A density functional perturbative approach for simple fluids: the structure of a nonuniform Lennard-Jones fluid at interfaces

International Nuclear Information System (INIS)

Kim, Soon-Chul; Lee, Song Hi

2004-01-01

A density functional perturbation approximation (DFPT), which is based both on the fundamental-measure theory (FMT) to the hard-sphere repulsion and on the weighted-density approximations (WDAs) to the attractive contribution, has been proposed for studying the structural properties of model fluids with an attractive part of the potential. The advantage of the present theory is the simplicity of the calculation of the weight function due to the attractive contribution. It has been applied to predict the equilibrium particle density distributions and adsorption isotherms of Lennard-Jones fluids at interfaces. The theoretical results show that the present theory describes quite well the adsorption isotherms of a Lennard-Jones ethane in a graphite slit pore as well as the equilibrium particle density distributions of a Lennard-Jones fluid near a planar slit pore

Analytic derivatives for perturbatively corrected ''double hybrid'' density functionals: Theory, implementation, and applications

International Nuclear Information System (INIS)

Neese, Frank; Schwabe, Tobias; Grimme, Stefan

2007-01-01

A recently proposed new family of density functionals [S. Grimme, J. Chem. Phys. 124, 34108 (2006)] adds a fraction of nonlocal correlation as a new ingredient to density functional theory (DFT). This fractional correlation energy is calculated at the level of second-order many-body perturbation theory (PT2) and replaces some of the semilocal DFT correlation of standard hybrid DFT methods. The new ''double hybrid'' functionals (termed, e.g., B2-PLYP) contain only two empirical parameters that have been adjusted in thermochemical calculations on parts of the G2/3 benchmark set. The methods have provided the lowest errors ever obtained by any DFT method for the full G3 set of molecules. In this work, the applicability of the new functionals is extended to the exploration of potential energy surfaces with analytic gradients. The theory of the analytic gradient largely follows the standard theory of PT2 gradients with some additional subtleties due to the presence of the exchange-correlation terms in the self-consistent field operator. An implementation is reported for closed-shell as well as spin-unrestricted reference determinants. Furthermore, the implementation includes external point charge fields and also accommodates continuum solvation models at the level of the conductor like screening model. The density fitting resolution of the identity (RI) approximation can be applied to the evaluation of the PT2 part with large gains in computational efficiency. For systems with ∼500-600 basis functions the evaluation of the double hybrid gradient is approximately four times more expensive than the calculation of the standard hybrid DFT gradient. Extensive test calculations are provided for main group elements and transition metal containing species. The results reveal that the B2-PLYP functional provides excellent molecular geometries that are superior compared to those from standard DFT and MP2

Linear theory of density perturbations in a neutrino+baryon universe

International Nuclear Information System (INIS)

Wasserman, I.

1981-01-01

Various aspects of the linear theory of density perturbations in a universe containing a significant population of massive neutrinos are calculated. Because linear perturbations in the neutrino density are subject to nonviscous damping on length scales smaller than the effective neutrino Jeans length, the fluctuation spectrum of the neutrino density perturbations just after photon decoupling is expected to peak near the maximum neutrino Jeans mass. The gravitational effects of nonneutrino species are included in calculating the maximum neutrino Jeans mass, which is found to be [M/sub J/(t)]/sub max/approx.10 17 M/sub sun//[m/sub ν/(eV)] 2 , about an order of magnitude smaller than is obtained when nonneutrino species are ignored. An explicit expression for the nonviscous damping of neutrino density perturbations less massive than the maximum neutrino Jeans mass is derived. The linear evolution of density perturbations after photon decoupling is discussed. Of particular interest is the possibility that fluctuations in the neutrino density induce baryon density perturbations after photon decoupling and that the maximum neutrino Jeans determines the characteristic bound mass of galaxy clusters

New mechanism for generating density perturbations from inflation

International Nuclear Information System (INIS)

Dvali, Gia; Gruzinov, Andrei; Zaldarriaga, Matias

2004-01-01

We propose a new mechanism to generate density perturbations in inflationary models. Spatial fluctuations in the decay rate of the inflaton field to ordinary matter lead to fluctuations in the reheating temperature. We argue that in most realistic models of inflation the coupling of the inflaton to normal matter is determined by the vacuum expectation values of fields in the theory. If those fields are light during inflation (this is a generic situation in the minimal models of supersymmetric inflation) they will fluctuate leading to density perturbations through the proposed mechanism. We show that these fluctuations could easily dominate over the ones generated through the standard mechanism. The new scenario has several consequences for inflation model building and observations. The proposed mechanism allows us to generate the observed level of density perturbations with a much lower scale of inflation and thus generically predicts a smaller level of gravitational waves. The relation between the slope of the spectrum of the produced density perturbations and the potential of the inflaton field is different from the standard relations obtained in the context of slow roll inflation. Because the field responsible for the fluctuations is not the inflaton, it can have significantly larger self-couplings and thus density perturbations could be non-Gaussian. The non-Gaussianity can be large enough to be detectable by CMB and large scale structure observations

The spectrum of density perturbations in an expanding universe

Science.gov (United States)

Silk, J.

1974-01-01

The basic dynamic equations that govern the evolution of perturbations in a Friedmann-Lemaitre universe are derived. General solutions describing the evolution of adiabatic perturbations in the density of matter are obtained, and the choice of the appropriate initial conditions is examined. The various perturbation modes are compared, and the effects of decoupling on the perturbation spectrum are studied. The scheme used to follow the evolution of density perturbations through decoupling is based on an extension of the Eddington approximation to the radiative transfer equation, and is strictly valid in both optically thick and thin limits.

Hydrogen, oxygen and hydroxyl on porous silicon surface: A joint density-functional perturbation theory and infrared spectroscopy approach

International Nuclear Information System (INIS)

Alfaro, Pedro; Palavicini, Alessio; Wang, Chumin

2014-01-01

Based on the density functional perturbation theory (DFPT), infrared absorption spectra of porous silicon are calculated by using an ordered pore model, in which columns of silicon atoms are removed along the [001] direction and dangling bonds are initially saturated with hydrogen atoms. When these atoms on the pore surface are gradually replaced by oxygen ones, the ab-initio infrared absorption spectra reveal oxygen, hydroxyl, and coupled hydrogen–oxygen vibrational modes. In a parallel way, freestanding porous silicon samples were prepared by using electrochemical etching and they were further thermally oxidized in a dry oxygen ambient. Fourier transform infrared spectroscopy was used to investigate the surface modifications caused by oxygen adsorption. In particular, the predicted hydroxyl and oxygen bound to the silicon pore surface are confirmed. Finally, a global analysis of measured transmittance spectra has been performed by means of a combined DFPT and thin-film optics approach. - Highlights: • The density functional perturbation theory is used to study infrared absorption. • An ordered pore model is used to investigate the oxidation in porous silicon (PSi). • Infrared transmittance spectra of oxidized PSi freestanding samples are measured

Effects of thermal inflation on small scale density perturbations

Energy Technology Data Exchange (ETDEWEB)

Hong, Sungwook E. [School of Physics, Korea Institute for Advanced Study, 85 Hoegiro, Seoul 130-722 (Korea, Republic of); Lee, Hyung-Joo; Lee, Young Jae; Stewart, Ewan D. [Department of Physics, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-338 (Korea, Republic of); Zoe, Heeseung, E-mail: swhong@kias.re.kr, E-mail: ohsk111@kaist.ac.kr, E-mail: noasac@kaist.ac.kr, E-mail: jcap@profstewart.org, E-mail: heezoe@dgist.ac.kr [School of Basic Science, Daegu Gyeongbuk Institute of Science and Technology (DGIST), 333 Techno jungang-daero, Daegu 711-873 (Korea, Republic of)

2015-06-01

In cosmological scenarios with thermal inflation, extra eras of moduli matter domination, thermal inflation and flaton matter domination exist between primordial inflation and the radiation domination of Big Bang nucleosynthesis. During these eras, cosmological perturbations on small scales can enter and re-exit the horizon, modifying the power spectrum on those scales. The largest modified scale, k{sub b}, touches the horizon size when the expansion changes from deflation to inflation at the transition from moduli domination to thermal inflation. We analytically calculate the evolution of perturbations from moduli domination through thermal inflation and evaluate the curvature perturbation on the constant radiation density hypersurface at the end of thermal inflation to determine the late time curvature perturbation. Our resulting transfer function suppresses the power spectrum by a factor 0∼ 5 at k >> k{sub b}, with k{sub b} corresponding to anywhere from megaparsec to subparsec scales depending on the parameters of thermal inflation. Thus, thermal inflation might be constrained or detected by small scale observations such as CMB distortions or 21cm hydrogen line observations.

Perturbation based Monte Carlo criticality search in density, enrichment and concentration

International Nuclear Information System (INIS)

Li, Zeguang; Wang, Kan; Deng, Jingkang

2015-01-01

Highlights: • A new perturbation based Monte Carlo criticality search method is proposed. • The method could get accurate results with only one individual criticality run. • The method is used to solve density, enrichment and concentration search problems. • Results show the feasibility and good performances of this method. • The relationship between results’ accuracy and perturbation order is discussed. - Abstract: Criticality search is a very important aspect in reactor physics analysis. Due to the advantages of Monte Carlo method and the development of computer technologies, Monte Carlo criticality search is becoming more and more necessary and feasible. Existing Monte Carlo criticality search methods need large amount of individual criticality runs and may have unstable results because of the uncertainties of criticality results. In this paper, a new perturbation based Monte Carlo criticality search method is proposed and discussed. This method only needs one individual criticality calculation with perturbation tallies to estimate k eff changing function using initial k eff and differential coefficients results, and solves polynomial equations to get the criticality search results. The new perturbation based Monte Carlo criticality search method is implemented in the Monte Carlo code RMC, and criticality search problems in density, enrichment and concentration are taken out. Results show that this method is quite inspiring in accuracy and efficiency, and has advantages compared with other criticality search methods

Assessing exchange-correlation functionals for elasticity and thermodynamics of α -ZrW2O8 : A density functional perturbation theory study

Science.gov (United States)

Weck, Philippe F.; Kim, Eunja; Greathouse, Jeffery A.; Gordon, Margaret E.; Bryan, Charles R.

2018-04-01

Elastic and thermodynamic properties of negative thermal expansion (NTE) α -ZrW2O8 have been calculated using PBEsol and PBE exchange-correlation functionals within the framework of density functional perturbation theory (DFPT). Measured elastic constants are reproduced within ∼ 2 % with PBEsol and ∼ 6 % with PBE. The thermal evolution of the Grüneisen parameter computed within the quasi-harmonic approximation exhibits negative values below the Debye temperature, consistent with observation. The standard molar heat capacity is predicted to be CP0 = 192.2 and 193.8 J mol-1K-1 with PBEsol and PBE, respectively. These results suggest superior accuracy of DFPT/PBEsol for studying the lattice dynamics, elasticity and thermodynamics of NTE materials.

Effect of Interface Structure on Thermal Boundary Conductance by using First-principles Density Functional Perturbation Theory

Institute of Scientific and Technical Information of China (English)

GAO Xue; ZHANG Yue; SHANG Jia-Xiang

2011-01-01

We choose a Si/Ge interface as a research object to investigate the infiuence of interface disorder on thermal boundary conductance. In the calculations, the diffuse mismatch model is used to study thermal boundary conductance between two non-metallic materials, while the phonon dispersion relationship is calculated by the first-principles density functional perturbation theory. The results show that interface disorder limits thermal transport. The increase of atomic spacing at the interface results in weakly coupled interfaces and a decrease in the thermal boundary conductance. This approach shows a simplistic method to investigate the relationship between microstructure and thermal conductivity.%We choose a Si/Ge interface as a research object to investigate the influence of interface disorder on thermal boundary conductance.In the calculations,the diffuse mismatch model is used to study thermal boundary conductance between two non-metallic materials,while the phonon dispersion relationship is calculated by the first-principles density functional perturbation theory.The results show that interface disorder limits thermal transport.The increase of atomic spacing at the interface results in weakly coupled interfaces and a decrease in the thermal boundary conductance.This approach shows a simplistic method to investigate the relationship between microstructure and thermal conductivity.It is well known that interfaces can play a dominant role in the overall thermal transport characteristics of structures whose length scale is less than the phonon mean free path.When heat flows across an interface between two different materials,there exists a temperature jump at the interface.Thermal boundary conductance (TBC),which describes the efficiency of heat flow at material interfaces,plays an importance role in the transport of thermal energy in nanometerscale devices,semiconductor superlattices,thin film multilayers and nanocrystalline materials.[1

DENSITY PERTURBATION BY ALFVÉN WAVES IN MAGNETO-PLASMA

Energy Technology Data Exchange (ETDEWEB)

Kumar, S.; Moon, Y.-J. [School of Space Research, Kyung Hee University, Yongin, Gyeonggi-Do, 446-701 (Korea, Republic of); Sharma, R. P. [Centre for Energy Studies, Indian Institute of Technology (IIT) Delhi, Hauz Khas, New Delhi, 110016 (India)

2016-12-20

In this article, we attempt to investigate the density perturbations along magnetic field by ponderomotive effects due to inertial Alfvén waves (AWs) in auroral ionosphere. For this study, we take high-frequency inertial AWs (pump) and their nonlinear interactions with low-frequency slow modes of AWs in that region. The dynamical equations representing these wave modes are known as the Zakharov like equation, and are solved numerically. From the results presented here, we notice the density perturbations in the direction of background magnetic fields. We also find that the deepest density cavity is associated with the strongest magnetic fields. The main reason for these nonlinear structures could be the ponderomotive effects due to the pump waves. The amplitude of these density structures varies with time until the modulation instability saturates. From our results, we estimate the amplitude of most intense cavity as ∼15% of the unperturbed plasma number density n {sub 0}, which is consistent with the observations. These density structures could be the locations for particle energizations in this region.

Response functions of cold neutron matter: density, spin and current fluctuations

Energy Technology Data Exchange (ETDEWEB)

Keller, Jochen; Sedrakian, Armen [Institut fuer Theoretische Physik, Goethe-Universitaet, Frankfurt am Main (Germany)

2014-07-01

We study the response of a single-component pair-correlated baryonic Fermi-liquid to density, spin, and their current perturbations. A complete set of response functions is calculated in the low-temperature regime. We derive the spectral functions of collective excitations associated with the density, density-current, spin, and spin-current perturbations. The dispersion relations of density and spin fluctuations are determined and it is shown that the density fluctuations lead to exciton-like undamped bound states, whereas the spin excitations correspond to diffusive modes above the pair-breaking threshold. The contribution of the collective pair-breaking modes to the specific heat of neutron matter at subnuclear densities is computed and is shown to be comparable to that of the degenerate electron gas at not too low temperatures.

On high-order perturbative calculations at finite density

CERN Document Server

Ghisoiu, Ioan; Kurkela, Aleksi; Romatschke, Paul; Säppi, Matias; Vuorinen, Aleksi

2017-01-01

We discuss the prospects of performing high-order perturbative calculations in systems characterized by a vanishing temperature but finite density. In particular, we show that the determination of generic Feynman integrals containing fermionic chemical potentials can be reduced to the evaluation of three-dimensional phase space integrals over vacuum on-shell amplitudes. Applications of these rules will be discussed in the context of the thermodynamics of cold and dense QCD, where it is argued that they facilitate an extension of the Equation of State of cold quark matter to higher perturbative orders.

Multiconfiguration Pair-Density Functional Theory Outperforms Kohn-Sham Density Functional Theory and Multireference Perturbation Theory for Ground-State and Excited-State Charge Transfer.

Science.gov (United States)

Ghosh, Soumen; Sonnenberger, Andrew L; Hoyer, Chad E; Truhlar, Donald G; Gagliardi, Laura

2015-08-11

The correct description of charge transfer in ground and excited states is very important for molecular interactions, photochemistry, electrochemistry, and charge transport, but it is very challenging for Kohn-Sham (KS) density functional theory (DFT). KS-DFT exchange-correlation functionals without nonlocal exchange fail to describe both ground- and excited-state charge transfer properly. We have recently proposed a theory called multiconfiguration pair-density functional theory (MC-PDFT), which is based on a combination of multiconfiguration wave function theory with a new type of density functional called an on-top density functional. Here we have used MC-PDFT to study challenging ground- and excited-state charge-transfer processes by using on-top density functionals obtained by translating KS exchange-correlation functionals. For ground-state charge transfer, MC-PDFT performs better than either the PBE exchange-correlation functional or CASPT2 wave function theory. For excited-state charge transfer, MC-PDFT (unlike KS-DFT) shows qualitatively correct behavior at long-range with great improvement in predicted excitation energies.

Are both symmetric and buckled dimers on Si(100) minima? Density functional and multireference perturbation theory calculations

International Nuclear Information System (INIS)

Jung, Yousung; Shao, Yihan; Gordon, Mark S.; Doren, Douglas J.; Head-Gordon, Martin

2003-01-01

We report a spin-unrestricted density functional theory (DFT) solution at the symmetric dimer structure for cluster models of Si(100). With this solution, it is shown that the symmetric structure is a minimum on the DFT potential energy surface, although higher in energy than the buckled structure. In restricted DFT calculations the symmetric structure is a saddle point connecting the two buckled minima. To further assess the effects of electron correlation on the relative energies of symmetric versus buckled dimers on Si(100), multireference second order perturbation theory (MRMP2) calculations are performed on these DFT optimized minima. The symmetric structure is predicted to be lower in energy than the buckled structure via MRMP2, while the reverse order is found by DFT. The implications for recent experimental interpretations are discussed

The anisotropy of the cosmic background radiation from local dynamic density perturbations

International Nuclear Information System (INIS)

Dyer, C.C.; Ip, P.S.S.

1988-01-01

Contrary to the usual assumption, it is shown here that the anisotropy of the cosmic background radiation need not be dominated by perturbations at the last scattering surface. The results of computer simulations are shown in which local dynamic density perturbations, in the form of Swiss cheese holes with finite, uniform density central lumps, are the main source of anisotropy of the cosmic background radiation. (author)

Generation of density perturbations by inflation in scalar-tensor gravity theories

Science.gov (United States)

Seshadri, T. R.

1992-02-01

Density perturbations arising out of the quantum fluctuations in a Brans-Dicke field in the context of extended inflation have been studied. We have used a model in which the Brans-Dicke parameter varies with time. We find that the density perturbations are large in magnitude and have a scale invariant spectrum. The origin of these is discussed and it is shown that these place further constraints on the model. Address after 15 Octobr 1991: Department of Physics and Astrophysics, University of Delhi 110 007, India.

Nuclear energy density functional from chiral pion-nucleon dynamics revisited

OpenAIRE

Kaiser, N.; Weise, W.

2009-01-01

We use a recently improved density-matrix expansion to calculate the nuclear energy density functional in the framework of in-medium chiral perturbation theory. Our calculation treats systematically the effects from $1\\pi$-exchange, iterated $1\\pi$-exchange, and irreducible $2\\pi$-exchange with intermediate $\\Delta$-isobar excitations, including Pauli-blocking corrections up to three-loop order. We find that the effective nucleon mass $M^*(\\rho)$ entering the energy density functional is iden...

On high-order perturbative calculations at finite density

Energy Technology Data Exchange (ETDEWEB)

Ghişoiu, Ioan, E-mail: ioan.ghisoiu@helsinki.fi [Helsinki Institute of Physics and Department of Physics, University of Helsinki (Finland); Gorda, Tyler, E-mail: tyler.gorda@helsinki.fi [Helsinki Institute of Physics and Department of Physics, University of Helsinki (Finland); Department of Physics, University of Colorado Boulder, Boulder, CO (United States); Kurkela, Aleksi, E-mail: aleksi.kurkela@cern.ch [Theoretical Physics Department, CERN, Geneva (Switzerland); Faculty of Science and Technology, University of Stavanger, Stavanger (Norway); Romatschke, Paul, E-mail: paul.romatschke@colorado.edu [Department of Physics, University of Colorado Boulder, Boulder, CO (United States); Center for Theory of Quantum Matter, University of Colorado, Boulder, CO (United States); Säppi, Matias, E-mail: matias.sappi@helsinki.fi [Helsinki Institute of Physics and Department of Physics, University of Helsinki (Finland); Vuorinen, Aleksi, E-mail: aleksi.vuorinen@helsinki.fi [Helsinki Institute of Physics and Department of Physics, University of Helsinki (Finland)

2017-02-15

We discuss the prospects of performing high-order perturbative calculations in systems characterized by a vanishing temperature but finite density. In particular, we show that the determination of generic Feynman integrals containing fermionic chemical potentials can be reduced to the evaluation of three-dimensional phase space integrals over vacuum on-shell amplitudes — a result reminiscent of a previously proposed “naive real-time formalism” for vacuum diagrams. Applications of these rules are discussed in the context of the thermodynamics of cold and dense QCD, where it is argued that they facilitate an extension of the Equation of State of cold quark matter to higher perturbative orders.

Perturbation theory of the quark-gluon plasma at finite temperature and baryon number density

International Nuclear Information System (INIS)

Anon.

1984-01-01

At very high energy densities, hadronic matter becomes an almost ideal gas of quarks and gluons. In these circumstances, the effects of particle interactions are small, and to some order in perturbation theory are computable by methods involving weak coupling expansions. To illustrate the perturbative methods which may be used to compute the thermodynamic potential, the results and methods which are employed to compute to first order in α/sub s/ are reviewed. The problem of the plasmon effect, and the necessity of using non-perturbative methods when going beyond first order in α/sub s/ in evaluating the thermodynamic potential are discussed. The results at zero temperature and finite baryon number density to second order in α/sub s/ are also reviewed. The method of renormalization group improving the weak coupling expansions by replacing the expansion by an expansion in a temperature and baryon number density dependent coupling which approaches zero at high energy densities is discussed. Non-perturbative effects such as instantons are briefly mentioned and the breakdown of perturbation theory for the thermodynamical at order α/sub s/ 3 for finite temperature is presented

Bond breaking and bond formation: how electron correlation is captured in many-body perturbation theory and density-functional theory.

Science.gov (United States)

Caruso, Fabio; Rohr, Daniel R; Hellgren, Maria; Ren, Xinguo; Rinke, Patrick; Rubio, Angel; Scheffler, Matthias

2013-04-05

For the paradigmatic case of H(2) dissociation, we compare state-of-the-art many-body perturbation theory in the GW approximation and density-functional theory in the exact-exchange plus random-phase approximation (RPA) for the correlation energy. For an unbiased comparison and to prevent spurious starting point effects, both approaches are iterated to full self-consistency (i.e., sc-RPA and sc-GW). The exchange-correlation diagrams in both approaches are topologically identical, but in sc-RPA they are evaluated with noninteracting and in sc-GW with interacting Green functions. This has a profound consequence for the dissociation region, where sc-RPA is superior to sc-GW. We argue that for a given diagrammatic expansion, sc-RPA outperforms sc-GW when it comes to bond breaking. We attribute this to the difference in the correlation energy rather than the treatment of the kinetic energy.

Density-functional theory in one dimension for contact-interacting fermions

International Nuclear Information System (INIS)

Magyar, R.J.; Burke, K.

2004-01-01

A density-functional theory is developed for fermions in one dimension, interacting via a δ function. Such systems provide a natural testing ground for questions of principle, as the local-density approximation should be highly accurate since for this interaction type the exchange contribution to the local-density approximation is intrinsically self-interaction-free. The exact-exchange contribution to the total energy is a local functional of the density. A local-density approximation for correlation is obtained using perturbation theory and Bethe ansatz results for the one-dimensional contact-interacting uniform Fermi gas. The ground-state energies are calculated for two finite systems, the analogs of helium and of Hooke's atom. The local-density approximation is shown to be excellent as expected

Density functional theory of the electrical double layer: the RFD functional

International Nuclear Information System (INIS)

Gillespie, Dirk; Valisko, Monika; Boda, Dezso

2005-01-01

Density functional theory (DFT) of electrolytes is applied to the electrical double layer under a wide range of conditions. The ions are charged, hard spheres of different size and valence, and the wall creating the double layer is uncharged, weakly charged, and strongly charged. Under all conditions, the density and electrostatic potential profiles calculated using the recently proposed RFD electrostatic functional (Gillespie et al 2002 J. Phys.: Condens. Matter 14 12129; 2003 Phys. Rev. E 68 031503) compare well to Monte Carlo simulations. When the wall is strongly charged, the RFD functional results agree with the results of a simpler perturbative electrostatic DFT, but the two functionals' results qualitatively disagree when the wall is uncharged or weakly charged. The RFD functional reproduces these phenomena of weakly charged double layers. It also reproduces bulk thermodynamic quantities calculated from pair correlation functions

Doppler reflectometry for the investigation of poloidally propagating density perturbations

International Nuclear Information System (INIS)

Hirsch, M.; Baldzuhn, J.; Kurzan, B.; Holzhauer, E.

1999-01-01

A modification of microwave reflectometry is discussed where the direction of observation is tilted with respect to the normal onto the reflecting surface. The experiment is similar to scattering where a finite resolution in k-space exists but keeps the radial localization of reflectometry. The observed poloidal wavenumber is chosen by Bragg's condition via the tilt angle and the resolution in k-space is determined by the antenna pattern. From the Doppler shift of the reflected wave the poloidal propagation velocity of density perturbations is obtained. The diagnostic capabilities of Doppler reflectometry are investigated using full wave code calculations. The method offers the possibility to observe changes in the poloidal propagation velocity of density perturbations and their radial shear with a temporal resolution of about 10μs. (authors)

Screening in weakly ionized dusty plasmas; effect of dust density perturbations

International Nuclear Information System (INIS)

Tolias, P.; Ratynskaia, S.

2013-01-01

The screening of the charge of a non-emitting dust grain immersed in a weakly ionized dusty plasma is studied on the basis of a self-consistent hydrodynamic description. The dust number density is considered large enough so that the test grain is not isolated from other grains and dust collective effects are important. Not only dust charge perturbations but also dust density perturbations are taken into account, the latter are shown to have a strong effect on both the short and long range part of the potential. The realization of collective attraction via the newly obtained potential is discussed, a mechanism that could be central to the understanding of phase-transitions and self-organization processes in dusty plasmas.

Efficient perturbation theory to improve the density matrix renormalization group

Science.gov (United States)

Tirrito, Emanuele; Ran, Shi-Ju; Ferris, Andrew J.; McCulloch, Ian P.; Lewenstein, Maciej

2017-02-01

The density matrix renormalization group (DMRG) is one of the most powerful numerical methods available for many-body systems. It has been applied to solve many physical problems, including the calculation of ground states and dynamical properties. In this work, we develop a perturbation theory of the DMRG (PT-DMRG) to greatly increase its accuracy in an extremely simple and efficient way. Using the canonical matrix product state (MPS) representation for the ground state of the considered system, a set of orthogonal basis functions {| ψi> } is introduced to describe the perturbations to the ground state obtained by the conventional DMRG. The Schmidt numbers of the MPS that are beyond the bond dimension cutoff are used to define these perturbation terms. The perturbed Hamiltonian is then defined as H˜i j= ; its ground state permits us to calculate physical observables with a considerably improved accuracy compared to the original DMRG results. We benchmark the second-order perturbation theory with the help of a one-dimensional Ising chain in a transverse field and the Heisenberg chain, where the precision of the DMRG is shown to be improved O (10 ) times. Furthermore, for moderate L the errors of the DMRG and PT-DMRG both scale linearly with L-1 (with L being the length of the chain). The linear relation between the dimension cutoff of the DMRG and that of the PT-DMRG at the same precision shows a considerable improvement in efficiency, especially for large dimension cutoffs. In the thermodynamic limit we show that the errors of the PT-DMRG scale with √{L-1}. Our work suggests an effective way to define the tangent space of the ground-state MPS, which may shed light on the properties beyond the ground state. This second-order PT-DMRG can be readily generalized to higher orders, as well as applied to models in higher dimensions.

Second-order perturbation theory with a density matrix renormalization group self-consistent field reference function: theory and application to the study of chromium dimer.

