molecular properties of fullerenols were systematically analyzed for structures with n=1, 2, 3, 4, 8, 10, 16, 18, 24, 32, and 36. From the electronic structure analysis of these molecules, we have evidenced an important effect related to the weak chemical reactivity of a possible C(60)(OH)(24) isomer. To investigate Raman scattering and the vibrational spectra of the different fullerenols, frequency calculations are carried out within the harmonic approximation. In this case a systematic study is only performed for n=1-4, 8, 10, 16, 18, and 24. Our results give good agreements with the expected changes in the spectral absorptions due to the hydroxylation of fullerenes.

Low nanomolar concentration of mercury chloride increases vascular reactivity to phenylephrine and local angiotensin production in rats

Exposure to mercury at nanomolar level affects cardiac function but its effects on vascular reactivity have yet to be investigated. Pressor responses to phenylephrine (PHE) were investigated in perfused rat tail arteries before and after treatment with 6 nM HgCl2 during 1 h,,in the presence (E+) and absence (E-) of endothelium, after L-NAME (10(-4) M), indomethacin (10(-5) M), enalaprilate (1 mu M), tempol (1 mu M) and deferoxamine (300 mu M) treatments. HgCl2 increased sensitivity (pD(2)) without modifying the maximum response (Em) to PHE, but the pD(2) increase was abolished after endothelial damage. L-NAME treatment increased pD(2) and Emax. However, in the presence of HgCl2, this increase was smaller, and it did not modify Emax. After indomethacin treatment, the increase of pD(2) induced by HgCl2 was maintained. Enalaprilate, tempol and deferoxamine reversed the increase of pD(2) evoked by HgCl2. HgCl2 increased the angiotensin converting enzyme (ACE) activity explaining the result obtained with enalaprilate. Results suggest that at nanomolar concentrations HgCl2 increase the vascular reactivity to PHE. This response is endothelium mediated and involves the reduction of NO bioavailability and the action of reactive oxygen species. The local ACE participates in mercury actions and depends on the angiotensin 11 generation. (c) 2007 Elsevier Inc. All rights reserved.

Antinociceptive effect of stimulating the occipital or retrosplenial cortex in rats

A role for the occipital or retrosplenial cortex in nociceptive processing has not been demonstrated yet, but connections from these cortices to brain structures involved in descending pain-inhibitory mechanisms were already demonstrated. This study demonstrated that the electrical stimulation of the occipital or retrosplenial cortex produces antinociception in the rat tail-flick and formalin tests. Bilateral lesions of the dorsolateral funiculus abolished the effect of cortical stimulation in the tail-flick test. Injection of glutamate into the same targets was also antinociceptive in the tail-flick test. No rats stimulated in the occipital or retrosplenial cortex showed any change in motor performance on the Rota-rod test, or had epileptiform changes in the EEG recording during or up to 3 hours after stimulation. The antinociception induced by occipital cortex stimulation persisted after neural block of the retrosplenial cortex. The effect of retrosplenial cortex stimulation also persisted after neural block of the occipital cortex. We conclude that stimulation of the occipital or retrosplenial cortex in rats leads to antinociception activating distinct descending pain-inhibitory mechanisms, and this is unlikely to result from a reduced motor performance or a postictal phenomenon. Perspective: This study presents evidence that stimulation of the retrosplenial or occipital cortex produces antinociception in rat models of acute pain. These findings enhance our understanding of the role of the cerebral cortex in control of pain. (C) 2010 by the American Pain Society

A nearly optimum linear-phase digital FIR filters design

A new simple method to design linear-phase finite impulse response (FIR) digital filters, based on the steepest-descent optimization method, is presented in this paper. Starting from the specifications of the desired frequency response and a maximum approximation error a nearly optimum digital filter is obtained. Tests have shown that this method is alternative to other traditional ones such as Frequency Sampling and Parks-McClellan, mainly when other than brick wall frequency response is required as a desired frequency response. (C) 2011 Elsevier Inc. All rights reserved.