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.

Radiative capture of nucleons at astrophysical energies with single-particle states

Radiative capture of nucleons at energies of astrophysical interest is one of the most important processes for nucleosynthesis. The nucleon capture can occur either by a compound nucleus reaction or by a direct process. The compound reaction cross sections are usually very small, especially for light nuclei. The direct capture proceeds either via the formation of a single-particle resonance or a non-resonant capture process. In this work we calculate radiative capture cross sections and astrophysical S-factors for nuclei in the mass region A < 20 using single-particle states. We carefully discuss the parameter fitting procedure adopted in the simplified two-body treatment of the capture process. Then we produce a detailed list of cases for which the model works well. Useful quantities, such as spectroscopic factors and asymptotic normalization coefficients, are obtained and compared to published data. (C) 2010 Elsevier Inc. All rights reserved.

Long-range ozone transport and its impact on respiratory and cardiovascular health in the north of Portugal

Ozone dynamics depend on meteorological characteristics such as wind, radiation, sunshine, air temperature and precipitation. The aim of this study was to determine ozone trajectories along the northern coast of Portugal during the summer months of 2005, when there was a spate of forest fires in the region, evaluating their impact on respiratory and cardiovascular health in the greater metropolitan area of Porto. We investigated the following diseases, as coded in the ninth revision of the International Classification of Diseases: hypertensive disease (codes 401-405); ischemic heart disease (codes 410-414); other cardiac diseases, including heart failure (codes 426-428); chronic obstructive pulmonary disease and allied conditions, including bronchitis and asthma (codes 490-496); and pneumoconiosis and other lung diseases due to external agents (codes 500-507). We evaluated ozone data from air quality monitoring stations in the study area, together with data collected through HYbrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model analysis of air mass circulation and synoptic-scale zonal wind from National Centers for Environmental Prediction data. High ozone levels in rural areas were attributed to the dispersion of pollutants induced by local circulation, as well as by mesoscale and synoptic scale processes. The fires of 2005 increased the levels of pollutants resulting from the direct emission of gases and particles into the atmosphere, especially when there were incoming frontal systems. For the meteorological case studies analyzed, peaks in ozone concentration were positively associated with higher rates of hospital admissions for cardiovascular diseases, although there were no significant associations between ozone peaks and admissions for respiratory diseases.

Finite-size particles, advection, and chaos: A collective phenomenon of intermittent bursting

We consider finite-size particles colliding elastically, advected by a chaotic flow. The collisionless dynamics has a quasiperiodic attractor and particles are advected towards this attractor. We show in this work that the collisions have dramatic effects in the system's dynamics, giving rise to collective phenomena not found in the one-particle dynamics. In particular, the collisions induce a kind of instability, in which particles abruptly spread out from the vicinity of the attractor, reaching the neighborhood of a coexisting chaotic saddle, in an autoexcitable regime. This saddle, not present in the dynamics of a single particle, emerges due to the collective particle interaction. We argue that this phenomenon is general for advected, interacting particles in chaotic flows.

Linear and nonlinear transport in a small charge-tunable open quantum ring

We experimentally study the Aharonov-Bohm-conductance oscillations under external gate voltage in a semiconductor quantum ring with a radius of 80 nm. We find that, in the linear regime, the resistance-oscillation plot in the voltage-magnetic-field plane corresponds to the quantum ring energy spectra. The chessboard pattern assembled by resistance diamonds, while loading the ring, is attributed to a short electron lifetime in the open configuration, which agrees with calculations within the single-particle model. Remarkably, the application of a small dc current allows observing strong deviations in the oscillation plot from this pattern accompanied by a magnetic-field symmetry break. We relate such behavior to the higher-order-conductance coefficients determined by electron-electron interactions in the nonlinear regime.

g factors of coexisting isomeric states in (188)Pb

The g factors of the 12(+), 11(-), and 8(-) isomeric states in (188)Pb were measured using the time-differential perturbed angular distribution method as g(12(+)) = -0.179(6), g(11(-)) = +1.03(3), and g(8(-)) = -0.037(7). The g factor of the 12(+) state follows the observed slight down-sloping evolution of the g factors of the i(13/2)(2) neutron spherical states with decreasing N. The g factors of the 11(-) and 8(-) isomers proposed as oblate and prolate deformed states, respectively, were interpreted within the rotational model, using calculated and empirical g factor values for the involved single-particle orbitals.