Science.gov (United States)

Kurashige, Yuki; Yanai, Takeshi

2011-09-07

We present a second-order perturbation theory based on a density matrix renormalization group self-consistent field (DMRG-SCF) reference function. The method reproduces the solution of the complete active space with second-order perturbation theory (CASPT2) when the DMRG reference function is represented by a sufficiently large number of renormalized many-body basis, thereby being named DMRG-CASPT2 method. The DMRG-SCF is able to describe non-dynamical correlation with large active space that is insurmountable to the conventional CASSCF method, while the second-order perturbation theory provides an efficient description of dynamical correlation effects. The capability of our implementation is demonstrated for an application to the potential energy curve of the chromium dimer, which is one of the most demanding multireference systems that require best electronic structure treatment for non-dynamical and dynamical correlation as well as large basis sets. The DMRG-CASPT2/cc-pwCV5Z calculations were performed with a large (3d double-shell) active space consisting of 28 orbitals. Our approach using large-size DMRG reference addressed the problems of why the dissociation energy is largely overestimated by CASPT2 with the small active space consisting of 12 orbitals (3d4s), and also is oversensitive to the choice of the zeroth-order Hamiltonian. © 2011 American Institute of Physics

Level density approach to perturbation theory and inverse-energy-weighted sum-rules

International Nuclear Information System (INIS)

Halemane, T.R.

1983-01-01

The terms in the familiar Rayleigh-Schroedinger perturbation series involve eigenvalues and eigenfunctions of the unperturbed operator. A level density formalism, that does not involve computation of eigenvalues and eigenfunctions, is given here for the perturbation series. In the CLT (central limit theorem) limit the expressions take very simple linear forms. The evaluation is in terms of moments and traces of operators and operator products. 3 references

Nuclear energy density functional from chiral pion-nucleon dynamics revisited

Science.gov (United States)

Kaiser, N.; Weise, W.

2010-05-01

We use a recently improved density-matrix expansion to calculate the nuclear energy density functional in the framework of in-medium chiral perturbation theory. Our calculation treats systematically the effects from 1 π-exchange, iterated 1 π-exchange, and irreducible 2 π-exchange with intermediate Δ-isobar excitations, including Pauli-blocking corrections up to three-loop order. We find that the effective nucleon mass M(ρ) entering the energy density functional is identical to the one of Fermi-liquid theory when employing the improved density-matrix expansion. The strength F(ρ) of the ( surface-term as provided by the pion-exchange dynamics is in good agreement with that of phenomenological Skyrme forces in the density region ρ/2short-range spin-orbit interaction. The strength function F(ρ) multiplying the square of the spin-orbit density comes out much larger than in phenomenological Skyrme forces and it has a pronounced density dependence.

Current Density Functional Theory Using Meta-Generalized Gradient Exchange-Correlation Functionals.

Science.gov (United States)

Furness, James W; Verbeke, Joachim; Tellgren, Erik I; Stopkowicz, Stella; Ekström, Ulf; Helgaker, Trygve; Teale, Andrew M

2015-09-08

We present the self-consistent implementation of current-dependent (hybrid) meta-generalized gradient approximation (mGGA) density functionals using London atomic orbitals. A previously proposed generalized kinetic energy density is utilized to implement mGGAs in the framework of Kohn-Sham current density functional theory (KS-CDFT). A unique feature of the nonperturbative implementation of these functionals is the ability to seamlessly explore a wide range of magnetic fields up to 1 au (∼235 kT) in strength. CDFT functionals based on the TPSS and B98 forms are investigated, and their performance is assessed by comparison with accurate coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) data. In the weak field regime, magnetic properties such as magnetizabilities and nuclear magnetic resonance shielding constants show modest but systematic improvements over generalized gradient approximations (GGA). However, in the strong field regime, the mGGA-based forms lead to a significantly improved description of the recently proposed perpendicular paramagnetic bonding mechanism, comparing well with CCSD(T) data. In contrast to functionals based on the vorticity, these forms are found to be numerically stable, and their accuracy at high field suggests that the extension of mGGAs to CDFT via the generalized kinetic energy density should provide a useful starting point for further development of CDFT approximations.

Optimized Perturbation Theory for Wave Functions of Quantum Systems

International Nuclear Information System (INIS)

Hatsuda, T.; Tanaka, T.; Kunihiro, T.

1997-01-01

The notion of the optimized perturbation, which has been successfully applied to energy eigenvalues, is generalized to treat wave functions of quantum systems. The key ingredient is to construct an envelope of a set of perturbative wave functions. This leads to a condition similar to that obtained from the principle of minimal sensitivity. Applications of the method to the quantum anharmonic oscillator and the double well potential show that uniformly valid wave functions with correct asymptotic behavior are obtained in the first-order optimized perturbation even for strong couplings. copyright 1997 The American Physical Society

Divergence of perturbation theory in large scale structures

Science.gov (United States)

Pajer, Enrico; van der Woude, Drian

2018-05-01

We make progress towards an analytical understanding of the regime of validity of perturbation theory for large scale structures and the nature of some non-perturbative corrections. We restrict ourselves to 1D gravitational collapse, for which exact solutions before shell crossing are known. We review the convergence of perturbation theory for the power spectrum, recently proven by McQuinn and White [1], and extend it to non-Gaussian initial conditions and the bispectrum. In contrast, we prove that perturbation theory diverges for the real space two-point correlation function and for the probability density function (PDF) of the density averaged in cells and all the cumulants derived from it. We attribute these divergences to the statistical averaging intrinsic to cosmological observables, which, even on very large and "perturbative" scales, gives non-vanishing weight to all extreme fluctuations. Finally, we discuss some general properties of non-perturbative effects in real space and Fourier space.

Density functional theory for polymeric systems in 2D

International Nuclear Information System (INIS)

Słyk, Edyta; Bryk, Paweł; Roth, Roland

2016-01-01

We propose density functional theory for polymeric fluids in two dimensions. The approach is based on Wertheim’s first order thermodynamic perturbation theory (TPT) and closely follows density functional theory for polymers proposed by Yu and Wu (2002 J. Chem. Phys . 117 2368). As a simple application we evaluate the density profiles of tangent hard-disk polymers at hard walls. The theoretical predictions are compared against the results of the Monte Carlo simulations. We find that for short chain lengths the theoretical density profiles are in an excellent agreement with the Monte Carlo data. The agreement is less satisfactory for longer chains. The performance of the theory can be improved by recasting the approach using the self-consistent field theory formalism. When the self-avoiding chain statistics is used, the theory yields a marked improvement in the low density limit. Further improvements for long chains could be reached by going beyond the first order of TPT. (paper)

Use of density functional theory orbitals in the GVVPT2 variant of second-order multistate multireference perturbation theory.

Science.gov (United States)

Hoffmann, Mark R; Helgaker, Trygve

2015-03-05

A new variation of the second-order generalized van Vleck perturbation theory (GVVPT2) for molecular electronic structure is suggested. In contrast to the established procedure, in which CASSCF or MCSCF orbitals are first obtained and subsequently used to define a many-electron model (or reference) space, the use of an orbital space obtained from the local density approximation (LDA) variant of density functional theory is considered. Through a final, noniterative diagonalization of an average Fock matrix within orbital subspaces, quasicanonical orbitals that are otherwise indistinguishable from quasicanonical orbitals obtained from a CASSCF or MCSCF calculation are obtained. Consequently, all advantages of the GVVPT2 method are retained, including use of macroconfigurations to define incomplete active spaces and rigorous avoidance of intruder states. The suggested variant is vetted on three well-known model problems: the symmetric stretching of the O-H bonds in water, the dissociation of N2, and the stretching of ground and excited states C2 to more than twice the equilibrium bond length of the ground state. It is observed that the LDA-based GVVPT2 calculations yield good results, of comparable quality to conventional CASSCF-based calculations. This is true even for the C2 model problem, in which the orbital space for each state was defined by the LDA orbitals. These results suggest that GVVPT2 can be applied to much larger problems than previously accessible.

Application of functional analysis to perturbation theory of differential equations. [nonlinear perturbation of the harmonic oscillator

Science.gov (United States)

Bogdan, V. M.; Bond, V. B.

1980-01-01

The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.

Quantal density functional theory II. Approximation methods and applications

International Nuclear Information System (INIS)

Sahni, Viraht

2010-01-01

This book is on approximation methods and applications of Quantal Density Functional Theory (QDFT), a new local effective-potential-energy theory of electronic structure. What distinguishes the theory from traditional density functional theory is that the electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and the correlation contribution to the kinetic energy -- the Correlation-Kinetic effects -- are separately and explicitly defined. As such it is possible to study each property of interest as a function of the different electron correlations. Approximations methods based on the incorporation of different electron correlations, as well as a many-body perturbation theory within the context of QDFT, are developed. The applications are to the few-electron inhomogeneous electron gas systems in atoms and molecules, as well as to the many-electron inhomogeneity at metallic surfaces. (orig.)

Phase transitions of titanite CaTiSiO5 from density functional perturbation theory

Science.gov (United States)

Malcherek, Thomas; Fischer, Michael

2018-02-01

Phonon dispersion of titanite CaTiSiO5 has been calculated using the variational density functional perturbation theory. The experimentally known out-of-center distortion of the Ti atom is confirmed. The distortion is associated with a Bu mode that is unstable for wave vectors normal to the octahedral chain direction of the C 2 /c aristotype structure. The layer of wave vectors with imaginary mode frequencies also comprises the Brillouin zone boundary point Y (0 ,1 ,0 ) , which is critical for the transition to the P 21/c ground-state structure. The phonon branch equivalent to the imaginary branch of the titanite aristotype is found to be stable in malayaite CaSnSiO5. The unstable phonon mode in titanite leads to the formation of transoriented short and long Ti-O1 bonds. The Ti as well as the connecting O1 atom exhibit strongly anomalous Born effective charges along the octahedral chain direction [001], indicative of the strong covalency in this direction. Accordingly and in contrast to malayaite, LO-TO splitting is very large in titanite. In the C 2 /c phase of titanite, the Ti-O1-Ti distortion chain is disordered with respect to neighboring distortion chains, as all chain configurations are equally unstable along the phonon branch. This result is in agreement with diffuse x-ray scattering in layers normal to the chain direction that is observed at temperatures close to the P 21/c to C 2 /c transition temperature and above. The resulting dynamic chains of correlated Ti displacements are expected to order in two dimensions to yield the P 21/c ground-state structure of titanite.

Non-perturbative construction of the Luttinger-Ward functional

Directory of Open Access Journals (Sweden)

M.Potthoff

2006-01-01

Full Text Available For a system of correlated electrons, the Luttinger-Ward functional provides a link between static thermodynamic quantities on the one hand and single-particle excitations on the other. The functional is useful in deriving several general properties of the system as well as in formulating the thermodynamically consistent approximations. Its original construction, however, is perturbative as it is based on the weak-coupling skeleton-diagram expansion. Here, it is shown that the Luttinger-Ward functional can be derived within a general functional-integral approach. This alternative and non-perturbative approach stresses the fact that the Luttinger-Ward functional is universal for a large class of models.

Spectral zeta function and non-perturbative effects in ABJM Fermi-gas

International Nuclear Information System (INIS)

Hatsuda, Yasuyuki

2015-03-01

The exact partition function in ABJM theory on three-sphere can be regarded as a canonical partition function of a non-interacting Fermi-gas with an unconventional Hamiltonian. All the information on the partition function is encoded in the discrete spectrum of this Hamiltonian. We explain how (quantum mechanical) non-perturbative corrections in the Fermi-gas system appear from a spectral consideration. Basic tools in our analysis are a Mellin-Barnes type integral representation and a spectral zeta function. From a consistency with known results, we conjecture that the spectral zeta function in the ABJM Fermi-gas has an infinite number of ''non-perturbative'' poles, which are invisible in the semi-classical expansion of the Planck constant. We observe that these poles indeed appear after summing up perturbative corrections. As a consequence, the perturbative resummation of the spectral zeta function causes non-perturbative corrections to the grand canonical partition function. We also present another example associated with a spectral problem in topological string theory. A conjectured non-perturbative free energy on the resolved conifold is successfully reproduced in this framework.

Reduced density matrix functional theory at finite temperature

Energy Technology Data Exchange (ETDEWEB)

Baldsiefen, Tim

2012-10-15

Density functional theory (DFT) is highly successful in many fields of research. There are, however, areas in which its performance is rather limited. An important example is the description of thermodynamical variables of a quantum system in thermodynamical equilibrium. Although the finite-temperature version of DFT (FT-DFT) rests on a firm theoretical basis and is only one year younger than its brother, groundstate DFT, it has been successfully applied to only a few problems. Because FT-DFT, like DFT, is in principle exact, these shortcomings can be attributed to the difficulties of deriving valuable functionals for FT-DFT. In this thesis, we are going to present an alternative theoretical description of quantum systems in thermal equilibrium. It is based on the 1-reduced density matrix (1RDM) of the system, rather than on its density and will rather cumbersomly be called finite-temperature reduced density matrix functional theory (FT-RDMFT). Its zero-temperature counterpart (RDMFT) proved to be successful in several fields, formerly difficult to address via DFT. These fields include, for example, the calculation of dissociation energies or the calculation of the fundamental gap, also for Mott insulators. This success is mainly due to the fact that the 1RDM carries more directly accessible ''manybody'' information than the density alone, leading for example to an exact description of the kinetic energy functional. This sparks the hope that a description of thermodynamical systems employing the 1RDM via FT-RDMFT can yield an improvement over FT-DFT. Giving a short review of RDMFT and pointing out difficulties when describing spin-polarized systems initiates our work. We then lay the theoretical framework for FT-RDMFT by proving the required Hohenberg-Kohn-like theorems, investigating and determining the domain of FT-RDMFT functionals and by deriving several properties of the exact functional. Subsequently, we present a perturbative method to

Reduced density matrix functional theory at finite temperature

International Nuclear Information System (INIS)

Baldsiefen, Tim

2012-10-01

Density functional theory (DFT) is highly successful in many fields of research. There are, however, areas in which its performance is rather limited. An important example is the description of thermodynamical variables of a quantum system in thermodynamical equilibrium. Although the finite-temperature version of DFT (FT-DFT) rests on a firm theoretical basis and is only one year younger than its brother, groundstate DFT, it has been successfully applied to only a few problems. Because FT-DFT, like DFT, is in principle exact, these shortcomings can be attributed to the difficulties of deriving valuable functionals for FT-DFT. In this thesis, we are going to present an alternative theoretical description of quantum systems in thermal equilibrium. It is based on the 1-reduced density matrix (1RDM) of the system, rather than on its density and will rather cumbersomly be called finite-temperature reduced density matrix functional theory (FT-RDMFT). Its zero-temperature counterpart (RDMFT) proved to be successful in several fields, formerly difficult to address via DFT. These fields include, for example, the calculation of dissociation energies or the calculation of the fundamental gap, also for Mott insulators. This success is mainly due to the fact that the 1RDM carries more directly accessible ''manybody'' information than the density alone, leading for example to an exact description of the kinetic energy functional. This sparks the hope that a description of thermodynamical systems employing the 1RDM via FT-RDMFT can yield an improvement over FT-DFT. Giving a short review of RDMFT and pointing out difficulties when describing spin-polarized systems initiates our work. We then lay the theoretical framework for FT-RDMFT by proving the required Hohenberg-Kohn-like theorems, investigating and determining the domain of FT-RDMFT functionals and by deriving several properties of the exact functional. Subsequently, we present a perturbative method to iteratively construct

Density perturbations due to the inhomogeneous discrete spatial structure of space-time

International Nuclear Information System (INIS)

Wolf, C.

1998-01-01

For the case that space-time permits an inhomogeneous discrete spatial structure due to varying gravitational fields or a foam-like structure of space-time, it is demonstrated that thermodynamic reasoning implies that matter-density perturbations will arise in the early universe

Gluon and ghost correlation functions of 2-color QCD at finite density

Science.gov (United States)

Hajizadeh, Ouraman; Boz, Tamer; Maas, Axel; Skullerud, Jon-Ivar

2018-03-01

2-color QCD, i. e. QCD with the gauge group SU(2), is the simplest non-Abelian gauge theory without sign problem at finite quark density. Therefore its study on the lattice is a benchmark for other non-perturbative approaches at finite density. To provide such benchmarks we determine the minimal-Landau-gauge 2-point and 3-gluon correlation functions of the gauge sector and the running gauge coupling at finite density. We observe no significant effects, except for some low-momentum screening of the gluons at and above the supposed high-density phase transition.

Discrete state perturbation theory via Green's functions

International Nuclear Information System (INIS)

Rubinson, W.

1975-01-01

The exposition of stationary-state perturbation theory via the Green's function method in Goldberger and Watson's Collision Theory is reworked in a way that makes explicit its mathematical basis. It is stressed that the theory consists of the construction of, and manipulations on, a mathematical identity. The perturbation series fall out of the identity almost immediately. The logical status of the method is commented on

Using projector augmented-wave (PAW) formalism inside the density-functional perturbation theory; L'utilisation du formalisme PAW en theorie de la fonctionnelle de la densite perturbee

Energy Technology Data Exchange (ETDEWEB)

Audouze, Ch

2006-07-01

In condensed matter physics, ab-initio simulation allows to get macroscopic quantities (for example equations of state) from microscopic ones, as phonon frequencies which characterize the vibration Eigenmodes of the system. Therefore, one can theoretically predict the behavior of the material at very high pressure conditions, which can be out of reach by experiences. Computations of phonon spectrum are obtained thanks to the linear response theory, where the equations of Density Functional Theory (as the Kohn-Sham model) are perturbed around their fundamental state. The linear response functionality is one of the options included in the ABINIT code, which is an open source package developed in particular by a team of the CEA-DAM (DPTA) and the Catholic University of Louvain-la-Neuve (Belgium). Nevertheless, in spite of using pseudopotentials, computations of phonon spectrum are not tractable for heavy chemical elements, even on massively parallel computers. In order to overcome this difficulty, the linear response theory had to be extended to the PAW (Projector Augmented-Waves) formalism. In this CEA report, we first detail the PAW model, giving to it a more mathematical framework. Then we establish the linear response equations within the PAW formalism, up to the third order derivative of the total energy, for an isolated molecular system and for generic perturbations. Lastly, all these results are specified to the particular case of atom displacements and for perturbations associated to the change of an external potential in which the molecule is set. (author)

Statistics of Smoothed Cosmic Fields in Perturbation Theory. I. Formulation and Useful Formulae in Second-Order Perturbation Theory

Science.gov (United States)

Matsubara, Takahiko

2003-02-01

We formulate a general method for perturbative evaluations of statistics of smoothed cosmic fields and provide useful formulae for application of the perturbation theory to various statistics. This formalism is an extensive generalization of the method used by Matsubara, who derived a weakly nonlinear formula of the genus statistic in a three-dimensional density field. After describing the general method, we apply the formalism to a series of statistics, including genus statistics, level-crossing statistics, Minkowski functionals, and a density extrema statistic, regardless of the dimensions in which each statistic is defined. The relation between the Minkowski functionals and other geometrical statistics is clarified. These statistics can be applied to several cosmic fields, including three-dimensional density field, three-dimensional velocity field, two-dimensional projected density field, and so forth. The results are detailed for second-order theory of the formalism. The effect of the bias is discussed. The statistics of smoothed cosmic fields as functions of rescaled threshold by volume fraction are discussed in the framework of second-order perturbation theory. In CDM-like models, their functional deviations from linear predictions plotted against the rescaled threshold are generally much smaller than that plotted against the direct threshold. There is still a slight meatball shift against rescaled threshold, which is characterized by asymmetry in depths of troughs in the genus curve. A theory-motivated asymmetry factor in the genus curve is proposed.

δ'-function perturbations and Neumann boundary-conditions by path integration

International Nuclear Information System (INIS)

Grosche, C.

1994-02-01

δ'-function perturbations and Neumann boundary conditions are incorporated into the path integral formalism. The starting point is the consideration of the path integral representation for the one dimensional Dirac particle together with a relativistic point interaction. The non-relativistic limit yields either a usual δ-function or a δ'-function perturbation; making their strengths infinitely repulsive one obtains Dirichlet, respectively Neumann boundary conditions in the path integral. (orig.)

Numerical stochastic perturbation theory in the Schroedinger functional

International Nuclear Information System (INIS)

Brambilla, Michele; Di Renzo, Francesco; Hesse, Dirk; Dalla Brida, Mattia; Sint, Stefan; Deutsches Elektronen-Synchrotron

2013-11-01

The Schroedinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the fact that perturbative calculations quickly become cumbersome with the inclusion of higher orders in the gauge coupling and hence the use of an automated perturbation theory framework is desirable. We present the implementation of the SF in numerical stochastic perturbation theory (NSPT) and compare first results for the running coupling at two loops in pure SU(3) Yang-Mills theory with the literature.

Numerical stochastic perturbation theory in the Schroedinger functional

Energy Technology Data Exchange (ETDEWEB)

Brambilla, Michele; Di Renzo, Francesco; Hesse, Dirk [Parma Univ. (Italy); INFN, Parma (Italy); Dalla Brida, Mattia [Trinity College Dublin (Ireland). School of Mathematics; Sint, Stefan [Trinity College Dublin (Ireland). School of Mathematics; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC

2013-11-15

The Schroedinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the fact that perturbative calculations quickly become cumbersome with the inclusion of higher orders in the gauge coupling and hence the use of an automated perturbation theory framework is desirable. We present the implementation of the SF in numerical stochastic perturbation theory (NSPT) and compare first results for the running coupling at two loops in pure SU(3) Yang-Mills theory with the literature.

Adiabatic density perturbations and matter generation from the minimal supersymmetric standard model.

Science.gov (United States)

Enqvist, Kari; Kasuya, Shinta; Mazumdar, Anupam

2003-03-07

We propose that the inflaton is coupled to ordinary matter only gravitationally and that it decays into a completely hidden sector. In this scenario both baryonic and dark matter originate from the decay of a flat direction of the minimal supersymmetric standard model, which is shown to generate the desired adiabatic perturbation spectrum via the curvaton mechanism. The requirement that the energy density along the flat direction dominates over the inflaton decay products fixes the flat direction almost uniquely. The present residual energy density in the hidden sector is typically shown to be small.

The MSW conversion of solar neutrinos and random matter density perturbations

International Nuclear Information System (INIS)

Nunokawa, H.; Rossi, A.; Valle, J.W.F.

1997-01-01

A generalization of the resonant neutrino conversion in matter, including a random component in the matter density profile is presented. The study is focused on the effect of such matter perturbations upon both large and small mixing angle MSW solutions to the solar neutrino problem. This is carried out both for the active-active ν e → ν μ , τ as well as active-sterile ν e → conversion channels. The small mixing MSW solution is much more stable than the large mixing solution has been found. Future solar neutrino experiments, such as Borexino, could probe solar matter density noise at the few percent level

The calculation of isotopic partition function ratios by a perturbation theory technique

International Nuclear Information System (INIS)

Singh, G.; Wolfsberg, M.

1975-01-01

The vibrational Hamiltonian of a molecule in the harmonic approximation, H = (1/2) Σ (g/subi/jp/subi/p/subj/ + f/subi/jq/subi/q/subj/), has been divided into a diagonal part (terms with i=j) and an off-diagonal part (inot-equalj), which is regarded as the perturbation. The vibrational partition function of the molecule is then calculated by Schwinger perturbation theory as the partition function of the unperturbed problem, corresponding to a collection of oscillators with frequencies 2πν/subi/' = (f/subi/ig/subi/i)/sup 1 / 2 /, plus perturbation correction terms which are calculated to second order. With the usual assumptions of isotope effect calculations that the molecular translations and rotations are classical and separable from the vibrations, the perturbation formulation of the vibrational partition function is easily transformed into a perturbation theory formulation of (reduced) isotopic partition function ratios. If, for example, the molecular potential function is expressed in terms of the displacements of bond stretches and bond angle bends from their respective equilibrium values, the unperturbed partition function ratio corresponds to the isotope effect expected for noninteracting bond-stretch and bond-angle-bend oscillators. Detailed comparison is made for a number of molecular systems of perturbation theory calculations of partition functions and isotopic partition function ratios with exact calculations carried out by actually obtaining the normal mode vibrational frequencies of the vibrational Hamiltonian. Good agreement is found. The utility of the perturbation theory formulation resides in the fact that it permits one to look at isotope effects in a very simple manner; some demonstrations are given

Recent progress on perturbative QCD fragmentation functions

International Nuclear Information System (INIS)

Cheung, K.

1995-05-01

The recent development of perturbative QCD (PQCD) fragmentation functions has strong impact on quarkonium production. I shall summarize B c meson production based on these PQCD fragmentation functions, as well as, the highlights of some recent activities on applying these PQCD fragmentation functions to explain anomalous J/ψ and ψ' production at the Tevatron. Finally, I discuss a fragmentation model based on the PQCD fragmentation functions for heavy quarks fragmenting into heavy-light mesons

Assessment of Kohn-Sham density functional theory and Møller-Plesset perturbation theory for ionic liquids.

Science.gov (United States)

Zahn, Stefan; MacFarlane, Douglas R; Izgorodina, Ekaterina I

2013-08-28

We present high-level benchmark calculations of interaction energies of 236 ion pair structures of ionic liquids constituting a new IL-2013 set. 33 different approaches using various basis sets are validated against these benchmark data. Overall, traditional functionals like B3LYP, without an explicit dispersion correction, should be avoided when investigating ionic liquids. We can recommend the third version of Grimme's empirical dispersion correction (DFT-D3) and the LC-BOP functional, as well as most functionals of the Minnesota family of the M0X type. Our results highlight the importance of diffuse basis set functions for the accurate prediction of the IL energetics using any DFT functional. The best combination of reasonable accuracy and reasonable cost was found to be the M06-L functional in combination with the 6-31++G** basis set, producing a remarkable mean absolute deviation of only 4.2 kJ mol(-1) and a maximum deviation of -12.5 kJ mol(-1). Second-order Møller-Plesset perturbation theory (MP2) in combination with counterpoise-corrected triple-ζ basis sets can also be recommended for reliable calculations of energetics of ionic liquids.

Local density approximation for a perturbative equation of state

International Nuclear Information System (INIS)

Astrakharchik, G. E.

2005-01-01

Knowledge of a series expansion of the equation of state provides a deep insight into the physical nature of a quantum system. Starting from a generic 'perturbative' equation of state of a homogeneous ultracold gas we make predictions for the properties of the gas in the presence of harmonic confinement. The local density approximation is used to obtain the chemical potential, total and release energies, Thomas-Fermi size, and density profile of a trapped system in three-, two-, and one-dimensional geometries. The frequencies of the lowest breathing modes are calculated using scaling and sum-rule approaches and could be used in an experiment as a high-precision tool for obtaining the expansion terms of the equation of state. The derived formalism is applied to dilute Bose and Fermi gases in different dimensions and to integrable one-dimensional models. The physical meaning of the expansion terms in a number of systems is discussed

Acoustic wavefield evolution as a function of source location perturbation

KAUST Repository

Alkhalifah, Tariq Ali

2010-12-01

The wavefield is typically simulated for seismic exploration applications through solving the wave equation for a specific seismic source location. The direct relation between the form (or shape) of the wavefield and the source location can provide insights useful for velocity estimation and interpolation. As a result, I derive partial differential equations that relate changes in the wavefield shape to perturbations in the source location, especially along the Earth\\'s surface. These partial differential equations have the same structure as the wave equation with a source function that depends on the background (original source) wavefield. The similarity in form implies that we can use familiar numerical methods to solve the perturbation equations, including finite difference and downward continuation. In fact, we can use the same Green\\'s function to solve the wave equation and its source perturbations by simply incorporating source functions derived from the background field. The solutions of the perturbation equations represent the coefficients of a Taylor\\'s series type expansion of the wavefield as a function of source location. As a result, we can speed up the wavefield calculation as we approximate the wavefield shape for sources in the vicinity of the original source. The new formula introduces changes to the background wavefield only in the presence of lateral velocity variation or in general terms velocity variations in the perturbation direction. The approach is demonstrated on the smoothed Marmousi model.

Alternative separation of exchange and correlation energies in range-separated density-functional perturbation theory

DEFF Research Database (Denmark)

Cornaton, Y.; Stoyanova, A.; Jensen, Hans Jørgen Aagaard

2013-01-01

of the noninteracting Kohn-Sham one. When second-order corrections to the density are neglected, the energy expression reduces to a range-separated double-hybrid (RSDH) type of functional, RSDHf, where "f" stands for "full-range integrals" as the regular full-range interaction appears explicitly in the energy...

Spin theory of the density functional: reduced matrices and density functions

International Nuclear Information System (INIS)

Pavlov, R.; Delchev, Y.; Pavlova, K.; Maruani, J.

1993-01-01

Expressions for the reduced matrices and density functions of N-fermion systems of arbitrary order s (1<=s<=N) are derived within the frame of rigorous spin approach to the density functional theory (DFT). Using the local-scale transformation method and taking into account the particle spin it is shown that the reduced matrices and density functions are functionals of the total one-fermion density. Similar dependence is found for the distribution density of s-particle aggregates. Generalization and applicability of DFT to the case of s-particle ensembles and aggregates is discussed. 14 refs

Effect of the nonlocal exchange on the performance of the orbital-dependent correlation functionals from second-order perturbation theory.

Science.gov (United States)

Schweigert, Igor V; Bartlett, Rodney J

2008-09-28

Adding a fraction of the nonlocal exchange operator to the local orbital-dependent exchange potential improves the many-body perturbation expansion based on the Kohn-Sham determinant. The effect of such a hybrid scheme on the performance of the orbital-dependent correlation functional from the second-order perturbation theory (PT2H) is investigated numerically. A small fraction of the nonlocal exchange is often sufficient to ensure the existence of the self-consistent solution for the PT2H potential. In the He and Be atoms, including 37% of the nonlocal exchange leads to the correlation energies and electronic densities that are very close to the exact ones. In molecules, varying the fraction of the nonlocal exchange may result in the PT2H energy closely reproducing the CCSD(T) value; however such a fraction depends on the system and does not always result in an accurate electronic density. We also numerically verify that the "semicanonical" perturbation series includes most of the beneficial effects of the nonlocal exchange without sacrificing the locality of the exchange potential.

Perturbation Theory of the Cosmological Log-Density Field

DEFF Research Database (Denmark)

Wang, Xin; Neyrinck, Mark; Szapudi, István

2011-01-01

, motivating an analytic study of it. In this paper, we develop cosmological perturbation theory for the power spectrum of this field. Our formalism is developed in the context of renormalized perturbation theory, which helps to regulate the convergence behavior of the perturbation series, and of the Taylor...

Restoring the consistency with the contact density theorem of a classical density functional theory of ions at a planar electrical double layer.

Science.gov (United States)

Gillespie, Dirk

2014-11-01

Classical density functional theory (DFT) of fluids is a fast and efficient theory to compute the structure of the electrical double layer in the primitive model of ions where ions are modeled as charged, hard spheres in a background dielectric. While the hard-core repulsive component of this ion-ion interaction can be accurately computed using well-established DFTs, the electrostatic component is less accurate. Moreover, many electrostatic functionals fail to satisfy a basic theorem, the contact density theorem, that relates the bulk pressure, surface charge, and ion densities at their distances of closest approach for ions in equilibrium at a smooth, hard, planar wall. One popular electrostatic functional that fails to satisfy the contact density theorem is a perturbation approach developed by Kierlik and Rosinberg [Phys. Rev. A 44, 5025 (1991)PLRAAN1050-294710.1103/PhysRevA.44.5025] and Rosenfeld [J. Chem. Phys. 98, 8126 (1993)JCPSA60021-960610.1063/1.464569], where the full free-energy functional is Taylor-expanded around a bulk (homogeneous) reference fluid. Here, it is shown that this functional fails to satisfy the contact density theorem because it also fails to satisfy the known low-density limit. When the functional is corrected to satisfy this limit, a corrected bulk pressure is derived and it is shown that with this pressure both the contact density theorem and the Gibbs adsorption theorem are satisfied.

Magnetic exchange couplings from noncollinear perturbation theory: dinuclear CuII complexes.

Science.gov (United States)

Phillips, Jordan J; Peralta, Juan E

2014-08-07

To benchmark the performance of a new method based on noncollinear coupled-perturbed density functional theory [J. Chem. Phys. 138, 174115 (2013)], we calculate the magnetic exchange couplings in a series of triply bridged ferromagnetic dinuclear Cu(II) complexes that have been recently synthesized [Phys. Chem. Chem. Phys. 15, 1966 (2013)]. We find that for any basis-set the couplings from our noncollinear coupled-perturbed methodology are practically identical to those of spin-projected energy-differences when a hybrid density functional approximation is employed. This demonstrates that our methodology properly recovers a Heisenberg description for these systems, and is robust in its predictive power of magnetic couplings. Furthermore, this indicates that the failure of density functional theory to capture the subtle variation of the exchange couplings in these complexes is not simply an artifact of broken-symmetry methods, but rather a fundamental weakness of current approximate density functionals for the description of magnetic couplings.

Fingerprints of primordial universe paradigms as features in density perturbations

International Nuclear Information System (INIS)

Chen Xingang

2011-01-01

Experimentally distinguishing different primordial universe paradigms that lead to the Big Bang model is an outstanding challenge in modern cosmology and astrophysics. We show that a generic type of signals that exist in primordial universe models can be used for such purpose. These signals are induced by tiny oscillations of massive fields and manifest as features in primordial density perturbations. They are capable of recording the time-dependence of the scale factor of the primordial universe, and therefore provide direct evidence for specific paradigm. These signals present special opportunities and challenges for experiments and data analyses.

No difference between mechanical perturbation training with compliant surface and manual perturbation training on knee functional performance after ACL rupture.

Science.gov (United States)

Nawasreh, Zakariya; Logerstedt, David; Failla, Mathew; Snyder-Mackler, Lynn

2017-10-27

Manual perturbation training improves dynamic knee stability and functional performance after anterior cruciate ligament rupture (ACL-rupture). However, it is limited to static standing position and does not allow time-specific perturbations at different phase of functional activities. The purpose of this study was to investigate whether administering mechanical perturbation training including compliant surface provides effects similar to manual perturbation training on knee functional measures after an acute ACL-rupture. Sixteen level I/II athletes with ACL-ruptures participated in this preliminary study. Eight patients received mechanical (Mechanical) and eight subjects received manual perturbation training (Manual). All patients completed a functional testing (isometric quadriceps strength, single-legged hop tests) and patient-reported measures (Knee Outcome Survey-Activities of Daily Living Scale (KOS-ADLS), Global Rating Score (GRS), International Knee Documentation Committee 2000 (IKDC 2000) at pre- and post-training. 2 × 2 ANOVA was used for data analysis. No significant group-by-time interactions were found for all measures (p > 0.18). Main effects of time were found for single hop (Pre-testing: 85.14% ± 21.07; Post-testing: 92.49% ± 17.55), triple hop (Pre-testing: 84.64% ± 14.17; Post-testing: 96.64% ± 11.14), KOS-ADLS (Pre-testing: 81.13% ± 11.12; Post-testing: 88.63% ± 12.63), GRS (Pre-testing: 68.63% ± 15.73; Post-testing: 78.81% ± 13.85), and IKDC 2000 (Pre-testing: 66.66% ± 9.85; Post-testing: 76.05% ± 14.62) (p training using compliant surfaces induce effects similar to manual perturbation training on knee functional performance after acute ACL-rupture. The clinical significance is both modes of training improve patients' functional-performance and limb-to-limb movement symmetry, and enhancing the patients' self-reported of knee functional measures after ACL rupture. Mechanical

Stochastic chaos induced by diffusion processes with identical spectral density but different probability density functions.

Science.gov (United States)

Lei, Youming; Zheng, Fan

2016-12-01

Stochastic chaos induced by diffusion processes, with identical spectral density but different probability density functions (PDFs), is investigated in selected lightly damped Hamiltonian systems. The threshold amplitude of diffusion processes for the onset of chaos is derived by using the stochastic Melnikov method together with a mean-square criterion. Two quasi-Hamiltonian systems, namely, a damped single pendulum and damped Duffing oscillator perturbed by stochastic excitations, are used as illustrative examples. Four different cases of stochastic processes are taking as the driving excitations. It is shown that in such two systems the spectral density of diffusion processes completely determines the threshold amplitude for chaos, regardless of the shape of their PDFs, Gaussian or otherwise. Furthermore, the mean top Lyapunov exponent is employed to verify analytical results. The results obtained by numerical simulations are in accordance with the analytical results. This demonstrates that the stochastic Melnikov method is effective in predicting the onset of chaos in the quasi-Hamiltonian systems.

The chirally rotated Schroedinger functional. Theoretical expectations and perturbative tests

International Nuclear Information System (INIS)

Dalla Brida, Mattia

2016-03-01

The chirally rotated Schroedinger functional (χSF) with massless Wilson-type fermions provides an alternative lattice regularization of the Schroedinger functional (SF), with different lattice symmetries and a common continuum limit expected from universality. The explicit breaking of flavour and parity symmetries needs to be repaired by tuning the bare fermion mass and the coefficient of a dimension 3 boundary counterterm. Once this is achieved one expects the mechanism of automatic O(a) improvement to be operational in the χSF, in contrast to the standard formulation of the SF. This is expected to significantly improve the attainable precision for step-scaling functions of some composite operators. Furthermore, the χSF offers new strategies to determine finite renormalization constants which are traditionally obtained from chiral Ward identities. In this paper we consider a complete set of fermion bilinear operators, define corresponding correlation functions and explain the relation to their standard SF counterparts. We discuss renormalization and O(a) improvement and then use this set-up to formulate the theoretical expectations which follow from universality. Expanding the correlation functions to one-loop order of perturbation theory we then perform a number of non-trivial checks. In the process we obtain the action counterterm coefficients to one-loop order and reproduce some known perturbative results for renormalization constants of fermion bilinears. By confirming the theoretical expectations, this perturbative study lends further support to the soundness of the χSF framework and prepares the ground for non-perturbative applications.

Self-consistent density functional calculation of the image potential at a metal surface

International Nuclear Information System (INIS)

Jung, J; Alvarellos, J E; Chacon, E; GarcIa-Gonzalez, P

2007-01-01

It is well known that the exchange-correlation (XC) potential at a metal surface has an image-like asymptotic behaviour given by -1/4(z-z 0 ), where z is the coordinate perpendicular to the surface. Using a suitable fully non-local functional prescription, we evaluate self-consistently the XC potential with the correct image behaviour for simple jellium surfaces in the range of metallic densities. This allows a proper comparison between the corresponding image-plane position, z 0 , and other related quantities such as the centroid of an induced charge by an external perturbation. As a by-product, we assess the routinely used local density approximation when evaluating electron density profiles, work functions, and surface energies by focusing on the XC effects included in the fully non-local description

Self-consistent density functional calculation of the image potential at a metal surface

Energy Technology Data Exchange (ETDEWEB)

Jung, J [Departamento de Fisica Fundamental, Universidad Nacional de Educacion a Distancia, Apartado 60141, 28080 Madrid (Spain); Alvarellos, J E [Departamento de Fisica Fundamental, Universidad Nacional de Educacion a Distancia, Apartado 60141, 28080 Madrid (Spain); Chacon, E [Instituto de Ciencias de Materiales de Madrid, Consejo Superior de Investigaciones CientIficas, E-28049 Madrid (Spain); GarcIa-Gonzalez, P [Departamento de Fisica Fundamental, Universidad Nacional de Educacion a Distancia, Apartado 60141, 28080 Madrid (Spain)

2007-07-04

It is well known that the exchange-correlation (XC) potential at a metal surface has an image-like asymptotic behaviour given by -1/4(z-z{sub 0}), where z is the coordinate perpendicular to the surface. Using a suitable fully non-local functional prescription, we evaluate self-consistently the XC potential with the correct image behaviour for simple jellium surfaces in the range of metallic densities. This allows a proper comparison between the corresponding image-plane position, z{sub 0}, and other related quantities such as the centroid of an induced charge by an external perturbation. As a by-product, we assess the routinely used local density approximation when evaluating electron density profiles, work functions, and surface energies by focusing on the XC effects included in the fully non-local description.

UV-Vis optoelectronic properties of α-SnWO4: A comparative experimental and density functional theory based study

KAUST Repository

Ziani, Ahmed; Harb, Moussab; Noureldine, Dalal; Takanabe, Kazuhiro

2015-01-01

and density functional perturbation theory using the HSE06 functional. The α-SnWO4 material shows an indirect bandgap of 1.52 eV with high absorption coefficient in the visible-light range (>2 × 105 cm−1). The results show relatively high dielectric constant

Obtaining Hartree-Fock and density functional theory doubly excited states with Car-Parrinello density matrix search

Science.gov (United States)

Liang, Wenkel; Isborn, Christine M.; Li, Xiaosong

2009-11-01

The calculation of doubly excited states is one of the major problems plaguing the modern day excited state workhorse methodology of linear response time dependent Hartree-Fock (TDHF) and density function theory (TDDFT). We have previously shown that the use of a resonantly tuned field within real-time TDHF and TDDFT is able to simultaneously excite both the α and β electrons to achieve the two-electron excited states of minimal basis H2 and HeH+ [C. M. Isborn and X. Li, J. Chem. Phys. 129, 204107 (2008)]. We now extend this method to many electron systems with the use of our Car-Parrinello density matrix search (CP-DMS) with a first-principles fictitious mass method for wave function optimization [X. Li, C. L. Moss, W. Liang, and Y. Feng, J. Chem. Phys. 130, 234115 (2009)]. Real-time TDHF/TDDFT is used during the application of the laser field perturbation, driving the electron density toward the doubly excited state. The CP-DMS method then converges the density to the nearest stationary state. We present these stationary state doubly excited state energies and properties at the HF and DFT levels for H2, HeH+, lithium hydride, ethylene, and butadiene.

Microscopically based energy density functionals for nuclei using the density matrix expansion. II. Full optimization and validation

Science.gov (United States)

Navarro Pérez, R.; Schunck, N.; Dyhdalo, A.; Furnstahl, R. J.; Bogner, S. K.

2018-05-01

in closed-shell nuclei, and the fission barrier of 240Pu. Quantitatively, they perform noticeably better than the more phenomenological Skyrme functionals. Conclusions: The inclusion of higher-order terms in the chiral perturbation expansion seems to produce a systematic improvement in predicting nuclear binding energies while the impact on other observables is not really significant. This result is especially promising since all the fits have been performed at the single-reference level of the energy density functional approach, where important collective correlations such as center-of-mass correction, rotational correction, or zero-point vibrational energies have not been taken into account yet.

Excitation energies from Görling-Levy perturbation theory along the range-separated adiabatic connection

Science.gov (United States)

Rebolini, Elisa; Teale, Andrew M.; Helgaker, Trygve; Savin, Andreas; Toulouse, Julien

2018-06-01

A Görling-Levy (GL)-based perturbation theory along the range-separated adiabatic connection is assessed for the calculation of electronic excitation energies. In comparison with the Rayleigh-Schrödinger (RS)-based perturbation theory this GL-based perturbation theory keeps the ground-state density constant at each order and thus gives the correct ionisation energy at each order. Excitation energies up to first order in the perturbation have been calculated numerically for the helium and beryllium atoms and the hydrogen molecule without introducing any density-functional approximations. In comparison with the RS-based perturbation theory, the present GL-based perturbation theory gives much more accurate excitation energies for Rydberg states but similar excitation energies for valence states.

The P(phi)2 Green's functions; asymptotic perturbation expansion

International Nuclear Information System (INIS)

Dimock, J.

1976-01-01

The real time Green's functions in the P(phi) 2 quantum field theory are infinitely differentiable functions of the coupling constant lambda up to and including lamba=0. It follows that the perturbation series are asymptotic as lambda→0 + . (Auth.)

Range-separated density-functional theory for molecular excitation energies

International Nuclear Information System (INIS)

Rebolini, E.

2014-01-01

Linear-response time-dependent density-functional theory (TDDFT) is nowadays a method of choice to compute molecular excitation energies. However, within the usual adiabatic semi-local approximations, it is not able to describe properly Rydberg, charge-transfer or multiple excitations. Range separation of the electronic interaction allows one to mix rigorously density-functional methods at short range and wave function or Green's function methods at long range. When applied to the exchange functional, it already corrects most of these deficiencies but multiple excitations remain absent as they need a frequency-dependent kernel. In this thesis, the effects of range separation are first assessed on the excitation energies of a partially-interacting system in an analytic and numerical study in order to provide guidelines for future developments of range-separated methods for excitation energy calculations. It is then applied on the exchange and correlation TDDFT kernels in a single-determinant approximation in which the long-range part of the correlation kernel vanishes. A long-range frequency-dependent second-order correlation kernel is then derived from the Bethe-Salpeter equation and added perturbatively to the range-separated TDDFT kernel in order to take into account the effects of double excitations. (author)

Analysis of the Effect of Electron Density Perturbations Generated by Gravity Waves on HF Communication Links

Science.gov (United States)

Fagre, M.; Elias, A. G.; Chum, J.; Cabrera, M. A.

2017-12-01

In the present work, ray tracing of high frequency (HF) signals in ionospheric disturbed conditions is analyzed, particularly in the presence of electron density perturbations generated by gravity waves (GWs). The three-dimensional numerical ray tracing code by Jones and Stephenson, based on Hamilton's equations, which is commonly used to study radio propagation through the ionosphere, is used. An electron density perturbation model is implemented to this code based upon the consideration of atmospheric GWs generated at a height of 150 km in the thermosphere and propagating up into the ionosphere. The motion of the neutral gas at these altitudes induces disturbances in the background plasma which affects HF signals propagation. To obtain a realistic model of GWs in order to analyze the propagation and dispersion characteristics, a GW ray tracing method with kinematic viscosity and thermal diffusivity was applied. The IRI-2012, HWM14 and NRLMSISE-00 models were incorporated to assess electron density, wind velocities, neutral temperature and total mass density needed for the ray tracing codes. Preliminary results of gravity wave effects on ground range and reflection height are presented for low-mid latitude ionosphere.

Intrinsic-density functionals

International Nuclear Information System (INIS)

Engel, J.

2007-01-01

The Hohenberg-Kohn theorem and Kohn-Sham procedure are extended to functionals of the localized intrinsic density of a self-bound system such as a nucleus. After defining the intrinsic-density functional, we modify the usual Kohn-Sham procedure slightly to evaluate the mean-field approximation to the functional, and carefully describe the construction of the leading corrections for a system of fermions in one dimension with a spin-degeneracy equal to the number of particles N. Despite the fact that the corrections are complicated and nonlocal, we are able to construct a local Skyrme-like intrinsic-density functional that, while different from the exact functional, shares with it a minimum value equal to the exact ground-state energy at the exact ground-state intrinsic density, to next-to-leading order in 1/N. We briefly discuss implications for real Skyrme functionals

The effect of random matter density perturbations on the large mixing angle solution to the solar neutrino problem

Science.gov (United States)

Guzzo, M. M.; Holanda, P. C.; Reggiani, N.

2003-08-01

The neutrino energy spectrum observed in KamLAND is compatible with the predictions based on the Large Mixing Angle realization of the MSW (Mikheyev-Smirnov-Wolfenstein) mechanism, which provides the best solution to the solar neutrino anomaly. From the agreement between solar neutrino data and KamLAND observations, we can obtain the best fit values of the mixing angle and square difference mass. When doing the fitting of the MSW predictions to the solar neutrino data, it is assumed the solar matter do not have any kind of perturbations, that is, it is assumed the the matter density monothonically decays from the center to the surface of the Sun. There are reasons to believe, nevertheless, that the solar matter density fluctuates around the equilibrium profile. In this work, we analysed the effect on the Large Mixing Angle parameters when the density matter randomically fluctuates around the equilibrium profile, solving the evolution equation in this case. We find that, in the presence of these density perturbations, the best fit values of the mixing angle and the square difference mass assume smaller values, compared with the values obtained for the standard Large Mixing Angle Solution without noise. Considering this effect of the random perturbations, the lowest island of allowed region for KamLAND spectral data in the parameter space must be considered and we call it very-low region.

UV-Vis optoelectronic properties of α-SnWO4: A comparative experimental and density functional theory based study

KAUST Repository

Ziani, Ahmed

2015-09-03

We report a combined experimental and theoretical study on the optoelectronic properties of α-SnWO4 for UV-Vis excitation. The experimentally measured values for thin films were systematically compared with high-accuracy density functional theory and density functional perturbation theory using the HSE06 functional. The α-SnWO4 material shows an indirect bandgap of 1.52 eV with high absorption coefficient in the visible-light range (>2 × 105 cm−1). The results show relatively high dielectric constant (>30) and weak diffusion properties (large effective masses) of excited carriers.

Multiconfiguration pair-density functional theory: barrier heights and main group and transition metal energetics.

Science.gov (United States)

Carlson, Rebecca K; Li Manni, Giovanni; Sonnenberger, Andrew L; Truhlar, Donald G; Gagliardi, Laura

2015-01-13

Kohn-Sham density functional theory, resting on the representation of the electronic density and kinetic energy by a single Slater determinant, has revolutionized chemistry, but for open-shell systems, the Kohn-Sham Slater determinant has the wrong symmetry properties as compared to an accurate wave function. We have recently proposed a theory, called multiconfiguration pair-density functional theory (MC-PDFT), in which the electronic kinetic energy and classical Coulomb energy are calculated from a multiconfiguration wave function with the correct symmetry properties, and the rest of the energy is calculated from a density functional, called the on-top density functional, that depends on the density and the on-top pair density calculated from this wave function. We also proposed a simple way to approximate the on-top density functional by translation of Kohn-Sham exchange-correlation functionals. The method is much less expensive than other post-SCF methods for calculating the dynamical correlation energy starting with a multiconfiguration self-consistent-field wave function as the reference wave function, and initial tests of the theory were quite encouraging. Here, we provide a broader test of the theory by applying it to bond energies of main-group molecules and transition metal complexes, barrier heights and reaction energies for diverse chemical reactions, proton affinities, and the water dimerization energy. Averaged over 56 data points, the mean unsigned error is 3.2 kcal/mol for MC-PDFT, as compared to 6.9 kcal/mol for Kohn-Sham theory with a comparable density functional. MC-PDFT is more accurate on average than complete active space second-order perturbation theory (CASPT2) for main-group small-molecule bond energies, alkyl bond dissociation energies, transition-metal-ligand bond energies, proton affinities, and the water dimerization energy.

Perturbation theory for BAO reconstructed fields: One-loop results in the real-space matter density field

Science.gov (United States)

Hikage, Chiaki; Koyama, Kazuya; Heavens, Alan

2017-08-01

We compute the power spectrum at one-loop order in standard perturbation theory for the matter density field to which a standard Lagrangian baryonic acoustic oscillation (BAO) reconstruction technique is applied. The BAO reconstruction method corrects the bulk motion associated with the gravitational evolution using the inverse Zel'dovich approximation (ZA) for the smoothed density field. We find that the overall amplitude of one-loop contributions in the matter power spectrum substantially decreases after reconstruction. The reconstructed power spectrum thereby approaches the initial linear spectrum when the smoothed density field is close enough to linear, i.e., the smoothing scale Rs≳10 h-1 Mpc . On smaller Rs, however, the deviation from the linear spectrum becomes significant on large scales (k ≲Rs-1 ) due to the nonlinearity in the smoothed density field, and the reconstruction is inaccurate. Compared with N-body simulations, we show that the reconstructed power spectrum at one-loop order agrees with simulations better than the unreconstructed power spectrum. We also calculate the tree-level bispectrum in standard perturbation theory to investigate non-Gaussianity in the reconstructed matter density field. We show that the amplitude of the bispectrum significantly decreases for small k after reconstruction and that the tree-level bispectrum agrees well with N-body results in the weakly nonlinear regime.

Perturbation theory corrections to the two-particle reduced density matrix variational method.

Science.gov (United States)

Juhasz, Tamas; Mazziotti, David A

2004-07-15

In the variational 2-particle-reduced-density-matrix (2-RDM) method, the ground-state energy is minimized with respect to the 2-particle reduced density matrix, constrained by N-representability conditions. Consider the N-electron Hamiltonian H(lambda) as a function of the parameter lambda where we recover the Fock Hamiltonian at lambda=0 and we recover the fully correlated Hamiltonian at lambda=1. We explore using the accuracy of perturbation theory at small lambda to correct the 2-RDM variational energies at lambda=1 where the Hamiltonian represents correlated atoms and molecules. A key assumption in the correction is that the 2-RDM method will capture a fairly constant percentage of the correlation energy for lambda in (0,1] because the nonperturbative 2-RDM approach depends more significantly upon the nature rather than the strength of the two-body Hamiltonian interaction. For a variety of molecules we observe that this correction improves the 2-RDM energies in the equilibrium bonding region, while the 2-RDM energies at stretched or nearly dissociated geometries, already highly accurate, are not significantly changed. At equilibrium geometries the corrected 2-RDM energies are similar in accuracy to those from coupled-cluster singles and doubles (CCSD), but at nonequilibrium geometries the 2-RDM energies are often dramatically more accurate as shown in the bond stretching and dissociation data for water and nitrogen. (c) 2004 American Institute of Physics.

Brain functional BOLD perturbation modelling for forward fMRI and inverse mapping

Science.gov (United States)

Robinson, Jennifer; Calhoun, Vince

2018-01-01

Purpose To computationally separate dynamic brain functional BOLD responses from static background in a brain functional activity for forward fMRI signal analysis and inverse mapping. Methods A brain functional activity is represented in terms of magnetic source by a perturbation model: χ = χ0 +δχ, with δχ for BOLD magnetic perturbations and χ0 for background. A brain fMRI experiment produces a timeseries of complex-valued images (T2* images), whereby we extract the BOLD phase signals (denoted by δP) by a complex division. By solving an inverse problem, we reconstruct the BOLD δχ dataset from the δP dataset, and the brain χ distribution from a (unwrapped) T2* phase image. Given a 4D dataset of task BOLD fMRI, we implement brain functional mapping by temporal correlation analysis. Results Through a high-field (7T) and high-resolution (0.5mm in plane) task fMRI experiment, we demonstrated in detail the BOLD perturbation model for fMRI phase signal separation (P + δP) and reconstructing intrinsic brain magnetic source (χ and δχ). We also provided to a low-field (3T) and low-resolution (2mm) task fMRI experiment in support of single-subject fMRI study. Our experiments show that the δχ-depicted functional map reveals bidirectional BOLD χ perturbations during the task performance. Conclusions The BOLD perturbation model allows us to separate fMRI phase signal (by complex division) and to perform inverse mapping for pure BOLD δχ reconstruction for intrinsic functional χ mapping. The full brain χ reconstruction (from unwrapped fMRI phase) provides a new brain tissue image that allows to scrutinize the brain tissue idiosyncrasy for the pure BOLD δχ response through an automatic function/structure co-localization. PMID:29351339

Brain functional BOLD perturbation modelling for forward fMRI and inverse mapping.

Science.gov (United States)

Chen, Zikuan; Robinson, Jennifer; Calhoun, Vince

2018-01-01

To computationally separate dynamic brain functional BOLD responses from static background in a brain functional activity for forward fMRI signal analysis and inverse mapping. A brain functional activity is represented in terms of magnetic source by a perturbation model: χ = χ0 +δχ, with δχ for BOLD magnetic perturbations and χ0 for background. A brain fMRI experiment produces a timeseries of complex-valued images (T2* images), whereby we extract the BOLD phase signals (denoted by δP) by a complex division. By solving an inverse problem, we reconstruct the BOLD δχ dataset from the δP dataset, and the brain χ distribution from a (unwrapped) T2* phase image. Given a 4D dataset of task BOLD fMRI, we implement brain functional mapping by temporal correlation analysis. Through a high-field (7T) and high-resolution (0.5mm in plane) task fMRI experiment, we demonstrated in detail the BOLD perturbation model for fMRI phase signal separation (P + δP) and reconstructing intrinsic brain magnetic source (χ and δχ). We also provided to a low-field (3T) and low-resolution (2mm) task fMRI experiment in support of single-subject fMRI study. Our experiments show that the δχ-depicted functional map reveals bidirectional BOLD χ perturbations during the task performance. The BOLD perturbation model allows us to separate fMRI phase signal (by complex division) and to perform inverse mapping for pure BOLD δχ reconstruction for intrinsic functional χ mapping. The full brain χ reconstruction (from unwrapped fMRI phase) provides a new brain tissue image that allows to scrutinize the brain tissue idiosyncrasy for the pure BOLD δχ response through an automatic function/structure co-localization.

Matter density perturbations in modified gravity models with arbitrary coupling between matter and geometry

DEFF Research Database (Denmark)

Nesseris, Savvas

2009-01-01

We consider theories with an arbitrary coupling between matter and gravity and obtain the perturbation equation of matter on subhorizon scales. Also, we derive the effective gravitational constant $G_{eff}$ and two parameters $\\Sigma$ and $\\eta$, which along with the perturbation equation...... of the matter density are useful to constrain the theory from growth factor and weak lensing observations. Finally, we use a completely solvable toy model which exhibits nontrivial phenomenology to investigate specific features of the theory. We obtain the analytic solution of the modified Friedmann equation...... for the scale factor $a$ in terms of time $t$ and use the age of the oldest star clusters and the primordial nucleosynthesis bounds in order to constrain the parameters of our toy model....