Artificial molecular quantum rings under magnetic field influence

The ground states of a few electrons confined in two vertically coupled quantum rings in the presence of an external magnetic field are studied systematically within the current spin-density functional theory. Electron-electron interactions combined with inter-ring tunneling affect the electronic structure and the persistent current. For small values of the external magnetic field, we recover the zero magnetic field molecular quantum ring ground state configurations. Increasing the magnetic field many angular momentum, spin, and isospin transitions are predicted to occur in the ground state. We show that these transitions follow certain rules, which are governed by the parity of the number of electrons, the single-particle picture, Hund's rules, and many-body effects. (C) 2009 American Institute of Physics. [doi:10.1063/1.3223360]

Spectroscopic evidence of extended states in the quantized Hall phase of weakly coupled GaAs/AlGaAs multilayers

The influence of interlayer coupling on the formation of the quantized Hall phase at the filling factor nu=2 was studied in multilayer GaAs/AlGaAs heterostructures. The disorder broadened Gaussian photoluminescence line due to localized electrons was found in the quantized Hall phase of the isolated multi-quanturn-well structure. On the other hand, the quantized Hall phase of weakly coupled multilayers emitted an unexpected asymmetrical line similar to that observed in metallic electron systems. We demonstrated that the observed asymmetry is caused by the partial population of extended electron states formed in the insulating quantized Hall phase due to spin-assisted interlayer percolation. A sharp decrease in the single-particle scattering time associated with these extended states was observed for the filling factor nu=2. (C) 2008 American Institute of Physics. [DOI: 10.1063/1.2978194]

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 known 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.

Molecular dynamics simulation of liquid trimethylphosphine

Structural and dynamical properties of liquid trimethylphosphine (TMP), (CH(3))(3)P, as a function of temperature is investigated by molecular dynamics (MD) simulations. The force field used in the MD simulations, which has been proposed from molecular mechanics and quantum chemistry calculations, is able to reproduce the experimental density of liquid TMP at room temperature. Equilibrium structure is investigated by the usual radial distribution function, g(r), and also in the reciprocal space by the static structure factor, S(k). On the basis of center of mass distances, liquid TMP behaves like a simple liquid of almost spherical particles, but orientational correlation due to dipole-dipole interactions is revealed at short-range distances. Single particle and collective dynamics are investigated by several time correlation functions. At high temperatures, diffusion and reorientation occur at the same time range as relaxation of the liquid structure. Decoupling of these dynamic properties starts below ca. 220 K, when rattling dynamics of a given TMP molecules due to the cage effect of neighbouring molecules becomes important. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3624408]

Evaluation of somatic cell count thresholds to detect subclinical mastitis in Gyr cows