Matter density perturbations in modified gravity models with arbitrary coupling between matter and geometry

International Nuclear Information System (INIS)

Nesseris, Savvas

2009-01-01

We consider theories with an arbitrary coupling between matter and gravity and obtain the perturbation equation of matter on subhorizon scales. Also, we derive the effective gravitational constant G eff and two parameters Σ and η, which along with the perturbation equation of the matter density are useful to constrain the theory from growth factor and weak lensing observations. Finally, we use a completely solvable toy model which exhibits nontrivial phenomenology to investigate specific features of the theory. We obtain the analytic solution of the modified Friedmann equation for the scale factor a in terms of time t and use the age of the oldest star clusters and the primordial nucleosynthesis bounds in order to constrain the parameters of our toy model.

Path integral methods for primordial density perturbations - sampling of constrained Gaussian random fields

International Nuclear Information System (INIS)

Bertschinger, E.

1987-01-01

Path integrals may be used to describe the statistical properties of a random field such as the primordial density perturbation field. In this framework the probability distribution is given for a Gaussian random field subjected to constraints such as the presence of a protovoid or supercluster at a specific location in the initial conditions. An algorithm has been constructed for generating samples of a constrained Gaussian random field on a lattice using Monte Carlo techniques. The method makes possible a systematic study of the density field around peaks or other constrained regions in the biased galaxy formation scenario, and it is effective for generating initial conditions for N-body simulations with rare objects in the computational volume. 21 references

Non-perturbative Green functions in quantum gauge theories

International Nuclear Information System (INIS)

Shabanov, S.V.

1991-01-01

Non-perturbative Green functions for gauge invariant variables are considered. The Green functions are found to be modified as compared with the usual ones in a definite gauge because of a physical configuration space (PCS) reduction. In the Yang-Mills theory with fermions this phenomenon follows from the Singer theorem about the absence of a global gauge condition for the fields tensing to zero at spatial infinity. 20 refs

The problem of the universal density functional and the density matrix functional theory

International Nuclear Information System (INIS)

Bobrov, V. B.; Trigger, S. A.

2013-01-01

The analysis in this paper shows that the Hohenberg-Kohn theorem is the constellation of two statements: (i) the mathematically rigorous Hohenberg-Kohn lemma, which demonstrates that the same ground-state density cannot correspond to two different potentials of an external field, and (ii) the hypothesis of the existence of the universal density functional. Based on the obtained explicit expression for the nonrel-ativistic particle energy in a local external field, we prove that the energy of the system of more than two non-interacting electrons cannot be a functional of the inhomogeneous density. This result is generalized to the system of interacting electrons. It means that the Hohenberg-Kohn lemma cannot provide justification of the universal density functional for fermions. At the same time, statements of the density functional theory remain valid when considering any number of noninteracting ground-state bosons due to the Bose condensation effect. In the framework of the density matrix functional theory, the hypothesis of the existence of the universal density matrix functional corresponds to the cases of noninteracting particles and to interaction in the Hartree-Fock approximation.

Nonperturbative perturbation theory

International Nuclear Information System (INIS)

Bender, C.M.

1989-01-01

In this talk we describe a recently proposed graphical perturbative calculational scheme for quantum field theory. The basic idea is to expand in the power of the interaction term. For example, to solve a λφ 4 theory in d-dimensional space-time, we introduce a small parameter δ and consider a λ(φ 2 ) 1+δ field theory. We show how to expand such a theory as a series in powers of δ. The resulting perturbation series appears to have a finite radius of convergence and numerical results for low-dimensional models are good. We have computed the two-point and four-point Green's functions to second order in powers of δ and the 2n-point Green's functions (n>2) to order δ. We explain how to renormalize the theory and show that, to first order in powers of δ, when δ>0 and d≥4 the theory is free. This conclusion remains valid to second order in powers of δ, and we believe that it remains valid to all orders in powers of δ. The new perturbative scheme is consistent with global supersymmetry invariance. We examine a two-dimensional supersymmetric quantum field theory in which we do not know of any other means for doing analytical calculations. We illustrate the power of this new technique by computing the ground-state energy density E to second order in this new perturbation theory. We show that there is a beautiful and delicate cancellation between infinite classes of graphs which leads to the result that E=0. (orig.)

Generalized nuclear Fukui functions in the framework of spin-polarized density-functional theory

International Nuclear Information System (INIS)

Chamorro, E.; Proft, F. de; Geerlings, P.

2005-01-01

An extension of Cohen's nuclear Fukui function is presented in the spin-polarized framework of density-functional theory (SP-DFT). The resulting new nuclear Fukui function indices Φ Nα and Φ Sα are intended to be the natural descriptors for the responses of the nuclei to changes involving charge transfer at constant multiplicity and also the spin polarization at constant number of electrons. These generalized quantities allow us to gain new insights within a perturbative scheme based on DFT. Calculations of the electronic and nuclear SP-DFT quantities are presented within a Kohn-Sham framework of chemical reactivity for a sample of molecules, including H 2 O, H 2 CO, and some simple nitrenes (NX) and phosphinidenes (PX), with X=H, Li, F, Cl, OH, SH, NH 2 , and PH 2 . Results have been interpreted in terms of chemical bonding in the context of Berlin's theorem, which provides a separation of the molecular space into binding and antibinding regions

Phytochemicals perturb membranes and promiscuously alter protein function.

Science.gov (United States)

Ingólfsson, Helgi I; Thakur, Pratima; Herold, Karl F; Hobart, E Ashley; Ramsey, Nicole B; Periole, Xavier; de Jong, Djurre H; Zwama, Martijn; Yilmaz, Duygu; Hall, Katherine; Maretzky, Thorsten; Hemmings, Hugh C; Blobel, Carl; Marrink, Siewert J; Koçer, Armağan; Sack, Jon T; Andersen, Olaf S

2014-08-15

A wide variety of phytochemicals are consumed for their perceived health benefits. Many of these phytochemicals have been found to alter numerous cell functions, but the mechanisms underlying their biological activity tend to be poorly understood. Phenolic phytochemicals are particularly promiscuous modifiers of membrane protein function, suggesting that some of their actions may be due to a common, membrane bilayer-mediated mechanism. To test whether bilayer perturbation may underlie this diversity of actions, we examined five bioactive phenols reported to have medicinal value: capsaicin from chili peppers, curcumin from turmeric, EGCG from green tea, genistein from soybeans, and resveratrol from grapes. We find that each of these widely consumed phytochemicals alters lipid bilayer properties and the function of diverse membrane proteins. Molecular dynamics simulations show that these phytochemicals modify bilayer properties by localizing to the bilayer/solution interface. Bilayer-modifying propensity was verified using a gramicidin-based assay, and indiscriminate modulation of membrane protein function was demonstrated using four proteins: membrane-anchored metalloproteases, mechanosensitive ion channels, and voltage-dependent potassium and sodium channels. Each protein exhibited similar responses to multiple phytochemicals, consistent with a common, bilayer-mediated mechanism. Our results suggest that many effects of amphiphilic phytochemicals are due to cell membrane perturbations, rather than specific protein binding.

A perturbative DFT approach for magnetic anisotropy

Energy Technology Data Exchange (ETDEWEB)

Khoo, Khoong Hong; Laskowski, Robert, E-mail: rolask@ihpc.a-star.edu.sg

2017-04-15

We develop a perturbative formalism for computing magnetocrystalline anisotropy within density functional theory and the magnetic force theorem. Instead of computing eigenvalues of the spin–orbit Hamiltonian for selected spin polarizations, as in the conventional “force theorem” approach, we show that the effect can be cast into a redefined form of the spin–orbit operator. This allows to separate the large eigenvalue shift due to spin-orbit interaction common for both polarizations from the much smaller magnetic anisotropy splitting. As a consequence the anisotropy splitting may by considered as a perturbation.

Numerical solution of Euler's equation by perturbed functionals

Science.gov (United States)

Dey, S. K.

1985-01-01

A perturbed functional iteration has been developed to solve nonlinear systems. It adds at each iteration level, unique perturbation parameters to nonlinear Gauss-Seidel iterates which enhances its convergence properties. As convergence is approached these parameters are damped out. Local linearization along the diagonal has been used to compute these parameters. The method requires no computation of Jacobian or factorization of matrices. Analysis of convergence depends on properties of certain contraction-type mappings, known as D-mappings. In this article, application of this method to solve an implicit finite difference approximation of Euler's equation is studied. Some representative results for the well known shock tube problem and compressible flows in a nozzle are given.

Effect of initial perturbation amplitude on Richtmyer-Meshkov flows induced by strong shocks

Energy Technology Data Exchange (ETDEWEB)

Dell, Z.; Abarzhi, S. I., E-mail: snezhana.abarzhi@gmail.com, E-mail: sabarji@andrew.cmu.edu [Mellon College of Science and Carnegie Mellon University – Qatar, Carnegie Mellon University, Pittsburgh, Pennsylvania 15231 (United States); Stellingwerf, R. F. [Stellingwerf Consulting, Huntsville, Alabama 35803 (United States)

2015-09-15

We systematically study the effect of the initial perturbation on Richtmyer-Meshkov (RM) flows induced by strong shocks in fluids with contrasting densities. Smooth Particle Hydrodynamics simulations are employed. A broad range of shock strengths and density ratios is considered. The amplitude of the initial single mode sinusoidal perturbation of the interface varies from 0% to 100% of its wavelength. The simulations results are compared, wherever possible, with four rigorous theories, and with other experiments and simulations, achieving good quantitative and qualitative agreement. Our study is focused on early time dynamics of the Richtmyer-Meshkov instability (RMI). We analyze the initial growth-rate of RMI immediately after the shock passage, when the perturbation amplitude increases linearly with time. For the first time, to the authors' knowledge, we find that the initial growth-rate of RMI is a non-monotone function of the initial perturbation amplitude, thus restraining the amount of energy that can be deposited by the shock at the interface. The maximum value of the initial growth-rate depends on the shock strength and the density ratio, whereas the corresponding value of the initial perturbation amplitude depends only slightly on the shock strength and density ratio.

Non-perturbative QCD correlation functions

Energy Technology Data Exchange (ETDEWEB)

Cyrol, Anton Konrad

2017-11-27

Functional methods provide access to the non-perturbative regime of quantum chromo- dynamics. Hence, they allow investigating confinement and chiral symmetry breaking. In this dissertation, correlation functions of Yang-Mills theory and unquenched two-flavor QCD are computed from the functional renormalization group. Employing a self-consistent vertex expansion of the effective action, Yang-Mills correlation functions are obtained in four as well as in three spacetime dimensions. To this end, confinement and Slavnov-Taylor identities are discussed. Our numerical results show very good agreement with corresponding lattice results. Next, unquenched two-flavor QCD is considered where it is shown that the unquenched two-flavor gluon propagator is insensitive to the pion mass. Furthermore, the necessity for consistent truncations is emphasized. Finally, correlation functions of finite-temperature Yang-Mills theory are computed in a truncation that includes the splitting of the gluon field into directions that are transverse and longitudinal to the heat bath. In particular, it includes the splitting of the three- and four-gluon vertices. The obtained gluon propagator allows to extract a Debye screening mass that coincides with the hard thermal loop screening mass at high temperatures, but is meaningful also at temperatures below the phase transition temperature.

Self-consistent many-body perturbation theory in range-separated density-functional theory

DEFF Research Database (Denmark)

Fromager, Emmanuel; Jensen, Hans Jørgen Aagaard

2008-01-01

effects adequately which, on the other hand, can be described by many-body perturbation theory MBPT. It is therefore of interest to develop a hybrid model which combines the best of both the MBPT and DFT approaches. This can be achieved by splitting the two-electron interaction into long-range and short...

Spin-Density Functionals from Current-Density Functional Theory and Vice Versa: A Road towards New Approximations

International Nuclear Information System (INIS)

Capelle, K.; Gross, E.

1997-01-01

It is shown that the exchange-correlation functional of spin-density functional theory is identical, on a certain set of densities, with the exchange-correlation functional of current-density functional theory. This rigorous connection is used to construct new approximations of the exchange-correlation functionals. These include a conceptually new generalized-gradient spin-density functional and a nonlocal current-density functional. copyright 1997 The American Physical Society

The bispectrum of matter perturbations from cosmic strings

Energy Technology Data Exchange (ETDEWEB)

Regan, Donough; Hindmarsh, Mark, E-mail: d.regan@sussex.ac.uk, E-mail: m.b.hindmarsh@sussex.ac.uk [Astronomy Centre, University of Sussex, Falmer, Brighton, BN1 9QH (United Kingdom)

2015-03-01

We present the first calculation of the bispectrum of the matter perturbations induced by cosmic strings. The calculation is performed in two different ways: the first uses the unequal time correlators (UETCs) of the string network - computed using a Gaussian model previously employed for cosmic string power spectra. The second approach uses the wake model, where string density perturbations are concentrated in sheet-like structures whose surface density grows with time. The qualitative and quantitative agreement of the two gives confidence to the results. An essential ingredient in the UETC approach is the inclusion of compensation factors in the integration with the Green's function of the matter and radiation fluids, and we show that these compensation factors must be included in the wake model also. We also present a comparison of the UETCs computed in the Gaussian model, and those computed in the unconnected segment model (USM) used by the standard cosmic string perturbation package CMBACT. We compare numerical estimates for the bispectrum of cosmic strings to those produced by perturbations from an inflationary era, and discover that, despite the intrinsically non-Gaussian nature of string-induced perturbations, the matter bispectrum is unlikely to produce competitive constraints on a population of cosmic strings.

Density Functional Theory Simulations of Semiconductors for Photovoltaic Applications: Hybrid Organic-Inorganic Perovskites and III/V Heterostructures

Directory of Open Access Journals (Sweden)

Jacky Even

2014-01-01

Full Text Available Potentialities of density functional theory (DFT based methodologies are explored for photovoltaic materials through the modeling of the structural and optoelectronic properties of semiconductor hybrid organic-inorganic perovskites and GaAs/GaP heterostructures. They show how the properties of these bulk materials, as well as atomistic relaxations, interfaces, and electronic band-lineups in small heterostructures, can be thoroughly investigated. Some limitations of available standard DFT codes are discussed. Recent improvements able to treat many-body effects or based on density-functional perturbation theory are also reviewed in the context of issues relevant to photovoltaic technologies.

A food chain model with impulsive perturbations and Holling IV functional response

International Nuclear Information System (INIS)

Zhang Shuwen; Wang Fengyan; Chen Lansun

2005-01-01

In this paper, we investigate a three trophic level food chain system with Holling IV functional responses and periodic constant impulsive perturbations of top predator. Conditions for extinction of predator are given. By using the Floquet theory of impulsive equation and small amplitude perturbation skills, we consider the local stability of predator eradication periodic solution. Further, influences of the impulsive perturbation on the inherent oscillation are studied numerically, which shows the rich dynamics in the positive octant

Laboratory Density Functionals

OpenAIRE

Giraud, B. G.

2007-01-01

We compare several definitions of the density of a self-bound system, such as a nucleus, in relation with its center-of-mass zero-point motion. A trivial deconvolution relates the internal density to the density defined in the laboratory frame. This result is useful for the practical definition of density functionals.

Benchmarking density-functional-theory calculations of rotational g tensors and magnetizabilities using accurate coupled-cluster calculations.

Science.gov (United States)

Lutnaes, Ola B; Teale, Andrew M; Helgaker, Trygve; Tozer, David J; Ruud, Kenneth; Gauss, Jürgen

2009-10-14

An accurate set of benchmark rotational g tensors and magnetizabilities are calculated using coupled-cluster singles-doubles (CCSD) theory and coupled-cluster single-doubles-perturbative-triples [CCSD(T)] theory, in a variety of basis sets consisting of (rotational) London atomic orbitals. The accuracy of the results obtained is established for the rotational g tensors by careful comparison with experimental data, taking into account zero-point vibrational corrections. After an analysis of the basis sets employed, extrapolation techniques are used to provide estimates of the basis-set-limit quantities, thereby establishing an accurate benchmark data set. The utility of the data set is demonstrated by examining a wide variety of density functionals for the calculation of these properties. None of the density-functional methods are competitive with the CCSD or CCSD(T) methods. The need for a careful consideration of vibrational effects is clearly illustrated. Finally, the pure coupled-cluster results are compared with the results of density-functional calculations constrained to give the same electronic density. The importance of current dependence in exchange-correlation functionals is discussed in light of this comparison.

Confinement bifurcation by current density profile perturbation in TUMAN-3M tokamak

International Nuclear Information System (INIS)

Lebedev, S.V.; Andreiko, M.V.; Askinazi, L.G.

2001-01-01

In the recent experiments performed on TUMAN-3M the possibility to switch on/off the H-mode by current density profile perturbations has been shown. The j(r) perturbations were created by fast Current Ramp Up/Down or by Magnetic Compression produced by a fast increase of the toroidal magnetic field. It was found that the Current Ramp Up (CRU) and Magnetic Compression (MC) are useful means for H-mode triggering. The Current Ramp Down (CRD) triggers H-L transition. The difference in the j(r) behavior in these experiments suggests the peripheral current density may not be the critical parameter controlling L-H and H-L transitions. Confinement bifurcation in the above experiments could be explained by the unified mechanism: variation of a turbulent transport resulting from radial electric field emerging near the edge in the conditions of alternating toroidal electric field Ej and different electron and ion collisionalities. According to the suggested model the toroidal field E φ arising in the periphery during the CRU and MC processes amplifies Ware drift, which mainly influences electron component. As a result the favorable for the transition negative (inward directed) E r emerges. In the CRD scenario, when E φ is opposite to the total plasma current direction, the mechanism should generate positive E r , which is thought to be unfavorable for the H-mode. The experimental data on L-H and H-L transitions in various scenarios and the results of the modeling of E r emerging in the CRU experiment are presented in the paper. (author)

Functional perturbative RG and CFT data in the ε-expansion

Energy Technology Data Exchange (ETDEWEB)

Codello, A. [Southern Denmark Univ., Odense (Denmark). CP3-Origins; INFN-Sezione di Bologna, Bologna (Italy); Safari, M. [INFN-Sezione di Bologna, Bologna (Italy); Bologna Univ. (Italy). Dipt di Fisica e Astronomia; Vacca, G.P. [INFN-Sezione di Bologna, Bologna (Italy); Zanusso, O. [INFN-Sezione di Bologna, Bologna (Italy); Jena Univ. (Germany). Theoretisch-Physikalisches Inst.

2018-01-15

We show how the use of standard perturbative RG in dimensional regularization allows for a renormalization group-based computation of both the spectrum and a family of coefficients of the operator product expansion (OPE) for a given universality class. The task is greatly simplified by a straightforward generalization of perturbation theory to a functional perturbative RG approach. We illustrate our procedure in the ε-expansion by obtaining the next-to-leading corrections for the spectrum and the leading corrections for the OPE coefficients of Ising and Lee-Yang universality classes and then give several results for the whole family of renormalizable multi-critical models φ{sup 2n}. Whenever comparison is possible our RG results explicitly match the ones recently derived in CFT frameworks. (orig.)

Applications of delta-functions perturbation to the pricing of derivative securities

NARCIS (Netherlands)

Decamps, M.; DeSchepper, A.; Goovaerts, M.J.

2004-01-01

In the recent econophysics literature, the use of functional integrals is widespread for the calculation of option prices. In this paper, we extend this approach in several directions by means of -function perturbations. First, we show that results about infinitely repulsive -function are applicable

External field as the functional of inhomogeneous density and the density matrix functional approach

NARCIS (Netherlands)

Bobrov, V.B.; Trigger, S.A.; Vlasov, Y.P.

2012-01-01

Based on the Hohenberg-Kohn lemma and the hypotheses of the density functional existence for the external-field potential, it is shown that the strict result of the density functional theory is the equation of the external-field potential as the density functional. This result leads to the

Orbital functionals in density-matrix- and current-density-functional theory

Energy Technology Data Exchange (ETDEWEB)

Helbig, N

2006-05-15

Density-Functional Theory (DFT), although widely used and very successful in the calculation of several observables, fails to correctly describe strongly correlated materials. In the first part of this work we, therefore, introduce reduced-densitymatrix- functional theory (RDMFT) which is one possible way to treat electron correlation beyond DFT. Within this theory the one-body reduced density matrix (1- RDM) is used as the basic variable. Our main interest is the calculation of the fundamental gap which proves very problematic within DFT. In order to calculate the fundamental gap we generalize RDMFT to fractional particle numbers M by describing the system as an ensemble of an N and an N+1 particle system (with N{<=}M{<=}N+1). For each fixed particle number, M, the total energy is minimized with respect to the natural orbitals and their occupation numbers. This leads to the total energy as a function of M. The derivative of this function with respect to the particle number has a discontinuity at integer particle number which is identical to the gap. In addition, we investigate the necessary and sufficient conditions for the 1- RDM of a system with fractional particle number to be N-representable. Numerical results are presented for alkali atoms, small molecules, and periodic systems. Another problem within DFT is the description of non-relativistic many-electron systems in the presence of magnetic fields. It requires the paramagnetic current density and the spin magnetization to be used as basic variables besides the electron density. However, electron-gas-based functionals of current-spin-density-functional Theory (CSDFT) exhibit derivative discontinuities as a function of the magnetic field whenever a new Landau level is occupied, which makes them difficult to use in practice. Since the appearance of Landau levels is, intrinsically, an orbital effect it is appealing to use orbital-dependent functionals. We have developed a CSDFT version of the optimized

Relativistic many-body perturbation-theory calculations based on Dirac-Fock-Breit wave functions

International Nuclear Information System (INIS)

Ishikawa, Y.; Quiney, H.M.

1993-01-01

A relativistic many-body perturbation theory based on the Dirac-Fock-Breit wave functions has been developed and implemented by employing analytic basis sets of Gaussian-type functions. The instantaneous Coulomb and low-frequency Breit interactions are treated using a unified formalism in both the construction of the Dirac-Fock-Breit self-consistent-field atomic potential and in the evaluation of many-body perturbation-theory diagrams. The relativistic many-body perturbation-theory calculations have been performed on the helium atom and ions of the helium isoelectronic sequence up to Z=50. The contribution of the low-frequency Breit interaction to the relativistic correlation energy is examined for the helium isoelectronic sequence

Heavy-quark fragmentation functions at next-to-leading perturbative QCD

Energy Technology Data Exchange (ETDEWEB)

Moosavi Nejad, S.M. [Yazd University, Faculty of Physics, Yazd (Iran, Islamic Republic of); Institute for Research in Fundamental Sciences (IPM), School of Particles and Accelerators, Tehran (Iran, Islamic Republic of); Sartipi Yarahmadi, P. [Yazd University, Faculty of Physics, Yazd (Iran, Islamic Republic of)

2016-10-15

It is well known that the dominant mechanism to produce hadronic bound states with large transverse momentum is fragmentation. This mechanism is described by the fragmentation functions (FFs) which are the universal and process-independent functions. Here, we review the perturbative FFs formalism as an appropriate tool for studying these hadronization processes and detail the extension of this formalism at next-to-leading order (NLO). Using Suzuki's model, we calculate the perturbative QCD FF for a heavy quark to fragment into a S-wave heavy meson at NLO. As an example, we study the LO and NLO FFs for a charm quark to split into the S-wave D-meson and compare our analytic results both with experimental data and well-known phenomenological models. (orig.)

Magnetic exchange couplings from constrained density functional theory: an efficient approach utilizing analytic derivatives.

Science.gov (United States)

Phillips, Jordan J; Peralta, Juan E

2011-11-14

We introduce a method for evaluating magnetic exchange couplings based on the constrained density functional theory (C-DFT) approach of Rudra, Wu, and Van Voorhis [J. Chem. Phys. 124, 024103 (2006)]. Our method shares the same physical principles as C-DFT but makes use of the fact that the electronic energy changes quadratically and bilinearly with respect to the constraints in the range of interest. This allows us to use coupled perturbed Kohn-Sham spin density functional theory to determine approximately the corrections to the energy of the different spin configurations and construct a priori the relevant energy-landscapes obtained by constrained spin density functional theory. We assess this methodology in a set of binuclear transition-metal complexes and show that it reproduces very closely the results of C-DFT. This demonstrates a proof-of-concept for this method as a potential tool for studying a number of other molecular phenomena. Additionally, routes to improving upon the limitations of this method are discussed. © 2011 American Institute of Physics

The chirally rotated Schrödinger functional: theoretical expectations and perturbative tests

International Nuclear Information System (INIS)

Brida, Mattia Dalla; Sint, Stefan; Vilaseca, Pol

2016-01-01

The chirally rotated Schrödinger functional (χSF) with massless Wilson-type fermions provides an alternative lattice regularization of the Schrödinger functional (SF), with different lattice symmetries and a common continuum limit expected from universality. The explicit breaking of flavour and parity symmetries needs to be repaired by tuning the bare fermion mass and the coefficient of a dimension 3 boundary counterterm. Once this is achieved one expects the mechanism of automatic O(a) improvement to be operational in the χSF, in contrast to the standard formulation of the SF. This is expected to significantly improve the attainable precision for step-scaling functions of some composite operators. Furthermore, the χSF offers new strategies to determine finite renormalization constants which are traditionally obtained from chiral Ward identities. In this paper we consider a complete set of fermion bilinear operators, define corresponding correlation functions and explain the relation to their standard SF counterparts. We discuss renormalization and O(a) improvement and then use this set-up to formulate the theoretical expectations which follow from universality. Expanding the correlation functions to one-loop order of perturbation theory we then perform a number of non-trivial checks. In the process we obtain the action counterterm coefficients to one-loop order and reproduce some known perturbative results for renormalization constants of fermion bilinears. By confirming the theoretical expectations, this perturbative study lends further support to the soundness of the χSF framework and prepares the ground for non-perturbative applications.

Density functional approach for the magnetism of β-TeVO4

Science.gov (United States)

Saúl, A.; Radtke, G.

2014-03-01

Density functional calculations have been carried out to investigate the microscopic origin of the magnetic properties of β-TeVO4. Two different approaches, based either on a perturbative treatment of the multiorbital Hubbard model in the strongly correlated limit or on the calculation of supercell total energy differences, have been employed to evaluate magnetic couplings in this compound. The picture provided by these two approaches is that of weakly coupled frustrated chains with ferromagnetic nearest-neighbor and antiferromagnetic second-nearest-neighbor couplings. These results, differing substantially from previous reports, should motivate further experimental investigations of the magnetic properties of this compound.

Local-scaling density-functional method: Intraorbit and interorbit density optimizations

International Nuclear Information System (INIS)

Koga, T.; Yamamoto, Y.; Ludena, E.V.

1991-01-01

The recently proposed local-scaling density-functional theory provides us with a practical method for the direct variational determination of the electron density function ρ(r). The structure of ''orbits,'' which ensures the one-to-one correspondence between the electron density ρ(r) and the N-electron wave function Ψ({r k }), is studied in detail. For the realization of the local-scaling density-functional calculations, procedures for intraorbit and interorbit optimizations of the electron density function are proposed. These procedures are numerically illustrated for the helium atom in its ground state at the beyond-Hartree-Fock level

Finite density two color chiral perturbation theory revisited

Science.gov (United States)

Adhikari, Prabal; Beleznay, Soma B.; Mannarelli, Massimo

2018-06-01

We revisit two-color, two-flavor chiral perturbation theory at finite isospin and baryon density. We investigate the phase diagram obtained varying the isospin and the baryon chemical potentials, focusing on the phase transition occurring when the two chemical potentials are equal and exceed the pion mass (which is degenerate with the diquark mass). In this case, there is a change in the order parameter of the theory that does not lend itself to the standard picture of first order transitions. We explore this phase transition both within a Ginzburg-Landau framework valid in a limited parameter space and then by inspecting the full chiral Lagrangian in all the accessible parameter space. Across the phase transition between the two broken phases the order parameter becomes an SU(2) doublet, with the ground state fixing the expectation value of the sum of the magnitude squared of the pion and the diquark fields. Furthermore, we find that the Lagrangian at equal chemical potentials is invariant under global SU(2) transformations and construct the effective Lagrangian of the three Goldstone degrees of freedom by integrating out the radial fluctuations.

Optical to ultraviolet spectra of sandwiches of benzene and transition metal atoms: Time dependent density functional theory and many-body calculations

DEFF Research Database (Denmark)

Martinez, Jose Ignacio; García Lastra, Juan Maria; Lopez, M. J.

2010-01-01

The optical spectra of sandwich clusters formed by transition metal atoms (titanium, vanadium, and chromium) intercalated between parallel benzene molecules have been studied by time-dependent density functional theory (TDDFT) and many-body perturbation theory. Sandwiches with different number...

Density functional study of molecular interactions in secondary structures of proteins.

Science.gov (United States)

Takano, Yu; Kusaka, Ayumi; Nakamura, Haruki

2016-01-01

Proteins play diverse and vital roles in biology, which are dominated by their three-dimensional structures. The three-dimensional structure of a protein determines its functions and chemical properties. Protein secondary structures, including α-helices and β-sheets, are key components of the protein architecture. Molecular interactions, in particular hydrogen bonds, play significant roles in the formation of protein secondary structures. Precise and quantitative estimations of these interactions are required to understand the principles underlying the formation of three-dimensional protein structures. In the present study, we have investigated the molecular interactions in α-helices and β-sheets, using ab initio wave function-based methods, the Hartree-Fock method (HF) and the second-order Møller-Plesset perturbation theory (MP2), density functional theory, and molecular mechanics. The characteristic interactions essential for forming the secondary structures are discussed quantitatively.

Wave-function functionals for the density

International Nuclear Information System (INIS)

Slamet, Marlina; Pan Xiaoyin; Sahni, Viraht

2011-01-01

We extend the idea of the constrained-search variational method for the construction of wave-function functionals ψ[χ] of functions χ. The search is constrained to those functions χ such that ψ[χ] reproduces the density ρ(r) while simultaneously leading to an upper bound to the energy. The functionals are thereby normalized and automatically satisfy the electron-nucleus coalescence condition. The functionals ψ[χ] are also constructed to satisfy the electron-electron coalescence condition. The method is applied to the ground state of the helium atom to construct functionals ψ[χ] that reproduce the density as given by the Kinoshita correlated wave function. The expectation of single-particle operators W=Σ i r i n , n=-2,-1,1,2, W=Σ i δ(r i ) are exact, as must be the case. The expectations of the kinetic energy operator W=-(1/2)Σ i ∇ i 2 , the two-particle operators W=Σ n u n , n=-2,-1,1,2, where u=|r i -r j |, and the energy are accurate. We note that the construction of such functionals ψ[χ] is an application of the Levy-Lieb constrained-search definition of density functional theory. It is thereby possible to rigorously determine which functional ψ[χ] is closer to the true wave function.

Third-Order Density Perturbation and One-Loop Power Spectrum in Dark-Energy-Dominated Universe

OpenAIRE

Takahashi, Ryuichi

2008-01-01

We investigate the third-order density perturbation and the one-loop correction to the linear power spectrum in the dark-energy cosmological model. Our main interest is to understand the dark-energy effect on baryon acoustic oscillations in a quasi-nonlinear regime ($k \\approx 0.1h$/Mpc). Analytical solutions and simple fitting formulae are presented for the dark-energy model with the general time-varying equation of state $w(a)$. It turns out that the power spectrum coincides with the approx...

Density functional theory

International Nuclear Information System (INIS)

Das, M.P.

1984-07-01

The state of the art of the density functional formalism (DFT) is reviewed. The theory is quantum statistical in nature; its simplest version is the well-known Thomas-Fermi theory. The DFT is a powerful formalism in which one can treat the effect of interactions in inhomogeneous systems. After some introductory material, the DFT is outlined from the two basic theorems, and various generalizations of the theorems appropriate to several physical situations are pointed out. Next, various approximations to the density functionals are presented and some practical schemes, discussed; the approximations include an electron gas of almost constant density and an electron gas of slowly varying density. Then applications of DFT in various diverse areas of physics (atomic systems, plasmas, liquids, nuclear matter) are mentioned, and its strengths and weaknesses are pointed out. In conclusion, more recent developments of DFT are indicated

Perturbation method for experimental determination of neutron spatial distribution in the reactor cell

International Nuclear Information System (INIS)

Takac, S.M.

1972-01-01

The method is based on perturbation of the reactor cell from a few up to few tens of percent. Measurements were performed for square lattice calls of zero power reactors Anna, NORA and RB, with metal uranium and uranium oxide fuel elements, water, heavy water and graphite moderators. Character and functional dependence of perturbations were obtained from the experimental results. Zero perturbation was determined by extrapolation thus obtaining the real physical neutron flux distribution in the reactor cell. Simple diffusion theory for partial plate cell perturbation was developed for verification of the perturbation method. The results of these calculation proved that introducing the perturbation sample in the fuel results in flattening the thermal neutron density dependent on the amplitude of the applied perturbation. Extrapolation applied for perturbed distributions was found to be justified

Accuracy of finite-difference harmonic frequencies in density functional theory.

Science.gov (United States)

Liu, Kuan-Yu; Liu, Jie; Herbert, John M

2017-07-15

Analytic Hessians are often viewed as essential for the calculation of accurate harmonic frequencies, but the implementation of analytic second derivatives is nontrivial and solution of the requisite coupled-perturbed equations engenders a sizable memory footprint for large systems, given that these equations are not required for energy and gradient calculations in density functional theory. Here, we benchmark the alternative approach to harmonic frequencies based on finite differences of analytic first derivatives, a procedure that is amenable to large-scale parallelization. Not only for absolute frequencies but also for isotopic and conformer-dependent frequency shifts in flexible molecules, we find that the finite-difference approach exhibits mean errors numbers. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Acoustic wavefield evolution as a function of source location perturbation

KAUST Repository

Alkhalifah, Tariq Ali

2010-01-01

differential equations have the same structure as the wave equation with a source function that depends on the background (original source) wavefield. The similarity in form implies that we can use familiar numerical methods to solve the perturbation equations

Spatiotemporal response of plasma edge density and temperature to non-axisymmetric magnetic perturbations at ASDEX Upgrade

International Nuclear Information System (INIS)

Fischer, R; Fuchs, J C; McDermott, R; Rathgeber, S K; Suttrop, W; Wolfrum, E; Willensdorfer, M

2012-01-01

Non-axisymmetric magnetic perturbations (MPs) were successfully applied at ASDEX Upgrade to substantially reduce the plasma energy loss and peak divertor power load that occur concomitant with type-I edge localized modes (ELMs). The response of electron density edge profiles and temperature and pressure pedestal-top values to MPs are reported. ELM mitigation is observed above an edge density threshold and independent of the MPs being resonant or non-resonant with the edge safety factor. The edge electron collisionality appears not to be appropriate to separate mitigated from non-mitigated discharges for the present high-collisionality plasmas. No significant change in the position or gradient of the edge density profile could be observed for the transition into the ELM-mitigated phase, except from the effect of the three-dimensional MP field which leads to an apparent profile shift. An increase in the density and decrease in the temperature at the pedestal-top balance such that the pressure saturates at the value of the pre-mitigated phase. The plasma stored energy, the normalized plasma pressure, and the H-mode quality factor follow closely the evolution of the pedestal-top pressure and thus remain almost unaffected. The temporal evolution of the ion effective charge shows that the impurity content does not increase although flushing through type-I ELMs is missing. The type-I ELMs are replaced in the mitigated phase by small-scale and high-frequency edge perturbations. The effect of the small bursts on the density profile, which is correlated with a transient increase of the divertor thermoelectric current, is small compared with the effect of the type-I ELMs. The residual scatter of the profiles in the mitigated phase is small directly after the transition into the ELM-mitigated phase and increases again when the pressure saturates at the value of the pre-mitigated phase. (paper)

Cosmological perturbations from quantum fluctuations to large scale structure

International Nuclear Information System (INIS)

Bardeen, J.M.

1988-01-01

Classical perturbation theory is developed from the 3 + 1 form of the Einstein equations. A somewhat unusual form of the perturbation equations in the synchronous gauge is recommended for carrying out computations, but interpretation is based on certain hypersurface-invariant combinations of the variables. The formalism is used to analyze the origin of density perturbations from quantum fluctuations during inflation, with particular emphasis on dealing with 'double inflation' and deviations from the Zel'dovich spectrum. The evolution of the density perturbation to the present gives the final density perturbation power spectrum, whose relationship to observed large scale structure is discussed in the context of simple cold-dark-matter biasing schemes. 86 refs

A thermodynamic perturbation theory for the surface tension and ion density profile of a liquid metal

International Nuclear Information System (INIS)

Evans, R.; Kumaravadivel, R.

1976-01-01

A simple scheme for determining the ion density profile and the surface tension of a liquid metal is described. Assuming that the interaction between metallic pseudo-ions is of the form introduced by Evans, an approximate expression for the excess free energy of the system is derived using the thermodynamic perturbation theory of Weeks, Chandler and Anderson. This excess free energy is then minimized with respect to a parameter which specifies the ion density profile, and the surface tension is given directly. From a consideration of the dependence of the interionic forces on the electron density it is predicted that the ions should take up a very steep density profile at the liquid metal surface. This behaviour is contrasted with that to be expected for rare-gas fluids in which the interatomic forces are density-independent. The values of the surface tension calculated for liquid Na, K and Al from a simplified version of the theory are in reasonable agreement with experiment. (author)

A note on the accuracy of KS-DFT densities

Science.gov (United States)

Ranasinghe, Duminda S.; Perera, Ajith; Bartlett, Rodney J.

2017-11-01

The accuracy of the density of wave function methods and Kohn-Sham (KS) density functionals is studied using moments of the density, ⟨rn ⟩ =∫ ρ (r )rnd τ =∫0∞4 π r2ρ (r ) rnd r ,where n =-1 ,-2,0,1,2 ,and 3 provides information about the short- and long-range behavior of the density. Coupled cluster (CC) singles, doubles, and perturbative triples (CCSD(T)) is considered as the reference density. Three test sets are considered: boron through neon neutral atoms, two and four electron cations, and 3d transition metals. The total density and valence only density are distinguished by dropping appropriate core orbitals. Among density functionals tested, CAMQTP00 and ωB97x show the least deviation for boron through neon neutral atoms. They also show accurate eigenvalues for the HOMO indicating that they should have a more correct long-range behavior for the density. For transition metals, some density functional approximations outperform some wave function methods, suggesting that the KS determinant could be a better starting point for some kinds of correlated calculations. By using generalized many-body perturbation theory (MBPT), the convergence of second-, third-, and fourth-order KS-MBPT for the density is addressed as it converges to the infinite-order coupled cluster result. For the transition metal test set, the deviations in the KS density functional theory methods depend on the amount of exact exchange the functional uses. Functionals with exact exchange close to 25% show smaller deviations from the CCSD(T) density.

Vibrational properties of SrCu{sub 2}O{sub 2} studied via Density Functional Theory calculations and compared to Raman and infrared spectroscopy measurements

Energy Technology Data Exchange (ETDEWEB)

Even, J., E-mail: jacky.even@insa.rennes.fr [Université Européenne de Bretagne, INSA, FOTON, UMR CNRS 6082, 20 Avenue des Buttes de Coësmes, F-35708 Rennes (France); Pedesseau, L.; Durand, O. [Université Européenne de Bretagne, INSA, FOTON, UMR CNRS 6082, 20 Avenue des Buttes de Coësmes, F-35708 Rennes (France); Modreanu, M. [Tyndall National Institute, Lee Maltings, Prospect Row, Cork (Ireland); Huyberechts, G. [FLAMAC, Technologiepark 903, 9052 Zwijnaarde (Belgium); Servet, B. [Thales Research and Technology France, Campus Polytechnique, 1, avenue Augustin Fresnel, 91767 Palaiseau cedex France (France); Chaix-Pluchery, O. [Laboratoire des Matériaux et du Génie Physique, Grenoble INP—Minatec, 3, parvis Louis Néel, BP 257, 38016 Grenoble Cedex 1 (France)

2013-08-31

The SrCu{sub 2}O{sub 2} material is a p-type transparent conductive oxide. A theoretical study of the SrCu{sub 2}O{sub 2} crystal is performed with a state of the art implementation of the Density Functional Theory. The simulated crystal structure is compared with available X-ray diffraction data and previous theoretical modeling. Density Functional Perturbation Theory is used to study the vibrational properties of the SrCu{sub 2}O{sub 2} crystal. A symmetry analysis of the optical phonon eigenvectors at the Brillouin zone center is proposed. The Raman spectra simulated using the derivatives of the dielectric susceptibility, show a good agreement with Raman scattering experimental results. - Highlights: ► The symmetry properties of the optical phonons of the SrCu{sub 2}O{sub 2} crystal are analyzed. ► Born charges and the dynamical matrix are calculated at the Brillouin zone center. ► Density Functional Perturbation Theory (DFPT) is used to compute Raman spectrum. ► DFPT Raman spectrum is compared with experimental results.

Semi-exact solution of elastic non-uniform thickness and density rotating disks by homotopy perturbation and Adomian's decomposition methods. Part I: Elastic solution

International Nuclear Information System (INIS)

Hojjati, M.H.; Jafari, S.

2008-01-01

In this work, two powerful analytical methods, namely homotopy perturbation method (HPM) and Adomian's decomposition method (ADM), are introduced to obtain distributions of stresses and displacements in rotating annular elastic disks with uniform and variable thicknesses and densities. The results obtained by these methods are then compared with the verified variational iteration method (VIM) solution. He's homotopy perturbation method which does not require a 'small parameter' has been used and a homotopy with an imbedding parameter p element of [0,1] is constructed. The method takes the full advantage of the traditional perturbation methods and the homotopy techniques and yields a very rapid convergence of the solution. Adomian's decomposition method is an iterative method which provides analytical approximate solutions in the form of an infinite power series for nonlinear equations without linearization, perturbation or discretization. Variational iteration method, on the other hand, is based on the incorporation of a general Lagrange multiplier in the construction of correction functional for the equation. This study demonstrates the ability of the methods for the solution of those complicated rotating disk cases with either no or difficult to find fairly exact solutions without the need to use commercial finite element analysis software. The comparison among these methods shows that although the numerical results are almost the same, HPM is much easier, more convenient and efficient than ADM and VIM

Equilibrium finite-frequency noise of an interacting mesoscopic capacitor studied in time-dependent density functional theory

Science.gov (United States)

Dittmann, Niklas; Splettstoesser, Janine; Helbig, Nicole

2018-03-01

We calculate the frequency-dependent equilibrium noise of a mesoscopic capacitor in time-dependent density functional theory (TDDFT). The capacitor is modeled as a single-level quantum dot with on-site Coulomb interaction and tunnel coupling to a nearby reservoir. The noise spectra are derived from linear-response conductances via the fluctuation-dissipation theorem. Thereby, we analyze the performance of a recently derived exchange-correlation potential with time-nonlocal density dependence in the finite-frequency linear-response regime. We compare our TDDFT noise spectra with real-time perturbation theory and find excellent agreement for noise frequencies below the reservoir temperature.

Disformal transformation of cosmological perturbations

Directory of Open Access Journals (Sweden)

Masato Minamitsuji

2014-10-01

Full Text Available We investigate the gauge-invariant cosmological perturbations in the gravity and matter frames in the general scalar–tensor theory where two frames are related by the disformal transformation. The gravity and matter frames are the extensions of the Einstein and Jordan frames in the scalar–tensor theory where two frames are related by the conformal transformation, respectively. First, it is shown that the curvature perturbation in the comoving gauge to the scalar field is disformally invariant as well as conformally invariant, which gives the predictions from the cosmological model where the scalar field is responsible both for inflation and cosmological perturbations. Second, in case that the disformally coupled matter sector also contributes to curvature perturbations, we derive the evolution equations of the curvature perturbation in the uniform matter energy density gauge from the energy (nonconservation in the matter sector, which are independent of the choice of the gravity sector. While in the matter frame the curvature perturbation in the uniform matter energy density gauge is conserved on superhorizon scales for the vanishing nonadiabatic pressure, in the gravity frame it is not conserved even if the nonadiabatic pressure vanishes. The formula relating two frames gives the amplitude of the curvature perturbation in the matter frame, once it is evaluated in the gravity frame.

Disformal transformation of cosmological perturbations

International Nuclear Information System (INIS)

Minamitsuji, Masato

2014-01-01

We investigate the gauge-invariant cosmological perturbations in the gravity and matter frames in the general scalar–tensor theory where two frames are related by the disformal transformation. The gravity and matter frames are the extensions of the Einstein and Jordan frames in the scalar–tensor theory where two frames are related by the conformal transformation, respectively. First, it is shown that the curvature perturbation in the comoving gauge to the scalar field is disformally invariant as well as conformally invariant, which gives the predictions from the cosmological model where the scalar field is responsible both for inflation and cosmological perturbations. Second, in case that the disformally coupled matter sector also contributes to curvature perturbations, we derive the evolution equations of the curvature perturbation in the uniform matter energy density gauge from the energy (non)conservation in the matter sector, which are independent of the choice of the gravity sector. While in the matter frame the curvature perturbation in the uniform matter energy density gauge is conserved on superhorizon scales for the vanishing nonadiabatic pressure, in the gravity frame it is not conserved even if the nonadiabatic pressure vanishes. The formula relating two frames gives the amplitude of the curvature perturbation in the matter frame, once it is evaluated in the gravity frame

Sensitivity and uncertainty analysis for functionals of the time-dependent nuclide density field

International Nuclear Information System (INIS)

Williams, M.L.; Weisbin, C.R.

1978-04-01

An approach to extend the present ORNL sensitivity program to include functionals of the time-dependent nuclide density field is developed. An adjoint equation for the nuclide field was derived previously by using generalized perturbation theory; the present derivation makes use of a variational principle and results in the same equation. The physical significance of this equation is discussed and compared to that of the time-dependent neutron adjoint equation. Computational requirements for determining sensitivity profiles and uncertainties for functionals of the time-dependent nuclide density vector are developed within the framework of the existing FORSS system; in this way the current capability is significantly extended. The development, testing, and use of an adjoint version of the ORIGEN isotope generation and depletion code are documented. Finally, a sample calculation is given which estimates the uncertainty in the plutonium inventory at shutdown of a PWR due to assumed uncertainties in uranium and plutonium cross sections. 8 figures, 4 tables

Pion parameters in nuclear medium from chiral perturbation theory and virial expansion

International Nuclear Information System (INIS)

Mallik, S.; Sarkar, Sourav

2004-01-01

We consider two methods to find the effective parameters of the pion traversing a nuclear medium. One is the first order chiral perturbation theoretic evaluation of the pion pole contribution to the two-point function of the axial-vector current. The other is the exact, first order virial expansion of the pion self-energy. We find that, although the results of chiral perturbation theory are not valid at normal nuclear density, those from the virial expansion may be reliable at such density. The latter predicts both the mass shift and the in-medium decay width of the pion to be small, of about a few MeV

Density functionals from deep learning

OpenAIRE

McMahon, Jeffrey M.

2016-01-01

Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional are required. In this work, a model based on deep learning is developed to approximate this functional. Deep learning allows computational models that are capable of naturally discovering intricate structure in large and/or high-dimensional data sets, with multiple levels of abstraction. As no assumptions are ...

Fast in vivo volume dose reconstruction via reference dose perturbation

International Nuclear Information System (INIS)

Lu, Weiguo; Chen, Mingli; Mo, Xiaohu; Parnell, Donald; Olivera, Gustavo; Galmarini, Daniel

2014-01-01

Purpose: Accurate on-line reconstruction of in-vivo volume dose that accounts for both machine and patient discrepancy is not clinically available. We present a simple reference-dose-perturbation algorithm that reconstructs in-vivo volume dose fast and accurately. Methods: We modelled the volume dose as a function of the fluence map and density image. Machine (output variation, jaw/leaf position errors, etc.) and patient (setup error, weight loss, etc.) discrepancies between the plan and delivery were modelled as perturbation of the fluence map and density image, respectively. Delivered dose is modelled as perturbation of the reference dose due to change of the fluence map and density image. We used both simulated and clinical data to validate the algorithm. The planned dose was used as the reference. The reconstruction was perturbed from the reference and accounted for output-variations and the registered daily image. The reconstruction was compared with the ground truth via isodose lines and the Gamma Index. Results: For various plans and geometries, the volume doses were reconstructed in few seconds. The reconstruction generally matched well with the ground truth. For the 3%/3mm criteria, the Gamma pass rates were 98% for simulations and 95% for clinical data. The differences mainly appeared on the surface of the phantom/patient. Conclusions: A novel reference-dose-perturbation dose reconstruction model is presented. The model accounts for machine and patient discrepancy from planning. The algorithm is simple, fast, yet accurate, which makes online in-vivo 3D dose reconstruction clinically feasible.

Cosmological perturbations in warm-tachyon inflationary universe model with viscous pressure

Energy Technology Data Exchange (ETDEWEB)

Setare, M.R., E-mail: rezakord@ipm.ir [Department of Science, Campus of Bijar, University of Kurdistan, Bijar (Iran, Islamic Republic of); Kamali, V., E-mail: vkamali1362@gmail.com [Department of Physics, Faculty of Science, Bu-Ali Sina University, Hamedan, 65178 (Iran, Islamic Republic of)

2014-09-07

We study the warm-tachyon inflationary universe model with viscous pressure in high-dissipation regime. General conditions which are required for this model to be realizable are derived in the slow-roll approximation. We present analytic expressions for density perturbation and amplitude of tensor perturbation in longitudinal gauge. Expressions of tensor-to-scalar ratio, scalar spectral index and its running are obtained. We develop our model by using exponential potential, the characteristics of this model are calculated for two specific cases in great details: 1. Dissipative parameter Γ and bulk viscous parameter ζ are constant parameters. 2. Dissipative parameter is a function of tachyon field ϕ and bulk viscous parameter is a function of matter-radiation mixture energy density ρ. The parameters of the model are restricted by recent observational data from the nine-year Wilkinson microwave anisotropy probe (WMAP9), Planck and BICEP2 data.

Cosmological perturbations in warm-tachyon inflationary universe model with viscous pressure

Directory of Open Access Journals (Sweden)

M.R. Setare

2014-09-01

Full Text Available We study the warm-tachyon inflationary universe model with viscous pressure in high-dissipation regime. General conditions which are required for this model to be realizable are derived in the slow-roll approximation. We present analytic expressions for density perturbation and amplitude of tensor perturbation in longitudinal gauge. Expressions of tensor-to-scalar ratio, scalar spectral index and its running are obtained. We develop our model by using exponential potential, the characteristics of this model are calculated for two specific cases in great details: 1. Dissipative parameter Γ and bulk viscous parameter ζ are constant parameters. 2. Dissipative parameter is a function of tachyon field ϕ and bulk viscous parameter is a function of matter-radiation mixture energy density ρ. The parameters of the model are restricted by recent observational data from the nine-year Wilkinson microwave anisotropy probe (WMAP9, Planck and BICEP2 data.

Cosmological perturbations in warm-tachyon inflationary universe model with viscous pressure

International Nuclear Information System (INIS)

Setare, M.R.; Kamali, V.

2014-01-01

We study the warm-tachyon inflationary universe model with viscous pressure in high-dissipation regime. General conditions which are required for this model to be realizable are derived in the slow-roll approximation. We present analytic expressions for density perturbation and amplitude of tensor perturbation in longitudinal gauge. Expressions of tensor-to-scalar ratio, scalar spectral index and its running are obtained. We develop our model by using exponential potential, the characteristics of this model are calculated for two specific cases in great details: 1. Dissipative parameter Γ and bulk viscous parameter ζ are constant parameters. 2. Dissipative parameter is a function of tachyon field ϕ and bulk viscous parameter is a function of matter-radiation mixture energy density ρ. The parameters of the model are restricted by recent observational data from the nine-year Wilkinson microwave anisotropy probe (WMAP9), Planck and BICEP2 data.

Using the MCNP Taylor series perturbation feature (efficiently) for shielding problems

Science.gov (United States)

Favorite, Jeffrey

2017-09-01

The Taylor series or differential operator perturbation method, implemented in MCNP and invoked using the PERT card, can be used for efficient parameter studies in shielding problems. This paper shows how only two PERT cards are needed to generate an entire parameter study, including statistical uncertainty estimates (an additional three PERT cards can be used to give exact statistical uncertainties). One realistic example problem involves a detailed helium-3 neutron detector model and its efficiency as a function of the density of its high-density polyethylene moderator. The MCNP differential operator perturbation capability is extremely accurate for this problem. A second problem involves the density of the polyethylene reflector of the BeRP ball and is an example of first-order sensitivity analysis using the PERT capability. A third problem is an analytic verification of the PERT capability.

Non-perturbative versus perturbative renormalization of lattice operators

International Nuclear Information System (INIS)

Goeckeler, M.; Technische Hochschule Aachen; Horsley, R.; Ilgenfritz, E.M.; Oelrich, H.; Forschungszentrum Juelich GmbH; Schierholz, G.; Forschungszentrum Juelich GmbH; Perlt, H.; Schiller, A.; Rakow, P.

1995-09-01

Our objective is to compute the moments of the deep-inelastic structure functions of the nucleon on the lattice. A major source of uncertainty is the renormalization of the lattice operators that enter the calculation. In this talk we compare the renormalization constants of the most relevant twist-two bilinear quark operators which we have computed non-perturbatively and perturbatively to one loop order. Furthermore, we discuss the use of tadpole improved perturbation theory. (orig.)

Ambiguities and symmetry relations associated with fermionic tensor densities

International Nuclear Information System (INIS)

Dallabona, G.; Battistel, O. A.

2004-01-01

We consider the consistent evaluation of perturbative (divergent) Green functions associated with fermionic tensor densities and the derivation of symmetry relations for them. We show that, in spite of current algebra methods being not applicable, it is possible to derive symmetry properties analogous to the Ward identities of vector and axial-vector densities. The proposed method, which is applicable to any previously chosen order of perturbative calculation, gives the same results as those of current algebra when such a tool is applicable. By using a very general calculational strategy, concerning the manipulations and calculations involving divergent Feynman integrals, we evaluate the purely fermionic two-point functions containing tensor vertices and derive their symmetry properties. The present investigation is the first step in the study and characterization of possible anomalies involving fermionic tensor densities, particularly in purely fermionic three-point functions

Second-Order Perturbation Theory for Generalized Active Space Self-Consistent-Field Wave Functions.

Science.gov (United States)

Ma, Dongxia; Li Manni, Giovanni; Olsen, Jeppe; Gagliardi, Laura

2016-07-12

A multireference second-order perturbation theory approach based on the generalized active space self-consistent-field (GASSCF) wave function is presented. Compared with the complete active space (CAS) and restricted active space (RAS) wave functions, GAS wave functions are more flexible and can employ larger active spaces and/or different truncations of the configuration interaction expansion. With GASSCF, one can explore chemical systems that are not affordable with either CASSCF or RASSCF. Perturbation theory to second order on top of GAS wave functions (GASPT2) has been implemented to recover the remaining electron correlation. The method has been benchmarked by computing the chromium dimer ground-state potential energy curve. These calculations show that GASPT2 gives results similar to CASPT2 even with a configuration interaction expansion much smaller than the corresponding CAS expansion.

Multicomponent density functional theory embedding formulation

Energy Technology Data Exchange (ETDEWEB)

Culpitt, Tanner; Brorsen, Kurt R.; Pak, Michael V.; Hammes-Schiffer, Sharon, E-mail: shs3@illinois.edu [Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Ave, Urbana, Illinois 61801 (United States)

2016-07-28

Multicomponent density functional theory (DFT) methods have been developed to treat two types of particles, such as electrons and nuclei, quantum mechanically at the same level. In the nuclear-electronic orbital (NEO) approach, all electrons and select nuclei, typically key protons, are treated quantum mechanically. For multicomponent DFT methods developed within the NEO framework, electron-proton correlation functionals based on explicitly correlated wavefunctions have been designed and used in conjunction with well-established electronic exchange-correlation functionals. Herein a general theory for multicomponent embedded DFT is developed to enable the accurate treatment of larger systems. In the general theory, the total electronic density is separated into two subsystem densities, denoted as regular and special, and different electron-proton correlation functionals are used for these two electronic densities. In the specific implementation, the special electron density is defined in terms of spatially localized Kohn-Sham electronic orbitals, and electron-proton correlation is included only for the special electron density. The electron-proton correlation functional depends on only the special electron density and the proton density, whereas the electronic exchange-correlation functional depends on the total electronic density. This scheme includes the essential electron-proton correlation, which is a relatively local effect, as well as the electronic exchange-correlation for the entire system. This multicomponent DFT-in-DFT embedding theory is applied to the HCN and FHF{sup −} molecules in conjunction with two different electron-proton correlation functionals and three different electronic exchange-correlation functionals. The results illustrate that this approach provides qualitatively accurate nuclear densities in a computationally tractable manner. The general theory is also easily extended to other types of partitioning schemes for multicomponent systems.