The objectives of this study were (1) to determine the sensitivity (Se) and specificity (Sp) of somatic cell count (SCC) thresholds to identify subclinical mastitis in Gyr cows caused by major and minor pathogens; (2) to study the effects of month of sampling, rear or front mammary quarters, herd, intramammary infection (IMI), and bacterial species on SCC at quarter level; and (3) to describe the prevalence of IMI in Gyr cows in commercial dairy herds. In total, 221 lactating Gyr cows from 3 commercial dairy farms were selected. Milk samples were collected from individual quarters once a month for 1 yr from all lactating cows for SCC and bacteriological analysis. Mammary quarters were considered the experimental units and the SCC results were log(10)-transformed. Four SCC thresholds (100, 200, 300 and 400 x 10(3) cells/mL) were used to determine Se and Sp to identify infected mammary quarters. The overall prevalence of IMI in quarter milk samples of Gyr cows was 49.8%, and the prevalence of minor pathogens was higher (31.9%) than that of major pathogens (17.8%). Quarter samples with microbial isolation presented higher SCC compared with negative samples. Sensitivity and Sp of selected SCC thresholds varied according to the group of pathogen (major and minor) involved in the IMI definition. Sensitivity increased and Sp decreased when mammary quarters with only major pathogens isolation were considered positive. The use of a single SCC analysis to classify quarters as uninfected or infected in Gyr cows may not be a useful test for this breed because Se and Sp of SCC at the studied thresholds were low. The occurrence of IMI and the bacterial species are the main factors responsible for SCC variation in mammary quarters of Gyr cows. Milk samples with major pathogens isolation elicited higher SCC than those with minor pathogens.

PL spectroscopy of Fermi electrons in regime of the quantum Hall effect

The influence of the interlayer coupling on formation of the quantized Hall phase at the filling factor v = 2 was studied in the multilayer GaAs/AlGaAs heterostructures The disorder broaden Gaussian photoluminescence line due to the localized electrons was found in the quantized Hall phase of the isolated multi-quantum well structure On the other hand. the quantized Hall phase of the weakly-coupled multilayers emitted an asymmetrical line similar to that one observed in the metallic electron systems. We demonstrated that the observed asymmetry indicates a formation of the Fermi Surface in the quantized Hall phase of the multilayer electron system due to the interlayer peicolation. A sharp decrease of the single-particle scattering time associated with the extended states oil the Fermi surface was observed at the filling factor v = 2. (C) 2009 Elsevier B.V All rights reserved

Spectroscopic evidence of extended states in quantized Hall phase of weakly coupled GaAs/AlGaAs multi-layers

The influence of the interlayer coupling on formation of the quantized Hall conductor phase at the filling factor v = 2 was studied in the multi-layer GaAs/AlGaAs heterostructures. The disorder broadened Gaussian photoluminescence line due to the localized electrons was found in the quantized Hall phase of the isolated multi-quantum well structure. On the other hand, the quantized Hall phase of the weakly coupled multi-layers emitted an unexpected asymmetrical line similar to that one observed in the metallic electron systems. We demonstrated that the observed asymmetry is caused by a partial population of the extended electron states formed in the quantized Hall conductor phase due to the interlayer percolation. A sharp decrease of the single-particle scattering time associated with these extended states was observed at the filling factor v = 2. (c) 2007 Elsevier B.V. All rights reserved.

Dependence of Response Functions and Orbital Functionals on Occupation Numbers

Explicitly orbital-dependent approximations to the exchange-correlation energy functional of density functional theory typically not only depend on the single-particle Kohn-Sham orbitals but also on their occupation numbers in the ground-state Slater determinant. The variational calculation of the corresponding exchange-correlation potentials with the optimized effective potential (OEP) method therefore also requires a variation of the occupation numbers with respect to a variation in the effective single-particle potential, which is usually not taken into account. Here it is shown under which circumstances this procedure is justified.

Orbital-polarization terms: From a phenomenological to a first-principles description of orbital magnetism in density-functional theory

Phenomenological orbital-polarizition (OP) terms have been repeatedly introduced in the single-particle equations of spin-density-functional theory, in order to improve the description of orbital magnetic moments in systems containing transition metal ions. Here we show that these ad hoc corrections can be interpreted as approximations to the exchange-correlation vector potential A(xc) of current-density functional theory (CDFT). This connection provides additional information on both approaches: phenomenological OP terms are connected to first-principles theory, leading to a rationale for their empirical success and a reassessment of their limitations and the approximations made in their derivation. Conversely, the connection of OP terms with CDFT leads to a set of simple approximations to the CDFT potential A(xc), with a number of desirable features that are absent from electron-gas-based functionals. (C) 2008 Wiley Periodicals, Inc.