Gauge-invariant perturbations in a spatially flat anisotropic universe

International Nuclear Information System (INIS)

Den, Mitsue.

1986-12-01

The gauge-invariant perturbations in a spatially flat anisotropic universe with an arbitrary dimension (= N) are studied. In a previous paper the equations for the perturbations with a wave vector k a in one of the axial directions were derived and their solutions were shown. In this paper the perturbations with k a in arbitrary directions are treated. The remarkable properties are that all three types (scalar, vector, and tensor) of perturbations are generally coupled, so that a density perturbation can be produced also by vector or tensor perturbations. The formulation is quite general, but the behavior of the perturbations is discussed in a simple case such that N = 4 and k a is orthogonal to one of the axial directions. In this case, the perturbations are divided into two groups which are dynamically decoupled from each other. The asymptotic behavior of the perturbations in the group containing the density perturbation is discussed. (author)

The SU(3) beta function from numerical stochastic perturbation theory

Energy Technology Data Exchange (ETDEWEB)

Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics and Astronomy; Perlt, H. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Bonn Univ. (Germany). Helmholtz Inst. fuer Strahlen- und Kernphysik; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Theoretical Physics Div.; Schierholz, G.; Schiller, A. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2013-09-15

The SU(3) beta function is derived from Wilson loops computed to 20th order in numerical stochastic perturbation theory. An attempt is made to include massless fermions, whose contribution is known analytically to 4th order. The question whether the theory admits an infrared stable fixed point is addressed.

The Euclidean three-point function in loop and perturbative gravity

International Nuclear Information System (INIS)

Rovelli, Carlo; Zhang Mingyi

2011-01-01

We compute the leading order of the three-point function in loop quantum gravity, using the vertex expansion of the Euclidean version of the new spin foam dynamics, in the region of γ < 1. We find results consistent with Regge calculus in the limit γ → 0, j → ∞. We also compute the tree-level three-point function of perturbative quantum general relativity in position space and discuss the possibility of directly comparing the two results.

Noise-induced perturbations of dispersion-managed solitons

International Nuclear Information System (INIS)

Li, Jinglai; Spiller, Elaine; Biondini, Gino

2007-01-01

We study noise-induced perturbations of dispersion-managed solitons. We do so by first developing soliton perturbation theory for the dispersion-managed nonlinear Schroedinger (DMNLS) equation, which governs the long-term behavior of optical fiber transmission systems and certain kinds of femtosecond lasers. We show that the eigenmodes and generalized eigenmodes of the linearized DMNLS equation around traveling-wave solutions can be generated from the invariances of the DMNLS equations, we quantify the perturbation-induced parameter changes of the solution in terms of the eigenmodes and the adjoint eigenmodes, and we obtain evolution equations for the solution parameters. We then apply these results to guide importance-sampled Monte Carlo (MC) simulations and reconstruct the probability density functions of the solution parameters under the effect of noise, and we compare with standard MC simulations of the unaveraged system. The comparison further validates the use of the DMNLS equation as a model for dispersion-managed systems

Schlieren visualization of flow-field modification over an airfoil by near-surface gas-density perturbations generated by a nanosecond-pulse-driven plasma actuator

International Nuclear Information System (INIS)

Komuro, Atsushi; Konno, Kaiki; Ando, Akira; Takashima, Keisuke; Kaneko, Toshiro; Tanaka, Naoki; Nonomura, Taku; Asai, Keisuke

2017-01-01

Gas-density perturbations near an airfoil surface generated by a nanosecond dielectric-barrier-discharge plasma actuator (ns-DBDPA) are visualized using a high-speed Schlieren imaging method. Wind-tunnel experiments are conducted for a wind speed of 20 m s −1 with an NACA0015 airfoil whose chord length is 100 mm. The results show that the ns-DBDPA first generates a pressure wave and then stochastic perturbations of the gas density near the leading edge of the airfoil. Two structures with different characteristics are observed in the stochastic perturbations. One structure propagates along the boundary between the shear layer and the main flow at a speed close to that of the main flow. The other propagates more slowly on the surface of the airfoil and causes mixing between the main and shear flows. It is observed that these two heated structures interact with each other, resulting in a recovery in the negative pressure coefficient at the leading edge of the airfoil. (paper)

Magnetic fields and density functional theory

Energy Technology Data Exchange (ETDEWEB)

Salsbury Jr., Freddie [Univ. of California, Berkeley, CA (United States)

1999-02-01

A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field density functional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local density functionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules.

Magnetic fields and density functional theory

International Nuclear Information System (INIS)

Salsbury, Freddie Jr.

1999-01-01

A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field density functional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local density functionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules

Selberg zeta functions and transfer operators an experimental approach to singular perturbations

CERN Document Server

Fraczek, Markus Szymon

2017-01-01

This book presents a method for evaluating Selberg zeta functions via transfer operators for the full modular group and its congruence subgroups with characters. Studying zeros of Selberg zeta functions for character deformations allows us to access the discrete spectra and resonances of hyperbolic Laplacians under both singular and non-singular perturbations. Areas in which the theory has not yet been sufficiently developed, such as the spectral theory of transfer operators or the singular perturbation theory of hyperbolic Laplacians, will profit from the numerical experiments discussed in this book. Detailed descriptions of numerical approaches to the spectra and eigenfunctions of transfer operators and to computations of Selberg zeta functions will be of value to researchers active in analysis, while those researchers focusing more on numerical aspects will benefit from discussions of the analytic theory, in particular those concerning the transfer operator method and the spectral theory of hyperbolic spac...

Adler function for light quarks in analytic perturbation theory

International Nuclear Information System (INIS)

Milton, K. A.; Solovtsov, I. L.; Solovtsova, O. P.

2001-01-01

The method of analytic perturbation theory, which avoids the problem of ghost-pole-type singularities and gives a self-consistent description of both spacelike and timelike regions, is applied to describe the 'light' Adler function corresponding to the nonstrange vector channel of the inclusive decay of the τ lepton. The role of threshold effects is investigated. The behavior of the quark-antiquark system near threshold is described by using a new relativistic resummation factor. It is shown that the method proposed leads to good agreement with the 'experimental' Adler function down to the lowest energy scale

Density dependence of the nuclear energy-density functional

Science.gov (United States)

Papakonstantinou, Panagiota; Park, Tae-Sun; Lim, Yeunhwan; Hyun, Chang Ho

2018-01-01

Background: The explicit density dependence in the coupling coefficients entering the nonrelativistic nuclear energy-density functional (EDF) is understood to encode effects of three-nucleon forces and dynamical correlations. The necessity for the density-dependent coupling coefficients to assume the form of a preferably small fractional power of the density ρ is empirical and the power is often chosen arbitrarily. Consequently, precision-oriented parametrizations risk overfitting in the regime of saturation and extrapolations in dilute or dense matter may lose predictive power. Purpose: Beginning with the observation that the Fermi momentum kF, i.e., the cubic root of the density, is a key variable in the description of Fermi systems, we first wish to examine if a power hierarchy in a kF expansion can be inferred from the properties of homogeneous matter in a domain of densities, which is relevant for nuclear structure and neutron stars. For subsequent applications we want to determine a functional that is of good quality but not overtrained. Method: For the EDF, we fit systematically polynomial and other functions of ρ1 /3 to existing microscopic, variational calculations of the energy of symmetric and pure neutron matter (pseudodata) and analyze the behavior of the fits. We select a form and a set of parameters, which we found robust, and examine the parameters' naturalness and the quality of resulting extrapolations. Results: A statistical analysis confirms that low-order terms such as ρ1 /3 and ρ2 /3 are the most relevant ones in the nuclear EDF beyond lowest order. It also hints at a different power hierarchy for symmetric vs. pure neutron matter, supporting the need for more than one density-dependent term in nonrelativistic EDFs. The functional we propose easily accommodates known or adopted properties of nuclear matter near saturation. More importantly, upon extrapolation to dilute or asymmetric matter, it reproduces a range of existing microscopic

Green's function method for perturbed Korteweg-de Vries equation

International Nuclear Information System (INIS)

Cai Hao; Huang Nianning

2003-01-01

The x-derivatives of squared Jost solution are the eigenfunctions with the zero eigenvalue of the linearized equation derived from the perturbed Korteweg-de Vries equation. A method similar to Green's function formalism is introduced to show the completeness of the squared Jost solutions in multi-soliton cases. It is not related to Lax equations directly, and thus it is beneficial to deal with the nonlinear equations with complicated Lax pair

Applications of δ-function perturbation to the pricing of derivative securities

Science.gov (United States)

Decamps, Marc; De Schepper, Ann; Goovaerts, Marc

2004-11-01

In the recent econophysics literature, the use of functional integrals is widespread for the calculation of option prices. In this paper, we extend this approach in several directions by means of δ-function perturbations. First, we show that results about infinitely repulsive δ-function are applicable to the pricing of barrier options. We also introduce functional integrals over skew paths that give rise to a new European option formula when combined with δ-function potential. We propose accurate closed-form approximations based on the theory of comonotonic risks in case the functional integrals are not analytically computable.

Density-functional theory for internal magnetic fields

Science.gov (United States)

Tellgren, Erik I.

2018-01-01

A density-functional theory is developed based on the Maxwell-Schrödinger equation with an internal magnetic field in addition to the external electromagnetic potentials. The basic variables of this theory are the electron density and the total magnetic field, which can equivalently be represented as a physical current density. Hence, the theory can be regarded as a physical current density-functional theory and an alternative to the paramagnetic current density-functional theory due to Vignale and Rasolt. The energy functional has strong enough convexity properties to allow a formulation that generalizes Lieb's convex analysis formulation of standard density-functional theory. Several variational principles as well as a Hohenberg-Kohn-like mapping between potentials and ground-state densities follow from the underlying convex structure. Moreover, the energy functional can be regarded as the result of a standard approximation technique (Moreau-Yosida regularization) applied to the conventional Schrödinger ground-state energy, which imposes limits on the maximum curvature of the energy (with respect to the magnetic field) and enables construction of a (Fréchet) differentiable universal density functional.

Density-density functionals and effective potentials in many-body electronic structure calculations

International Nuclear Information System (INIS)

Reboredo, Fernando A.; Kent, Paul R.

2008-01-01

We demonstrate the existence of different density-density functionals designed to retain selected properties of the many-body ground state in a non-interacting solution starting from the standard density functional theory ground state. We focus on diffusion quantum Monte Carlo applications that require trial wave functions with optimal Fermion nodes. The theory is extensible and can be used to understand current practices in several electronic structure methods within a generalized density functional framework. The theory justifies and stimulates the search of optimal empirical density functionals and effective potentials for accurate calculations of the properties of real materials, but also cautions on the limits of their applicability. The concepts are tested and validated with a near-analytic model.

On the accuracy of density-functional theory exchange-correlation functionals for H bonds in small water clusters: Benchmarks approaching the complete basis set limit

Science.gov (United States)

Santra, Biswajit; Michaelides, Angelos; Scheffler, Matthias

2007-11-01

The ability of several density-functional theory (DFT) exchange-correlation functionals to describe hydrogen bonds in small water clusters (dimer to pentamer) in their global minimum energy structures is evaluated with reference to second order Møller-Plesset perturbation theory (MP2). Errors from basis set incompleteness have been minimized in both the MP2 reference data and the DFT calculations, thus enabling a consistent systematic evaluation of the true performance of the tested functionals. Among all the functionals considered, the hybrid X3LYP and PBE0 functionals offer the best performance and among the nonhybrid generalized gradient approximation functionals, mPWLYP and PBE1W perform best. The popular BLYP and B3LYP functionals consistently underbind and PBE and PW91 display rather variable performance with cluster size.

Excited-state density functional theory

International Nuclear Information System (INIS)

Harbola, Manoj K; Hemanadhan, M; Shamim, Md; Samal, P

2012-01-01

Starting with a brief introduction to excited-state density functional theory, we present our method of constructing modified local density approximated (MLDA) energy functionals for the excited states. We show that these functionals give accurate results for kinetic energy and exchange energy compared to the ground state LDA functionals. Further, with the inclusion of GGA correction, highly accurate total energies for excited states are obtained. We conclude with a brief discussion on the further direction of research that include the construction of correlation energy functional and exchange potential for excited states.

Angle-dependent strong-field molecular ionization rates with tuned range-separated time-dependent density functional theory

Energy Technology Data Exchange (ETDEWEB)

Sissay, Adonay [Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803 (United States); Abanador, Paul; Mauger, François; Gaarde, Mette; Schafer, Kenneth J. [Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803 (United States); Lopata, Kenneth, E-mail: klopata@lsu.edu [Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803 (United States); Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803 (United States)

2016-09-07

Strong-field ionization and the resulting electronic dynamics are important for a range of processes such as high harmonic generation, photodamage, charge resonance enhanced ionization, and ionization-triggered charge migration. Modeling ionization dynamics in molecular systems from first-principles can be challenging due to the large spatial extent of the wavefunction which stresses the accuracy of basis sets, and the intense fields which require non-perturbative time-dependent electronic structure methods. In this paper, we develop a time-dependent density functional theory approach which uses a Gaussian-type orbital (GTO) basis set to capture strong-field ionization rates and dynamics in atoms and small molecules. This involves propagating the electronic density matrix in time with a time-dependent laser potential and a spatial non-Hermitian complex absorbing potential which is projected onto an atom-centered basis set to remove ionized charge from the simulation. For the density functional theory (DFT) functional we use a tuned range-separated functional LC-PBE*, which has the correct asymptotic 1/r form of the potential and a reduced delocalization error compared to traditional DFT functionals. Ionization rates are computed for hydrogen, molecular nitrogen, and iodoacetylene under various field frequencies, intensities, and polarizations (angle-dependent ionization), and the results are shown to quantitatively agree with time-dependent Schrödinger equation and strong-field approximation calculations. This tuned DFT with GTO method opens the door to predictive all-electron time-dependent density functional theory simulations of ionization and ionization-triggered dynamics in molecular systems using tuned range-separated hybrid functionals.

Angle-dependent strong-field molecular ionization rates with tuned range-separated time-dependent density functional theory

International Nuclear Information System (INIS)

Sissay, Adonay; Abanador, Paul; Mauger, François; Gaarde, Mette; Schafer, Kenneth J.; Lopata, Kenneth

2016-01-01

Strong-field ionization and the resulting electronic dynamics are important for a range of processes such as high harmonic generation, photodamage, charge resonance enhanced ionization, and ionization-triggered charge migration. Modeling ionization dynamics in molecular systems from first-principles can be challenging due to the large spatial extent of the wavefunction which stresses the accuracy of basis sets, and the intense fields which require non-perturbative time-dependent electronic structure methods. In this paper, we develop a time-dependent density functional theory approach which uses a Gaussian-type orbital (GTO) basis set to capture strong-field ionization rates and dynamics in atoms and small molecules. This involves propagating the electronic density matrix in time with a time-dependent laser potential and a spatial non-Hermitian complex absorbing potential which is projected onto an atom-centered basis set to remove ionized charge from the simulation. For the density functional theory (DFT) functional we use a tuned range-separated functional LC-PBE*, which has the correct asymptotic 1/r form of the potential and a reduced delocalization error compared to traditional DFT functionals. Ionization rates are computed for hydrogen, molecular nitrogen, and iodoacetylene under various field frequencies, intensities, and polarizations (angle-dependent ionization), and the results are shown to quantitatively agree with time-dependent Schrödinger equation and strong-field approximation calculations. This tuned DFT with GTO method opens the door to predictive all-electron time-dependent density functional theory simulations of ionization and ionization-triggered dynamics in molecular systems using tuned range-separated hybrid functionals.

Non-Perturbative QCD Coupling and Beta Function from Light Front Holography

International Nuclear Information System (INIS)

Brodsky, Stanley J.

2010-01-01

The light-front holographic mapping of classical gravity in AdS space, modified by a positive-sign dilaton background, leads to a non-perturbative effective coupling α s AdS (Q 2 ). It agrees with hadron physics data extracted from different observables, such as the effective charge defined by the Bjorken sum rule, as well as with the predictions of models with built-in confinement and lattice simulations. It also displays a transition from perturbative to nonperturbative conformal regimes at a momentum scale ∼ 1 GeV. The resulting β-function appears to capture the essential characteristics of the full β-function of QCD, thus giving further support to the application of the gauge/gravity duality to the confining dynamics of strongly coupled QCD. Commensurate scale relations relate observables to each other without scheme or scale ambiguity. In this paper we extrapolate these relations to the nonperturbative domain, thus extending the range of predictions based on α s AdS (Q 2 ).

Spectral function from Reduced Density Matrix Functional Theory

Science.gov (United States)

Romaniello, Pina; di Sabatino, Stefano; Berger, Jan A.; Reining, Lucia

2015-03-01

In this work we focus on the calculation of the spectral function, which determines, for example, photoemission spectra, from reduced density matrix functional theory. Starting from its definition in terms of the one-body Green's function we derive an expression for the spectral function that depends on the natural occupation numbers and on an effective energy which accounts for all the charged excitations. This effective energy depends on the two-body as well as higher-order density matrices. Various approximations to this expression are explored by using the exactly solvable Hubbard chains.

Ground-state densities from the Rayleigh-Ritz variation principle and from density-functional theory.

Science.gov (United States)

Kvaal, Simen; Helgaker, Trygve

2015-11-14

The relationship between the densities of ground-state wave functions (i.e., the minimizers of the Rayleigh-Ritz variation principle) and the ground-state densities in density-functional theory (i.e., the minimizers of the Hohenberg-Kohn variation principle) is studied within the framework of convex conjugation, in a generic setting covering molecular systems, solid-state systems, and more. Having introduced admissible density functionals as functionals that produce the exact ground-state energy for a given external potential by minimizing over densities in the Hohenberg-Kohn variation principle, necessary and sufficient conditions on such functionals are established to ensure that the Rayleigh-Ritz ground-state densities and the Hohenberg-Kohn ground-state densities are identical. We apply the results to molecular systems in the Born-Oppenheimer approximation. For any given potential v ∈ L(3/2)(ℝ(3)) + L(∞)(ℝ(3)), we establish a one-to-one correspondence between the mixed ground-state densities of the Rayleigh-Ritz variation principle and the mixed ground-state densities of the Hohenberg-Kohn variation principle when the Lieb density-matrix constrained-search universal density functional is taken as the admissible functional. A similar one-to-one correspondence is established between the pure ground-state densities of the Rayleigh-Ritz variation principle and the pure ground-state densities obtained using the Hohenberg-Kohn variation principle with the Levy-Lieb pure-state constrained-search functional. In other words, all physical ground-state densities (pure or mixed) are recovered with these functionals and no false densities (i.e., minimizing densities that are not physical) exist. The importance of topology (i.e., choice of Banach space of densities and potentials) is emphasized and illustrated. The relevance of these results for current-density-functional theory is examined.

Developments in perturbation theory

International Nuclear Information System (INIS)

Greenspan, E.

1976-01-01

Included are sections dealing with perturbation expressions for reactivity, methods for the calculation of perturbed fluxes, integral transport theory formulations for reactivity, generalized perturbation theory, sensitivity and optimization studies, multigroup calculations of bilinear functionals, and solution of inhomogeneous Boltzmann equations with singular operators

New correlation potential for the local-spin-density functional formalism. II

International Nuclear Information System (INIS)

Kolar, M.; Farkas, L.

1982-01-01

Using the new parameterization for the correlation potential which seems to be the best that is at present available within the local-spin-density (LSD) functional formalism, the Fermi contact term in light atoms (up to Ni) is calculated. Although the overall improvement of the previous LSD results is obtained, discrepancy between theory and experiment remains rather large. It seems that the local approximation for exchange and correlation fails to predict such quantities as magnetic-moment density near the nucleus. It is also shown that the self-interaction correction does not remedy this failure. Further, the effect of the nonzero nuclear radius is investigated and found to be most important in the lightest atoms (e.g. a factor of 0.664 appears in the case of Li). This fact was omitted in all previous calculations and throws doubt on the reported excellent agreement of the results of many-body perturbation theory with experiment. It was also verified that the contact approximation of the Fermi contact term is really good enough. (author)

Metal-ligand delocalization and spin density in the CuCl2 and [CuCl4](2-) molecules: Some insights from wave function theory.

Science.gov (United States)

Giner, Emmanuel; Angeli, Celestino

2015-09-28

The aim of this paper is to unravel the physical phenomena involved in the calculation of the spin density of the CuCl2 and [CuCl4](2-) systems using wave function methods. Various types of wave functions are used here, both variational and perturbative, to analyse the effects impacting the spin density. It is found that the spin density on the chlorine ligands strongly depends on the mixing between two types of valence bond structures. It is demonstrated that the main difficulties found in most of the previous studies based on wave function methods come from the fact that each valence bond structure requires a different set of molecular orbitals and that using a unique set of molecular orbitals in a variational procedure leads to the removal of one of them from the wave function. Starting from these results, a method to compute the spin density at a reasonable computational cost is proposed.

Cluster perturbation theory for calculation of electronic properties of ensembles of metal nanoclusters

Science.gov (United States)

Zhumagulov, Yaroslav V.; Krasavin, Andrey V.; Kashurnikov, Vladimir A.

2018-05-01

The method is developed for calculation of electronic properties of an ensemble of metal nanoclusters with the use of cluster perturbation theory. This method is applied to the system of gold nanoclusters. The Greens function of single nanocluster is obtained by ab initio calculations within the framework of the density functional theory, and then is used in Dyson equation to group nanoclusters together and to compute the Greens function as well as the electron density of states of the whole ensemble. The transition from insulator state of a single nanocluster to metallic state of bulk gold is observed.

PERTURBATION OF VOLTAGE-SENSITIVE Ca2+ CHANNEL FUNCTION BY VOLATILE ORGANIC SOLVENTS.

Science.gov (United States)

The mechanisms underlying the acute neurophysiological and behavioral effects of volatile organic compounds (VOCs) remain to be elucidated. However, the function of neuronal ion channels is perturbed by VOCs. The present study examined effects of toluene (TOL), trichloroethylene ...

Ignition condition and gain prediction for perturbed inertial confinement fusion targets

International Nuclear Information System (INIS)

Kishony, Roy; Shvarts, Dov

2001-01-01

The effect of perturbations on hot spot ignition is studied using full two-dimensional (2D) numerical simulations of the National Ignition Facility [J. D. Lindl, Phys. Plasmas 2, 3933 (1995)] direct drive Laboratory for Laser Energetics target design and newly derived 2D self-similar solutions for a perturbed burn wave propagation. It is shown that the required implosion velocity needed for ignition increases with the perturbation mode number and final amplitude, reaching an asymptotic value for high enough perturbation mode numbers, when the entire mixing zone no longer contributes to the ignition of the hot spot. Using the new self-similar solutions, ignition conditions for various perturbation mode numbers and amplitudes are obtained. These ignition conditions, which correspond to areal densities higher than needed for ignition in the symmetric case, are translated to a required increase in the implosion velocity needed for ignition, using the 1D Levendahl-Lindl scaling, in good agreement with the full 2D numerical simulation results. Finally, using the above results, a model for predicting the gain of a perturbed targets as a function of the perturbation spectra (single-mode and multi-mode) is presented, in good agreement with full numerical simulations

SECOND-ORDER SOLUTIONS OF COSMOLOGICAL PERTURBATION IN THE MATTER-DOMINATED ERA

International Nuclear Information System (INIS)

Hwang, Jai-chan; Noh, Hyerim; Gong, Jinn-Ouk

2012-01-01

We present the growing mode solutions of cosmological perturbations to the second order in the matter-dominated era. We also present several gauge-invariant combinations of perturbation variables to the second order in the most general fluid context. Based on these solutions, we study the Newtonian correspondence of relativistic perturbations to the second order. In addition to the previously known exact relativistic/Newtonian correspondence of density and velocity perturbations to the second order in the comoving gauge, here we show that in the sub-horizon limit we have the correspondences for density, velocity, and potential perturbations in the zero-shear gauge and in the uniform-expansion gauge to the second order. Density perturbation in the uniform-curvature gauge also shows the correspondence to the second order in the sub-horizon scale. We also identify the relativistic gravitational potential that shows exact correspondence to the Newtonian one to the second order.

Single-particle energies and density of states in density functional theory

Science.gov (United States)

van Aggelen, H.; Chan, G. K.-L.

2015-07-01

Time-dependent density functional theory (TD-DFT) is commonly used as the foundation to obtain neutral excited states and transition weights in DFT, but does not allow direct access to density of states and single-particle energies, i.e. ionisation energies and electron affinities. Here we show that by extending TD-DFT to a superfluid formulation, which involves operators that break particle-number symmetry, we can obtain the density of states and single-particle energies from the poles of an appropriate superfluid response function. The standard Kohn- Sham eigenvalues emerge as the adiabatic limit of the superfluid response under the assumption that the exchange- correlation functional has no dependence on the superfluid density. The Kohn- Sham eigenvalues can thus be interpreted as approximations to the ionisation energies and electron affinities. Beyond this approximation, the formalism provides an incentive for creating a new class of density functionals specifically targeted at accurate single-particle eigenvalues and bandgaps.

Two-point Green's functions in quantum electrodynamics at finite temperature and density

International Nuclear Information System (INIS)

Bechler, A.

1981-01-01

One-particle propagators of the relativistic electron--positron gas are systematically investigated. With the nonvanishing chemical potential the neutrality of the whole system is secured by a uniformly charged classical background described by a classical current J/sub μ/. Due to the translational invariance of this model it is natural to investigate the properties of the propagators in the momentum space. The Fourier-transforms of the Green's functions have been expressed in terms of the generalized spectral Lehmann representation and the second-order spectral functions of the photon and electron propagators have been found. The matter-dependent part of the propagator is finite and only the vacuum part has to be renormalized with the use of standard renormalization counterterms. The singularities of the gauge-independent photon propagator have been further investigated with the use of the spectral representation and nonperturbative expressions for the spectrum of collective excitations have been obtained. In the second order of perturbation they reproduce the asymptotic formulas at T→0 and T→infinity cited previously in the literature. In particular, the relativistic plasma frequency (photon effective mass) has been expressed in a simple form in terms of the integrals over the spectral functions. Our formulas for the relativistic plasmon mass squared Ω 2 exhibit an interesting property that at some temperature and density Ω 2 should become negative. However, simple estimates show that this phenomenon occurs at highly nonrealistic temperatures of the order of e 137 , i.e., in the region where the perturbation theory fails. The damping of the collective excitations is also considered

Density of states functions for photonic crystals

International Nuclear Information System (INIS)

McPhedran, R.C.; McOrist, J.; Sterke, C.M. de; Nicorovici, N.A.; Botten, L.C.; Asatryan, A.A.

2004-01-01

We discuss density of states functions for photonic crystals, in the context of the two-dimensional problem for arrays of cylinders of arbitrary cross section. We introduce the mutual density of states (MDOS), and show that this function can be used to calculate both the local density of states (LDOS), which gives position information for emission of radiation from photonic crystals, and the spectral density of states (SDOS), which gives angular information. We establish the connection between MDOS, LDOS, SDOS and the conventional density of states, which depends only on frequency. We relate all four functions to the band structure and propagating states within the crystal, and give numerical examples of the relation between band structure and density of states functions

Nonlocal kinetic-energy-density functionals

International Nuclear Information System (INIS)

Garcia-Gonzalez, P.; Alvarellos, J.E.; Chacon, E.

1996-01-01

In this paper we present nonlocal kinetic-energy functionals T[n] within the average density approximation (ADA) framework, which do not require any extra input when applied to any electron system and recover the exact kinetic energy and the linear response function of a homogeneous system. In contrast with previous ADA functionals, these present good behavior of the long-range tail of the exact weight function. The averaging procedure for the kinetic functional (averaging the Fermi momentum of the electron gas, instead of averaging the electron density) leads to a functional without numerical difficulties in the calculation of extended systems, and it gives excellent results when applied to atoms and jellium surfaces. copyright 1996 The American Physical Society

The sine-Gordon model and the small κ+ region of light- cone perturbation theory

International Nuclear Information System (INIS)

Griffin, P.A.

1992-01-01

The non-perturbative ultraviolet divergence of the sine-Gordon model is used to study the k + = 0 region of light-cone perturbation theory. The light-cone vacuum is shown to be unstable at the non- perturbative β 2 = 8π critical point by a light-cone version of Coleman's variational method. Vacuum bubbles, which are k + = 0 diagram in light-cone field theory and are individually finite and non-vanishing for all β, conspire to generate ultraviolet divergences of the light-cone energy density. The k + = 0 region of momentum also contributed to connected Green's functions: the connected two point function will not diverge, as it should, at the critical point unless diagrams which contribute only at k + = 0 are properly included. This analysis shows in a simple way how the k + = 0 region cannot be ignored even for connected diagrams. This phenomenon is expected to occur in higher dimensional gauge theories starting at two loop order in light-cone perturbation theory

Nonlinear spherical perturbations in quintessence models of dark energy

Science.gov (United States)

Pratap Rajvanshi, Manvendra; Bagla, J. S.

2018-06-01

Observations have confirmed the accelerated expansion of the universe. The accelerated expansion can be modelled by invoking a cosmological constant or a dynamical model of dark energy. A key difference between these models is that the equation of state parameter w for dark energy differs from ‑1 in dynamical dark energy (DDE) models. Further, the equation of state parameter is not constant for a general DDE model. Such differences can be probed using the variation of scale factor with time by measuring distances. Another significant difference between the cosmological constant and DDE models is that the latter must cluster. Linear perturbation analysis indicates that perturbations in quintessence models of dark energy do not grow to have a significant amplitude at small length scales. In this paper we study the response of quintessence dark energy to non-linear perturbations in dark matter. We use a fully relativistic model for spherically symmetric perturbations. In this study we focus on thawing models. We find that in response to non-linear perturbations in dark matter, dark energy perturbations grow at a faster rate than expected in linear perturbation theory. We find that dark energy perturbation remains localised and does not diffuse out to larger scales. The dominant drivers of the evolution of dark energy perturbations are the local Hubble flow and a supression of gradients of the scalar field. We also find that the equation of state parameter w changes in response to perturbations in dark matter such that it also becomes a function of position. The variation of w in space is correlated with density contrast for matter. Variation of w and perturbations in dark energy are more pronounced in response to large scale perturbations in matter while the dependence on the amplitude of matter perturbations is much weaker.

Exchange-correlation energies of atoms from efficient density functionals: influence of the electron density

Science.gov (United States)

Tao, Jianmin; Ye, Lin-Hui; Duan, Yuhua

2017-12-01

The primary goal of Kohn-Sham density functional theory is to evaluate the exchange-correlation contribution to electronic properties. However, the accuracy of a density functional can be affected by the electron density. Here we apply the nonempirical Tao-Mo (TM) semilocal functional to study the influence of the electron density on the exchange and correlation energies of atoms and ions, and compare the results with the commonly used nonempirical semilocal functionals local spin-density approximation (LSDA), Perdew-Burke-Ernzerhof (PBE), Tao-Perdew-Staroverov-Scuseria (TPSS), and hybrid functional PBE0. We find that the spin-restricted Hartree-Fock density yields the exchange and correlation energies in good agreement with the Optimized Effective Potential method, particularly for spherical atoms and ions. However, the errors of these semilocal and hybrid functionals become larger for self-consistent densities. We further find that the quality of the electron density have greater effect on the exchange-correlation energies of kinetic energy density-dependent meta-GGA functionals TPSS and TM than on those of the LSDA and GGA, and therefore, should have greater influence on the performance of meta-GGA functionals. Finally, we show that the influence of the density quality on PBE0 is slightly reduced, compared to that of PBE, due to the exact mixing.

A multiconfigurational hybrid density-functional theory

DEFF Research Database (Denmark)

Sharkas, Kamal; Savin, Andreas; Jensen, Hans Jørgen Aagaard

2012-01-01

We propose a multiconfigurational hybrid density-functional theory which rigorously combines a multiconfiguration self-consistent-field calculation with a density-functional approximation based on a linear decomposition of the electron-electron interaction. This gives a straightforward extension ...

Assessing Hubbard-corrected AM05+U and PBEsol+U density functionals for strongly correlated oxides CeO_2 and Ce_2O_3

International Nuclear Information System (INIS)

Weck, Philippe F.; Kim, Eunja

2016-01-01

The structure–property relationships of bulk CeO_2 and Ce_2O_3 have been investigated using AM05 and PBEsol exchange–correlation functionals within the frameworks of Hubbard-corrected density functional theory (DFT+U) and density functional perturbation theory (DFPT+U). Compared with conventional PBE+U, RPBE+U, PW91+U and LDA+U functionals, AM05+U and PBEsol+U describe experimental crystalline parameters and properties of CeO_2 and Ce_2O_3 with superior accuracy, especially when +U is chosen close to its value derived by the linear-response approach. Lastly, the present findings call for a reexamination of some of the problematic oxide materials featuring strong f- and d-electron correlation using AM05+U and PBEsol+U.

Excitonic effects in solids : time-dependent density functional theory versus the Bethe-Salpeter equation

International Nuclear Information System (INIS)

Sagmeister, S.

2009-01-01

The aim of this work is to compare two state-of-the-art methods for the investigation of excitonic effects in solids, namely Time-Dependent Density Functional Theory (TDDFT) and Many-Body Perturbation Theory (MBPT), for selected simple gap systems as well as semiconducting polymers. Within TDDFT, the linear response framework is used and the Dyson equation for the density-density response function is solved, whereas within MBPT, the Bethe-Salpeter equation (BSE) for the electron-hole correlation function is solved. The dielectric function is obtained as a last step. Both techniques take into account the excitonic effects caused by the interaction of electron-hole pairs. In the former these effects are included in the exchange-correlation (xc) kernel, whereas in the latter they are located in the interaction kernel of the BSE. Kohn-Sham single-particle wave functions obtained from Density Functional Theory within the linearized augmented planewave (LAPW) method are used to calculate all relevant quantities of the formalism. For the simple systems GaAs, Si and LiF are chosen. The role of several approximations to the xc kernel is studied and it is found that for GaAs and Si simple semi-empirical models provide a dielectric function in accordance with the BSE. For the case of LiF, being a system with a weak screening and a strongly bound exciton, only an xc kernel derived from MBPT yields reasonable results but still a slight discrepancy to the BSE is observed. Finally, the semiconducting polymers poly-acetylene and poly(phenylene-vinylene) (PPV) are studied. For both materials the concept of semi-empirical approximations to the xc kernel turns out to be ambiguous due to their low-dimensional character. In the case of poly-acetylene, the xc kernel derived from MBPT yields a dielectric function which is in close but not exact agreement with the one obtained from the BSE. (author) [de

Local density approximation for exchange in excited-state density functional theory

OpenAIRE

Harbola, Manoj K.; Samal, Prasanjit

2004-01-01

Local density approximation for the exchange energy is made for treatment of excited-states in density-functional theory. It is shown that taking care of the state-dependence of the LDA exchange energy functional leads to accurate excitation energies.

Green’s functions for spin boson systems: Beyond conventional perturbation theories

Energy Technology Data Exchange (ETDEWEB)

Liu, Junjie [State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433 (China); Xu, Hui [Collaborative Innovation Center of Advanced Microstructures, Fudan University, Shanghai 200433 (China); Wu, Chang-Qin [State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433 (China); Collaborative Innovation Center of Advanced Microstructures, Fudan University, Shanghai 200433 (China)

2016-12-20

Unraveling general properties of Green’s functions of quantum dissipative systems is of both experimental relevance and theoretical interest. Here, we study the spin-boson model as a prototype. By utilizing the Majorana-fermion representation together with the polaron transformation, we establish a theoretical approach to analyze Green’s functions of the spin-boson model. In contrast to conventional perturbation theories either in the tunneling energy or in the system-bath coupling strength, the proposed scheme gives reliable results over wide regimes of the coupling strength, bias, as well as temperature. To demonstrate the utility of the approach, we consider the susceptibility as well as the symmetrized spin correlation function (SSCF) which can be expressed in terms of Green’s functions. Thorough investigations are made on systems embedded in Ohmic or sub-Ohmic bosonic baths. We found the so-obtained SSCF is the same as that of the non-interacting blip approximation (NIBA) in unbiased systems while it is applicable for a wider range of temperature in the biased systems compared with the NIBA. We also show that a previous perturbation result is recovered as a weak coupling limit of the so-obtained SSCF. Furthermore, by studying the quantum criticality of the susceptibility, we confirm the validity of the quantum-to-classical mapping in the whole sub-Ohmic regime.

Energy vs. density on paths toward more exact density functionals.

Science.gov (United States)

Kepp, Kasper P

2018-03-14

Recently, the progression toward more exact density functional theory has been questioned, implying a need for more formal ways to systematically measure progress, i.e. a "path". Here I use the Hohenberg-Kohn theorems and the definition of normality by Burke et al. to define a path toward exactness and "straying" from the "path" by separating errors in ρ and E[ρ]. A consistent path toward exactness involves minimizing both errors. Second, a suitably diverse test set of trial densities ρ' can be used to estimate the significance of errors in ρ without knowing the exact densities which are often inaccessible. To illustrate this, the systems previously studied by Medvedev et al., the first ionization energies of atoms with Z = 1 to 10, the ionization energy of water, and the bond dissociation energies of five diatomic molecules were investigated using CCSD(T)/aug-cc-pV5Z as benchmark at chemical accuracy. Four functionals of distinct designs was used: B3LYP, PBE, M06, and S-VWN. For atomic cations regardless of charge and compactness up to Z = 10, the energy effects of the different ρ are energy-wise insignificant. An interesting oscillating behavior in the density sensitivity is observed vs. Z, explained by orbital occupation effects. Finally, it is shown that even large "normal" problems such as the Co-C bond energy of cobalamins can use simpler (e.g. PBE) trial densities to drastically speed up computation by loss of a few kJ mol -1 in accuracy. The proposed method of using a test set of trial densities to estimate the sensitivity and significance of density errors of functionals may be useful for testing and designing new balanced functionals with more systematic improvement of densities and energies.

Streamer properties and associated x-rays in perturbed air

Science.gov (United States)

Köhn, C.; Chanrion, O.; Babich, L. P.; Neubert, T.

2018-01-01

Streamers are ionization waves in electric discharges. One of the key ingredients of streamer propagation is an ambient gas that serves as a source of free electrons. Here, we explore the dependence of streamer dynamics on different spatial distributions of ambient air molecules. We vary the spatial profile of air parallel and perpendicular to the ambient electric field. We consider local sinusoidal perturbations of 5%-100%, as induced from discharge shock waves. We use a cylindrically symmetric particle-in-cell code to simulate the evolution of bidirectional streamers and compare the electron density, electric field, streamer velocity and electron energy of streamers in uniform air and in perturbed air. In all considered cases, the motion is driven along in decreasing air density and damped along increasing air density. Perturbations of at most 5%-10% change the velocity differences by up to approximately 40%. Perturbations perpendicular to the electric field additionally squeeze or branch streamers. Air variations can thus partly explain the difference of velocities and morphologies of streamer discharges. In cases with large perturbations, electrons gain energies of up to 30 keV compared to 100 eV in uniformly distributed air. For such perturbations parallel to the ambient electric field, we see the spontaneous initiation of a negative streamer; for perpendicular perturbations, x-rays with energies of up to 20 keV are emitted within 0.17 ns.

Automated lattice perturbation theory in the Schroedinger functional. Implementation and applications in HQET

International Nuclear Information System (INIS)

Hesse, Dirk

2012-01-01

The author developed the pastor software package for automated lattice perturbation theory calculations in the Schroedinger functional scheme. The pastor code consists of two building blocks, dealing with the generation of Feynman rules and Feynman diagrams respectively. Accepting a rather generic class of lattice gauge and fermion actions, passed to the code in a symbolic form as input, a low level part of pastor will generate Feynman rules to an arbitrary order in the bare coupling with a trivial or an Abelian background field. The second, high level part of pastor is a code generator whose output relies on the vertex generator. It writes programs that evaluate Feynman diagrams for a class of Schroedinger functional observables up to one loop order automatically, the relevant O(a) improvement terms are taken into account. We will describe the algorithms used for implementation of both parts of the code in detail, and provide cross checks with perturbative and non-perturbative data to demonstrate the correctness of our code. We demonstrate the usefulness of the pastor package through various applications taken from the matching process of heavy quark effective theory with quantum chromodynamics. We have e.g. completed a one loop analysis for new candidates for matching observables timely and with rather small effort, highlighting two advantages of an automated software setup. The results that were obtained so far will be useful as a guideline for further non-perturbative studies.

Automated lattice perturbation theory in the Schroedinger functional. Implementation and applications in HQET

Energy Technology Data Exchange (ETDEWEB)

Hesse, Dirk

2012-07-13

The author developed the pastor software package for automated lattice perturbation theory calculations in the Schroedinger functional scheme. The pastor code consists of two building blocks, dealing with the generation of Feynman rules and Feynman diagrams respectively. Accepting a rather generic class of lattice gauge and fermion actions, passed to the code in a symbolic form as input, a low level part of pastor will generate Feynman rules to an arbitrary order in the bare coupling with a trivial or an Abelian background field. The second, high level part of pastor is a code generator whose output relies on the vertex generator. It writes programs that evaluate Feynman diagrams for a class of Schroedinger functional observables up to one loop order automatically, the relevant O(a) improvement terms are taken into account. We will describe the algorithms used for implementation of both parts of the code in detail, and provide cross checks with perturbative and non-perturbative data to demonstrate the correctness of our code. We demonstrate the usefulness of the pastor package through various applications taken from the matching process of heavy quark effective theory with quantum chromodynamics. We have e.g. completed a one loop analysis for new candidates for matching observables timely and with rather small effort, highlighting two advantages of an automated software setup. The results that were obtained so far will be useful as a guideline for further non-perturbative studies.

Reduced density-matrix functional theory: Correlation and spectroscopy.

Science.gov (United States)

Di Sabatino, S; Berger, J A; Reining, L; Romaniello, P

2015-07-14

In this work, we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the calculation of total energies, occupation numbers, removal/addition energies, and spectral functions. We use the exactly solvable Hubbard dimer at 1/4 and 1/2 fillings as test systems. This allows us to analyze the underlying physics and to elucidate the origin of the observed trends. For comparison, we also report the results of the GW approximation, where the self-energy functional is approximated, but no further hypothesis is made concerning the approximations of the observables. In particular, we focus on the atomic limit, where the two sites of the dimer are pulled apart and electrons localize on either site with equal probability, unless a small perturbation is present: this is the regime of strong electron correlation. In this limit, using the Hubbard dimer at 1/2 filling with or without a spin-symmetry-broken ground state allows us to explore how degeneracies and spin-symmetry breaking are treated in RDMFT. We find that, within the used approximations, neither in RDMFT nor in GW, the signature of strong correlation is present, when looking at the removal/addition energies and spectral function from the spin-singlet ground state, whereas both give the exact result for the spin-symmetry broken case. Moreover, we show how the spectroscopic properties change from one spin structure to the other.

Non-Perturbative QCD Coupling and Beta Function from Light Front Holography

Energy Technology Data Exchange (ETDEWEB)

Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; de Teramond, Guy F.; /Costa Rica U.; Deur, Alexandre; /Jefferson Lab

2010-05-26

The light-front holographic mapping of classical gravity in AdS space, modified by a positive-sign dilaton background, leads to a non-perturbative effective coupling {alpha}{sub s}{sup AdS} (Q{sup 2}). It agrees with hadron physics data extracted from different observables, such as the effective charge defined by the Bjorken sum rule, as well as with the predictions of models with built-in confinement and lattice simulations. It also displays a transition from perturbative to nonperturbative conformal regimes at a momentum scale {approx} 1 GeV. The resulting {beta}-function appears to capture the essential characteristics of the full {beta}-function of QCD, thus giving further support to the application of the gauge/gravity duality to the confining dynamics of strongly coupled QCD. Commensurate scale relations relate observables to each other without scheme or scale ambiguity. In this paper we extrapolate these relations to the nonperturbative domain, thus extending the range of predictions based on {alpha}{sub s}{sup AdS} (Q{sup 2}).

Scalar perturbations in two-temperature cosmological plasmas

NARCIS (Netherlands)

Moortgat, J.B.; Marklund, M.

2006-01-01

We study the properties of density perturbations of a two-component plasma with a temperature difference on a homogeneous and isotropic background. For this purpose, we extend the general relativistic gauge-invariant and covariant (GIC) perturbation theory to include a multifluid with a particular

Analytic cubic and quartic force fields using density-functional theory

Energy Technology Data Exchange (ETDEWEB)

Ringholm, Magnus; Gao, Bin; Thorvaldsen, Andreas J.; Ruud, Kenneth [Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Tromsø—The Arctic University of Norway, 9037 Tromsø (Norway); Jonsson, Dan [Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Tromsø—The Arctic University of Norway, 9037 Tromsø (Norway); High Performance Computing Group, University of Tromsø—The Arctic University of Norway, 9037 Tromsø (Norway); Bast, Radovan [Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, AlbaNova University Center, S-10691 Stockholm, Sweden and PDC Center for High Performance Computing, Royal Institute of Technology, S-10044 Stockholm (Sweden); Ekström, Ulf; Helgaker, Trygve [Center for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, 0315 Oslo (Norway)

2014-01-21

We present the first analytic implementation of cubic and quartic force constants at the level of Kohn–Sham density-functional theory. The implementation is based on an open-ended formalism for the evaluation of energy derivatives in an atomic-orbital basis. The implementation relies on the availability of open-ended codes for evaluation of one- and two-electron integrals differentiated with respect to nuclear displacements as well as automatic differentiation of the exchange–correlation kernels. We use generalized second-order vibrational perturbation theory to calculate the fundamental frequencies of methane, ethane, benzene, and aniline, comparing B3LYP, BLYP, and Hartree–Fock results. The Hartree–Fock anharmonic corrections agree well with the B3LYP corrections when calculated at the B3LYP geometry and from B3LYP normal coordinates, suggesting that the inclusion of electron correlation is not essential for the reliable calculation of cubic and quartic force constants.

Multireference second order perturbation theory with a simplified treatment of dynamical correlation.

Science.gov (United States)

Xu, Enhua; Zhao, Dongbo; Li, Shuhua

2015-10-13

A multireference second order perturbation theory based on a complete active space configuration interaction (CASCI) function or density matrix renormalized group (DMRG) function has been proposed. This method may be considered as an approximation to the CAS/A approach with the same reference, in which the dynamical correlation is simplified with blocked correlated second order perturbation theory based on the generalized valence bond (GVB) reference (GVB-BCPT2). This method, denoted as CASCI-BCPT2/GVB or DMRG-BCPT2/GVB, is size consistent and has a similar computational cost as the conventional second order perturbation theory (MP2). We have applied it to investigate a number of problems of chemical interest. These problems include bond-breaking potential energy surfaces in four molecules, the spectroscopic constants of six diatomic molecules, the reaction barrier for the automerization of cyclobutadiene, and the energy difference between the monocyclic and bicyclic forms of 2,6-pyridyne. Our test applications demonstrate that CASCI-BCPT2/GVB can provide comparable results with CASPT2 (second order perturbation theory based on the complete active space self-consistent-field wave function) for systems under study. Furthermore, the DMRG-BCPT2/GVB method is applicable to treat strongly correlated systems with large active spaces, which are beyond the capability of CASPT2.

Radiation perturbation theory in gravity and quantum universe as a hydrogen atom

International Nuclear Information System (INIS)

Pervushin, V.N.

1992-01-01

In quantum theory of gravity of the (n+1)-dimensional space-time the Faddeev-Popov functional integral is constructed for radiation perturbation theory. In this version the Universe expansion looks as the collective superfluid motion of quantum space, and the vacuum energy density plays the role of the hidden mass. 6 refs

Third-Order Density Perturbation and One-Loop Power Spectrum in Dark-Energy-Dominated Universe(Astrophysics and Cosmology)

OpenAIRE

Ryuichi, TAKAHASHI; Department of Physics and Astrophysics, Nagoya University

2008-01-01

We investigate the third-order density perturbation and the one-loop correction to the linear power spectrum in the dark-energy cosmological model. Our main interest is to understand the dark-energy effect on baryon acoustic oscillations in a quasi-nonlinear regime (k≈0.1h/Mpc). Analytical solutions and simple fitting formulae are presented for the dark-energy model with the general time-varying equation of state w(a). It turns out that the power spectrum coincides with the approximate res...

Relativistic density functional for nuclear structure

CERN Document Server

2016-01-01

This book aims to provide a detailed introduction to the state-of-the-art covariant density functional theory, which follows the Lorentz invariance from the very beginning and is able to describe nuclear many-body quantum systems microscopically and self-consistently. Covariant density functional theory was introduced in nuclear physics in the 1970s and has since been developed and used to describe the diversity of nuclear properties and phenomena with great success. In order to provide an advanced and updated textbook of covariant density functional theory for graduate students and nuclear physics researchers, this book summarizes the enormous amount of material that has accumulated in the field of covariant density functional theory over the last few decades as well as the latest developments in this area. Moreover, the book contains enough details for readers to follow the formalism and theoretical results, and provides exhaustive references to explore the research literature.

Linear perturbation theory for tidal streams and the small-scale CDM power spectrum

Science.gov (United States)

Bovy, Jo; Erkal, Denis; Sanders, Jason L.

2017-04-01

Tidal streams in the Milky Way are sensitive probes of the population of low-mass dark matter subhaloes predicted in cold dark matter (CDM) simulations. We present a new calculus for computing the effect of subhalo fly-bys on cold streams based on the action-angle representation of streams. The heart of this calculus is a line-of-parallel-angle approach that calculates the perturbed distribution function of a stream segment by undoing the effect of all relevant impacts. This approach allows one to compute the perturbed stream density and track in any coordinate system in minutes for realizations of the subhalo distribution down to 105 M⊙, accounting for the stream's internal dispersion and overlapping impacts. We study the statistical properties of density and track fluctuations with large suites of simulations of the effect of subhalo fly-bys. The one-dimensional density and track power spectra along the stream trace the subhalo mass function, with higher mass subhaloes producing power only on large scales, while lower mass subhaloes cause structure on smaller scales. We also find significant density and track bispectra that are observationally accessible. We further demonstrate that different projections of the track all reflect the same pattern of perturbations, facilitating their observational measurement. We apply this formalism to data for the Pal 5 stream and make a first rigorous determination of 10^{+11}_{-6} dark matter subhaloes with masses between 106.5 and 109 M⊙ within 20 kpc from the Galactic centre [corresponding to 1.4^{+1.6}_{-0.9} times the number predicted by CDM-only simulations or to fsub(r matter is clumpy on the smallest scales relevant for galaxy formation.

Critique of the foundations of time-dependent density-functional theory

International Nuclear Information System (INIS)

Schirmer, J.; Dreuw, A.

2007-01-01

The general expectation that, in principle, the time-dependent density-functional theory (TDDFT) is an exact formulation of the time evolution of an interacting N-electron system is critically reexamined. It is demonstrated that the previous TDDFT foundation, resting on four theorems by Runge and Gross (RG) [Phys. Rev. Lett. 52, 997 (1984)], is invalid because undefined phase factors corrupt the RG action integral functionals. Our finding confirms much of a previous analysis by van Leeuwen [Int. J. Mod. Phys. B 15, 1969 (2001)]. To analyze the RG theorems and other aspects of TDDFT, an utmost simplification of the Kohn-Sham (KS) concept has been introduced, in which the ground-state density is obtained from a single KS equation for one spatial (spinless) orbital. The time-dependent (TD) form of this radical Kohn-Sham (rKS) scheme, which has the same validity status as the ordinary KS version, has proved to be a valuable tool for analysis. The rKS concept is used to clarify also the alternative nonvariational formulation of TD KS theory. We argue that it is just a formal theory, allowing one to reproduce but not predict the time development of the exact density of the interacting N-electron system. Besides the issue of the formal exactness of TDDFT, it is shown that both the static and time-dependent KS linear response equations neglect the particle-particle (p-p) and hole-hole (h-h) matrix elements of the perturbing operator. For a local (multiplicative) operator this does not lead to a loss of information due to a remarkable general property of local operators. Accordingly, no logical inconsistency arises with respect to DFT, because DFT requires any external potential to be local. For a general nonlocal operator the error resulting from the neglected matrix elements is of second order in the electronic repulsion

Locality of correlation in density functional theory

Energy Technology Data Exchange (ETDEWEB)

Burke, Kieron [Department of Chemistry, University of California, Irvine, California 92697 (United States); Cancio, Antonio [Department of Physics and Astronomy, Ball State University, Muncie, Indiana 47306 (United States); Gould, Tim [Qld Micro- and Nanotechnology Centre, Griffith University, Nathan, Qld 4111 (Australia); Pittalis, Stefano [CNR-Istituto di Nanoscienze, Via Campi 213A, I-41125 Modena (Italy)

2016-08-07

The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi (TF) approximation in the non-relativistic semiclassical (or large-Z) limit for all matter, i.e., the kinetic energy becomes local. Exchange also becomes local in this limit. Numerical data on the correlation energy of atoms support the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around a large particle number are equivalent to local density approximations and their strong relevance to density functional approximations. Analyzing highly accurate atomic correlation energies, we show that E{sub C} → −A{sub C} ZlnZ + B{sub C}Z as Z → ∞, where Z is the atomic number, A{sub C} is known, and we estimate B{sub C} to be about 37 mhartree. The local density approximation yields A{sub C} exactly, but a very incorrect value for B{sub C}, showing that the local approximation is less relevant for the correlation alone. This limit is a benchmark for the non-empirical construction of density functional approximations. We conjecture that, beyond atoms, the leading correction to the local density approximation in the large-Z limit generally takes this form, but with B{sub C} a functional of the TF density for the system. The implications for the construction of approximate density functionals are discussed.

Functional derivative of noninteracting kinetic energy density functional

International Nuclear Information System (INIS)

Liu Shubin; Ayers, Paul W.

2004-01-01

Proofs from different theoretical frameworks, namely, the Hohenbergh-Kohn theorems, the Kohn-Sham scheme, and the first-order density matrix representation, have been presented in this paper to show that the functional derivative of the noninteracting kinetic energy density functional can uniquely be expressed as the negative of the Kohn-Sham effective potential, arbitrary only to an additive orbital-independent constant. Key points leading to the current result as well as confusion about the quantity in the literature are briefly discussed

Fluid dynamic propagation of initial baryon number perturbations on a Bjorken flow background

CERN Document Server

Floerchinger, Stefan

2015-01-01

Baryon number density perturbations offer a possible route to experimentally measure baryon number susceptibilities and heat conductivity of the quark gluon plasma. We study the fluid dynamical evolution of local and event-by-event fluctuations of baryon number density, flow velocity and energy density on top of a (generalized) Bjorken expansion. To that end we use a background-fluctuation splitting and a Bessel-Fourier decomposition for the fluctuating part of the fluid dynamical fields with respect to the azimuthal angle, the radius in the transverse plane and rapidity. We examine how the time evolution of linear perturbations depends on the equation of state as well as on shear viscosity, bulk viscosity and heat conductivity for modes with different azimuthal, radial and rapidity wave numbers. Finally we discuss how this information is accessible to experiments in terms of the transverse and rapidity dependence of correlation functions for baryonic particles in high energy nuclear collisions.

Density functionals in the laboratory frame

International Nuclear Information System (INIS)

Giraud, B. G.

2008-01-01

We compare several definitions of the density of a self-bound system, such as a nucleus, in relation with its center-of-mass zero-point motion. A trivial deconvolution relates the internal density to the density defined in the laboratory frame. This result is useful for the practical definition of density functionals

Characterization of Scrape-Off layer turbulence changes induced by a non-axisymmetric magnetic perturbation in an ASDEX upgrade low density L-mode

International Nuclear Information System (INIS)

Mueller, H.W.; Carralero, D.; Birkenmeier, G.; Conway, G.D.; Fischer, R.; Happel, T.; Manz, P.; Suttrop, W.; Wolfrum, E.

2014-01-01

In the tokamak ASDEX Upgrade the influence of a non-axisymmetric n = 2 error field on the turbulence in the far scrape-off layer of a low density L-mode discharge has been studied. There is no density pump-out with the non-axisymmetric perturbation but an increase of the scrape-off layer density at the outer midplane. While the relative ion saturation current fluctuation level in the far scrape-off layer is decreasing, the skewness rises and especially the excess kurtosis grows by a factor of 1.5-3. The frequency of intermittent events (blobs) is increasing by 50 %. Also the poloidal velocity grows with the magnetic perturbation while the typical turbulent structure size becomes smaller by a factor 5-10 about 20-25 mm outside the separatrix. The local spectral density has been calculated from a two-point measurement of the ion saturation current. It is used to derive a dispersion relation. Two poloidal propagation velocities depending on the wave number have been found. One is an upper limit for the bulk E x B velocity and the second one the lower limit of the phase velocity. There is a significant contribution of the phase velocity to the propagation speed in the far scrape-off layer. (copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

Density-functional expansion methods: Grand challenges.

Science.gov (United States)

Giese, Timothy J; York, Darrin M

2012-03-01

We discuss the source of errors in semiempirical density functional expansion (VE) methods. In particular, we show that VE methods are capable of well-reproducing their standard Kohn-Sham density functional method counterparts, but suffer from large errors upon using one or more of these approximations: the limited size of the atomic orbital basis, the Slater monopole auxiliary basis description of the response density, and the one- and two-body treatment of the core-Hamiltonian matrix elements. In the process of discussing these approximations and highlighting their symptoms, we introduce a new model that supplements the second-order density-functional tight-binding model with a self-consistent charge-dependent chemical potential equalization correction; we review our recently reported method for generalizing the auxiliary basis description of the atomic orbital response density; and we decompose the first-order potential into a summation of additive atomic components and many-body corrections, and from this examination, we provide new insights and preliminary results that motivate and inspire new approximate treatments of the core-Hamiltonian.

Periodic subsystem density-functional theory

International Nuclear Information System (INIS)

Genova, Alessandro; Pavanello, Michele; Ceresoli, Davide

2014-01-01

By partitioning the electron density into subsystem contributions, the Frozen Density Embedding (FDE) formulation of subsystem Density Functional Theory (DFT) has recently emerged as a powerful tool for reducing the computational scaling of Kohn–Sham DFT. To date, however, FDE has been employed to molecular systems only. Periodic systems, such as metals, semiconductors, and other crystalline solids have been outside the applicability of FDE, mostly because of the lack of a periodic FDE implementation. To fill this gap, in this work we aim at extending FDE to treat subsystems of molecular and periodic character. This goal is achieved by a dual approach. On one side, the development of a theoretical framework for periodic subsystem DFT. On the other, the realization of the method into a parallel computer code. We find that periodic FDE is capable of reproducing total electron densities and (to a lesser extent) also interaction energies of molecular systems weakly interacting with metallic surfaces. In the pilot calculations considered, we find that FDE fails in those cases where there is appreciable density overlap between the subsystems. Conversely, we find FDE to be in semiquantitative agreement with Kohn–Sham DFT when the inter-subsystem density overlap is low. We also conclude that to make FDE a suitable method for describing molecular adsorption at surfaces, kinetic energy density functionals that go beyond the GGA level must be employed

Periodic subsystem density-functional theory

Science.gov (United States)

Genova, Alessandro; Ceresoli, Davide; Pavanello, Michele

2014-11-01

By partitioning the electron density into subsystem contributions, the Frozen Density Embedding (FDE) formulation of subsystem Density Functional Theory (DFT) has recently emerged as a powerful tool for reducing the computational scaling of Kohn-Sham DFT. To date, however, FDE has been employed to molecular systems only. Periodic systems, such as metals, semiconductors, and other crystalline solids have been outside the applicability of FDE, mostly because of the lack of a periodic FDE implementation. To fill this gap, in this work we aim at extending FDE to treat subsystems of molecular and periodic character. This goal is achieved by a dual approach. On one side, the development of a theoretical framework for periodic subsystem DFT. On the other, the realization of the method into a parallel computer code. We find that periodic FDE is capable of reproducing total electron densities and (to a lesser extent) also interaction energies of molecular systems weakly interacting with metallic surfaces. In the pilot calculations considered, we find that FDE fails in those cases where there is appreciable density overlap between the subsystems. Conversely, we find FDE to be in semiquantitative agreement with Kohn-Sham DFT when the inter-subsystem density overlap is low. We also conclude that to make FDE a suitable method for describing molecular adsorption at surfaces, kinetic energy density functionals that go beyond the GGA level must be employed.

Optimal random perturbations for stochastic approximation using a simultaneous perturbation gradient approximation

DEFF Research Database (Denmark)

Sadegh, Payman; Spall, J. C.

1998-01-01

simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on picking a simultaneous perturbation (random) vector in a Monte Carlo fashion as part of generating the approximation to the gradient. This paper derives the optimal distribution for the Monte Carlo...

Degenerate RS perturbation theory. [Rayleigh-Schroedinger energies and wave functions

Science.gov (United States)

Hirschfelder, J. O.; Certain, P. R.

1974-01-01

A concise, systematic procedure is given for determining the Rayleigh-Schroedinger energies and wave functions of degenerate states to arbitrarily high orders even when the degeneracies of the various states are resolved in arbitrary orders. The procedure is expressed in terms of an iterative cycle in which the energy through the (2n + 1)-th order is expressed in terms of the partially determined wave function through the n-th order. Both a direct and an operator derivation are given. The two approaches are equivalent and can be transcribed into each other. The direct approach deals with the wave functions (without the use of formal operators) and has the advantage that it resembles the usual treatment of nondegenerate perturbations and maintains close contact with the basic physics. In the operator approach, the wave functions are expressed in terms of infinite-order operators which are determined by the successive resolution of the space of the zeroth-order functions.

Quantal density functional theory

CERN Document Server

Sahni, Viraht

2016-01-01

This book deals with quantal density functional theory (QDFT) which is a time-dependent local effective potential theory of the electronic structure of matter. The treated time-independent QDFT constitutes a special case. In the 2nd edition, the theory is extended to include the presence of external magnetostatic fields. The theory is a description of matter based on the ‘quantal Newtonian’ first and second laws which is in terms of “classical” fields that pervade all space, and their quantal sources. The fields, which are explicitly defined, are separately representative of electron correlations due to the Pauli exclusion principle, Coulomb repulsion, correlation-kinetic, correlation-current-density, and correlation-magnetic effects. The book further describes Schrödinger theory from the new physical perspective of fields and quantal sources. It also describes traditional Hohenberg-Kohn-Sham DFT, and explains via QDFT the physics underlying the various energy functionals and functional derivatives o...

Spin Density Distribution in Open-Shell Transition Metal Systems: A Comparative Post-Hartree-Fock, Density Functional Theory, and Quantum Monte Carlo Study of the CuCl2 Molecule.

Science.gov (United States)

Caffarel, Michel; Giner, Emmanuel; Scemama, Anthony; Ramírez-Solís, Alejandro

2014-12-09

We present a comparative study of the spatial distribution of the spin density of the ground state of CuCl2 using Density Functional Theory (DFT), quantum Monte Carlo (QMC), and post-Hartree-Fock wave function theory (WFT). A number of studies have shown that an accurate description of the electronic structure of the lowest-lying states of this molecule is particularly challenging due to the interplay between the strong dynamical correlation effects in the 3d shell and the delocalization of the 3d hole over the chlorine atoms. More generally, this problem is representative of the difficulties encountered when studying open-shell metal-containing molecular systems. Here, it is shown that qualitatively different results for the spin density distribution are obtained from the various quantum-mechanical approaches. At the DFT level, the spin density distribution is found to be very dependent on the functional employed. At the QMC level, Fixed-Node Diffusion Monte Carlo (FN-DMC) results are strongly dependent on the nodal structure of the trial wave function. Regarding wave function methods, most approaches not including a very high amount of dynamic correlation effects lead to a much too high localization of the spin density on the copper atom, in sharp contrast with DFT. To shed some light on these conflicting results Full CI-type (FCI) calculations using the 6-31G basis set and based on a selection process of the most important determinants, the so-called CIPSI approach (Configuration Interaction with Perturbative Selection done Iteratively) are performed. Quite remarkably, it is found that for this 63-electron molecule and a full CI space including about 10(18) determinants, the FCI limit can almost be reached. Putting all results together, a natural and coherent picture for the spin distribution is proposed.

Standard Clock in primordial density perturbations and cosmic microwave background

International Nuclear Information System (INIS)

Chen, Xingang; Namjoo, Mohammad Hossein

2014-01-01

Standard Clocks in the primordial epoch leave a special type of features in the primordial perturbations, which can be used to directly measure the scale factor of the primordial universe as a function of time a(t), thus discriminating between inflation and alternatives. We have started to search for such signals in the Planck 2013 data using the key predictions of the Standard Clock. In this Letter, we summarize the key predictions of the Standard Clock and present an interesting candidate example in Planck 2013 data. Motivated by this candidate, we construct and compute full Standard Clock models and use the more complete prediction to make more extensive comparison with data. Although this candidate is not yet statistically significant, we use it to illustrate how Standard Clocks appear in Cosmic Microwave Background (CMB) and how they can be further tested by future data. We also use it to motivate more detailed theoretical model building

Reduced density matrix functional theory via a wave function based approach

Energy Technology Data Exchange (ETDEWEB)

Schade, Robert; Bloechl, Peter [Institute for Theoretical Physics, Clausthal University of Technology, Clausthal (Germany); Pruschke, Thomas [Institute for Theoretical Physics, University of Goettingen, Goettingen (Germany)

2016-07-01

We propose a new method for the calculation of the electronic and atomic structure of correlated electron systems based on reduced density matrix functional theory (rDMFT). The density-matrix functional is evaluated on the fly using Levy's constrained search formalism. The present implementation rests on a local approximation of the interaction reminiscent to that of dynamical mean field theory (DMFT). We focus here on additional approximations to the exact density-matrix functional in the local approximation and evaluate their performance.

A real-space stochastic density matrix approach for density functional electronic structure.

Science.gov (United States)

Beck, Thomas L

2015-12-21

The recent development of real-space grid methods has led to more efficient, accurate, and adaptable approaches for large-scale electrostatics and density functional electronic structure modeling. With the incorporation of multiscale techniques, linear-scaling real-space solvers are possible for density functional problems if localized orbitals are used to represent the Kohn-Sham energy functional. These methods still suffer from high computational and storage overheads, however, due to extensive matrix operations related to the underlying wave function grid representation. In this paper, an alternative stochastic method is outlined that aims to solve directly for the one-electron density matrix in real space. In order to illustrate aspects of the method, model calculations are performed for simple one-dimensional problems that display some features of the more general problem, such as spatial nodes in the density matrix. This orbital-free approach may prove helpful considering a future involving increasingly parallel computing architectures. Its primary advantage is the near-locality of the random walks, allowing for simultaneous updates of the density matrix in different regions of space partitioned across the processors. In addition, it allows for testing and enforcement of the particle number and idempotency constraints through stabilization of a Feynman-Kac functional integral as opposed to the extensive matrix operations in traditional approaches.

Solitonic Integrable Perturbations of Parafermionic Theories

CERN Document Server

Fernández-Pousa, C R; Hollowood, Timothy J; Miramontes, J L

1997-01-01

The quantum integrability of a class of massive perturbations of the parafermionic conformal field theories associated to compact Lie groups is established by showing that they have quantum conserved densities of scale dimension 2 and 3. These theories are integrable for any value of a continuous vector coupling constant, and they generalize the perturbation of the minimal parafermionic models by their first thermal operator. The classical equations-of-motion of these perturbed theories are the non-abelian affine Toda equations which admit (charged) soliton solutions whose semi-classical quantization is expected to permit the identification of the exact S-matrix of the theory.

Analytic perturbation theory for screened Coulomb potential: full continuum wave function

International Nuclear Information System (INIS)

Bechler, A.; Ennan, Mc J.; Pratt, R.H.

1979-01-01

An analytic perturbation theory developed previously is used to find a continuum screened-Coulomb wave function characterized by definite asymptotic momentum. This wave function satisfies an inhomogeneous partial differential equation which is solved in parabolic coordinates; the solution depends on both parabolic variables. We calculate partial wave projections of this solution and show that we can choose to add a solution of the homogeneous equation such that the partial wave projections become equal to the normalized continuum radial function found previously. However, finding the unique solution with given asymptotic linear momentum will require either using boundary conditions to determine the unique needed solution of the homogeneous equation or equivalently specifying the screened-Coulomb phase-shifts. (author)

Decay of autoionizing states in time-dependent density functional and reduced density matrix functional theory

Energy Technology Data Exchange (ETDEWEB)

Kapoor, Varun; Brics, Martins; Bauer, Dieter [Institut fuer Physik, Universitaet Rostock, 18051 Rostock (Germany)

2013-07-01

Autoionizing states are inaccessible to time-dependent density functional theory (TDDFT) using known, adiabatic Kohn-Sham (KS) potentials. We determine the exact KS potential for a numerically exactly solvable model Helium atom interacting with a laser field that is populating an autoionizing state. The exact single-particle density of the population in the autoionizing state corresponds to that of the energetically lowest quasi-stationary state in the exact KS potential. We describe how this exact potential controls the decay by a barrier whose height and width allows for the density to tunnel out and decay with the same rate as in the ab initio time-dependent Schroedinger calculation. However, devising a useful exchange-correlation potential that is capable of governing such a scenario in general and in more complex systems is hopeless. As an improvement over TDDFT, time-dependent reduced density matrix functional theory has been proposed. We are able to obtain for the above described autoionization process the exact time-dependent natural orbitals (i.e., the eigenfunctions of the exact, time-dependent one-body reduced density matrix) and study the potentials that appear in the equations of motion for the natural orbitals and the structure of the two-body density matrix expanded in them.

Magnetizability and rotational g tensors for density fitted local second-order Møller-Plesset perturbation theory using gauge-including atomic orbitals

International Nuclear Information System (INIS)

Loibl, Stefan; Schütz, Martin

2014-01-01

In this paper, we present theory and implementation of an efficient program for calculating magnetizabilities and rotational g tensors of closed-shell molecules at the level of local second-order Møller-Plesset perturbation theory (MP2) using London orbitals. Density fitting is employed to factorize the electron repulsion integrals with ordinary Gaussians as fitting functions. The presented program for the calculation of magnetizabilities and rotational g tensors is based on a previous implementation of NMR shielding tensors reported by S. Loibl and M. Schütz [J. Chem. Phys. 137, 084107 (2012)]. Extensive test calculations show (i) that the errors introduced by density fitting are negligible, and (ii) that the errors of the local approximation are still rather small, although larger than for nuclear magnetic resonance (NMR) shielding tensors. Electron correlation effects for magnetizabilities are tiny for most of the molecules considered here. MP2 appears to overestimate the correlation contribution of magnetizabilities such that it does not constitute an improvement over Hartree-Fock (when comparing to higher-order methods like CCSD(T)). For rotational g tensors the situation is different and MP2 provides a significant improvement in accuracy over Hartree-Fock. The computational performance of the new program was tested for two extended systems, the larger comprising about 2200 basis functions. It turns out that a magnetizability (or rotational g tensor) calculation takes about 1.5 times longer than a corresponding NMR shielding tensor calculation

Closed form bound-state perturbation theory

Directory of Open Access Journals (Sweden)

Ollie J. Rose

1980-01-01

Full Text Available The perturbed Schrödinger eigenvalue problem for bound states is cast into integral form using Green's Functions. A systematic algorithm is developed and applied to the resulting equation giving rise to approximate solutions expressed as functions of the given perturbation parameter. As a by-product, convergence radii for the traditional Rayleigh-Schrödinger and Brillouin-Wigner perturbation theories emerge in a natural way.

Perturbed invariant subspaces and approximate generalized functional variable separation solution for nonlinear diffusion-convection equations with weak source

Science.gov (United States)

Xia, Ya-Rong; Zhang, Shun-Li; Xin, Xiang-Peng

2018-03-01

In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.

Neutral wind and density perturbations in the thermosphere created by gravity waves observed by the TIDDBIT sounder

Science.gov (United States)

Vadas, Sharon L.; Crowley, Geoff

2017-06-01

In this paper, we study the 10 traveling ionospheric disturbances (TIDs) observed at zobs˜283 km by the TIDDBIT ionospheric sounder on 30 October 2007 at 0400-0700 UT near Wallops Island, USA. These TIDs propagated northwest/northward and were previously found to be secondary gravity waves (GWs) from tropical storm Noel. An instrumented sounding rocket simultaneously measured a large neutral wind peak uH' with a similar azimuth at z ˜ 325 km. Using the measured TID amplitudes and wave vectors from the TIDDBIT system, together with ion-neutral theory, GW dissipative polarization relations and ray tracing, we determine the GW neutral horizontal wind and density perturbations as a function of altitude from 220 to 380 km. We find that there is a serious discrepancy between the GW dissipative theory and the observations unless the molecular viscosity, μ, decreases with altitude in the middle to upper thermosphere. Assuming that μ∝ρ¯q, where ρ¯ is the density, we find using GW dissipative theory that the GWs could have been observed at zobs and that one or more of the GWs could have caused the uH' wind peak at z≃325 km if q ˜ 0.67 for z≥220 km. This implies that the kinematic viscosity, ν=μ/ρ¯, increases less rapidly with altitude for z≥220 km: ν∝1/ρ¯0.33. This dependence makes sense because as ρ¯→0, the distance between molecules goes to infinity, which implies no molecular collisions and therefore no molecular viscosity μ.

Perturbation methods for power and reactivity reconstruction

International Nuclear Information System (INIS)

Palmiotti, G.; Salvatores, M.; Estiot, J.C.; Broccoli, U.; Bruna, G.; Gomit, J.M.

1987-01-01

This paper deals with recent developments and applications in perturbation methods. Two types of methods are used. The first one is an explicit method, which allows the explicit reconstruction of a perturbed flux using a linear combination of a library of functions. In our application, these functions are the harmonics (i.e. the high order eigenfunctions of the system). The second type is based on the Generalized Perturbation Theory GPT and needs the calculation of an importance function for each integral parameter of interest. Recent developments of a particularly useful high order formulation allows to obtain satisfactory results also for very large perturbations

Metal-ligand delocalization and spin density in the CuCl{sub 2} and [CuCl{sub 4}]{sup 2−} molecules: Some insights from wave function theory

Energy Technology Data Exchange (ETDEWEB)

Giner, Emmanuel, E-mail: gnrmnl@unife.it; Angeli, Celestino, E-mail: anc@unife.it [Dipartimento di Scienze Chimiche e Famaceutiche, Universita di Ferrara, Via Fossato di Mortara 17, I-44121 Ferrara (Italy)

2015-09-28

The aim of this paper is to unravel the physical phenomena involved in the calculation of the spin density of the CuCl{sub 2} and [CuCl{sub 4}]{sup 2−} systems using wave function methods. Various types of wave functions are used here, both variational and perturbative, to analyse the effects impacting the spin density. It is found that the spin density on the chlorine ligands strongly depends on the mixing between two types of valence bond structures. It is demonstrated that the main difficulties found in most of the previous studies based on wave function methods come from the fact that each valence bond structure requires a different set of molecular orbitals and that using a unique set of molecular orbitals in a variational procedure leads to the removal of one of them from the wave function. Starting from these results, a method to compute the spin density at a reasonable computational cost is proposed.

Self-Interaction Error in Density Functional Theory: An Appraisal.

Science.gov (United States)

Bao, Junwei Lucas; Gagliardi, Laura; Truhlar, Donald G

2018-05-03

Self-interaction error (SIE) is considered to be one of the major sources of error in most approximate exchange-correlation functionals for Kohn-Sham density-functional theory (KS-DFT), and it is large with all local exchange-correlation functionals and with some hybrid functionals. In this work, we consider systems conventionally considered to be dominated by SIE. For these systems, we demonstrate that by using multiconfiguration pair-density functional theory (MC-PDFT), the error of a translated local density-functional approximation is significantly reduced (by a factor of 3) when using an MCSCF density and on-top density, as compared to using KS-DFT with the parent functional; the error in MC-PDFT with local on-top functionals is even lower than the error in some popular KS-DFT hybrid functionals. Density-functional theory, either in MC-PDFT form with local on-top functionals or in KS-DFT form with some functionals having 50% or more nonlocal exchange, has smaller errors for SIE-prone systems than does CASSCF, which has no SIE.

Density functional theory and parallel processing

International Nuclear Information System (INIS)

Ward, R.C.; Geist, G.A.; Butler, W.H.

1987-01-01

The authors demonstrate a method for obtaining the ground state energies and charge densities of a system of atoms described within density functional theory using simulated annealing on a parallel computer

Rational Density Functional Selection Using Game Theory.

Science.gov (United States)

McAnanama-Brereton, Suzanne; Waller, Mark P

2018-01-22

Theoretical chemistry has a paradox of choice due to the availability of a myriad of density functionals and basis sets. Traditionally, a particular density functional is chosen on the basis of the level of user expertise (i.e., subjective experiences). Herein we circumvent the user-centric selection procedure by describing a novel approach for objectively selecting a particular functional for a given application. We achieve this by employing game theory to identify optimal functional/basis set combinations. A three-player (accuracy, complexity, and similarity) game is devised, through which Nash equilibrium solutions can be obtained. This approach has the advantage that results can be systematically improved by enlarging the underlying knowledge base, and the deterministic selection procedure mathematically justifies the density functional and basis set selections.

Alteration in neonatal nutrition causes perturbations in hypothalamic neural circuits controlling reproductive function.

Science.gov (United States)

Caron, Emilie; Ciofi, Philippe; Prevot, Vincent; Bouret, Sebastien G

2012-08-15

It is increasingly accepted that alterations of the early life environment may have lasting impacts on physiological functions. In particular, epidemiological and animal studies have indicated that changes in growth and nutrition during childhood and adolescence can impair reproductive function. However, the precise biological mechanisms that underlie these programming effects of neonatal nutrition on reproduction are still poorly understood. Here, we used a mouse model of divergent litter size to investigate the effects of early postnatal overnutrition and undernutrition on the maturation of hypothalamic circuits involved in reproductive function. Neonatally undernourished females display attenuated postnatal growth associated with delayed puberty and defective development of axonal projections from the arcuate nucleus to the preoptic region. These alterations persist into adulthood and specifically affect the organization of neural projections containing kisspeptin, a key neuropeptide involved in pubertal activation and fertility. Neonatal overfeeding also perturbs the development of neural projections from the arcuate nucleus to the preoptic region, but it does not result in alterations in kisspeptin projections. These studies indicate that alterations in the early nutritional environment cause lasting and deleterious effects on the organization of neural circuits involved in the control of reproduction, and that these changes are associated with lifelong functional perturbations.

Subsystem density functional theory with meta-generalized gradient approximation exchange-correlation functionals.

Science.gov (United States)

Śmiga, Szymon; Fabiano, Eduardo; Laricchia, Savio; Constantin, Lucian A; Della Sala, Fabio

2015-04-21

We analyze the methodology and the performance of subsystem density functional theory (DFT) with meta-generalized gradient approximation (meta-GGA) exchange-correlation functionals for non-bonded molecular systems. Meta-GGA functionals depend on the Kohn-Sham kinetic energy density (KED), which is not known as an explicit functional of the density. Therefore, they cannot be directly applied in subsystem DFT calculations. We propose a Laplacian-level approximation to the KED which overcomes this limitation and provides a simple and accurate way to apply meta-GGA exchange-correlation functionals in subsystem DFT calculations. The so obtained density and energy errors, with respect to the corresponding supermolecular calculations, are comparable with conventional approaches, depending almost exclusively on the approximations in the non-additive kinetic embedding term. An embedding energy error decomposition explains the accuracy of our method.

Perturbative Gaussianizing transforms for cosmological fields

Science.gov (United States)

Hall, Alex; Mead, Alexander

2018-01-01

Constraints on cosmological parameters from large-scale structure have traditionally been obtained from two-point statistics. However, non-linear structure formation renders these statistics insufficient in capturing the full information content available, necessitating the measurement of higher order moments to recover information which would otherwise be lost. We construct quantities based on non-linear and non-local transformations of weakly non-Gaussian fields that Gaussianize the full multivariate distribution at a given order in perturbation theory. Our approach does not require a model of the fields themselves and takes as input only the first few polyspectra, which could be modelled or measured from simulations or data, making our method particularly suited to observables lacking a robust perturbative description such as the weak-lensing shear. We apply our method to simulated density fields, finding a significantly reduced bispectrum and an enhanced correlation with the initial field. We demonstrate that our method reconstructs a large proportion of the linear baryon acoustic oscillations, improving the information content over the raw field by 35 per cent. We apply the transform to toy 21 cm intensity maps, showing that our method still performs well in the presence of complications such as redshift-space distortions, beam smoothing, pixel noise and foreground subtraction. We discuss how this method might provide a route to constructing a perturbative model of the fully non-Gaussian multivariate likelihood function.

The structure and binding energy of K+endash ether complexes: A comparison of MP2, RI-MP2, and density functional methods

International Nuclear Information System (INIS)

Feller, D.; Apra, E.; Nichols, J.A.; Bernholdt, D.E.

1996-01-01

The structures and binding energies of several cation:ether complexes (K + :dimethyl ether, K + :dimethoxyethane, K + :12-crown-4 and K + :18-crown-6) were determined with second and fourth order perturbation theory using correlation consistent basis sets. Several of these are the largest correlated calculations yet attempted on crown ethers. The observed systematic convergence to the complete basis set limit provides a standard by which the accuracy of previous studies can be measured and facilitates the calibration of density functional methods. Recent Fouier transform ion cyclotron resonance experiments predicted K + :18-crown-6 binding energies which were significantly smaller than ab initio calculations. None of the potential sources of error examined in the present study were large enough to explain this difference. Although the 6-31+G* basis set used in an earlier theoretical study was smaller than the smallest of the correlation consistent basis sets, with suitable correction for basis set superposition error, it appears capable of yielding binding energies within several kcal/mol of the basis set limit. Perturbation theory calculations exploiting the open-quote open-quote resolution of the identity close-quote close-quote approximation were found to faithfully reproduce binding energies and conformational differences. Although the cation endash ether interaction is dominated by classical electrostatics, the accuracy of density functional techniques was found to be quite sensitive to the choice of functionals. The local density SVWN procedure performed well for binding energies and conformational differences, while underestimating K + O distances by up to 0.08 A. The gradient-corrected Becke endash Lee endash Yang endash Parr functional underestimated the K + :12c4 binding energy by 4 endash 7 kcal/mol or 15%. copyright 1996 American Institute of Physics

Uniform magnetic fields in density-functional theory

Science.gov (United States)

Tellgren, Erik I.; Laestadius, Andre; Helgaker, Trygve; Kvaal, Simen; Teale, Andrew M.

2018-01-01

We construct a density-functional formalism adapted to uniform external magnetic fields that is intermediate between conventional density functional theory and Current-Density Functional Theory (CDFT). In the intermediate theory, which we term linear vector potential-DFT (LDFT), the basic variables are the density, the canonical momentum, and the paramagnetic contribution to the magnetic moment. Both a constrained-search formulation and a convex formulation in terms of Legendre-Fenchel transformations are constructed. Many theoretical issues in CDFT find simplified analogs in LDFT. We prove results concerning N-representability, Hohenberg-Kohn-like mappings, existence of minimizers in the constrained-search expression, and a restricted analog to gauge invariance. The issue of additivity of the energy over non-interacting subsystems, which is qualitatively different in LDFT and CDFT, is also discussed.

Satellite orbits perturbed by direct solar radiation pressure: general expansion of the disturbing function

International Nuclear Information System (INIS)

Hughes, S.

1977-01-01

An expression is derived for the solar radiation pressure disturbing function on an Earth satellite orbit which takes into account the variation of the solar radiation flux with distance from the Sun's centre and the absorption of radiation by the satellite. This expression is then expanded in terms of the Keplerian elements of the satellite and solar orbits using Kaula's method (Astr. J.; 67:300 (1962)). The Kaula inclination functions are replaced by an equivalent set of modified Allan (Proc. R. Soc. A.; 288:60 (1965)) inclination functions. The resulting expression reduces to the form commonly used in solar radiation pressure perturbation studies (e.g. Aksnes, Cel. Mech.; 13:89 (1976)), when certain terms are neglected. If, as happens quite often in practice, a satellite's orbit is in near-resonance with certain of these neglected terms, these near-resonant terms can cause changes in the satellite's orbital elements comparable to those produced by the largest term in Aksnes's expression. A new expression for the solar radiation pressure disturbing function expansion is suggested for use in future studies of satellite orbits perturbed by solar radiation pressure. (author)

density functional theory approach

Indian Academy of Sciences (India)

YOGESH ERANDE

2017-07-27

Jul 27, 2017 ... a key role in all optical switching devices, since their optical properties can be .... optimized in the gas phase using Density Functional Theory. (DFT).39 The ...... The Mediation of Electrostatic Effects by Sol- vents J. Am. Chem.

Comment on 'Density perturbations in the ekpyrotic scenario'

International Nuclear Information System (INIS)

Martin, Jerome; Peter, Patrick; Pinto-Neto, Nelson; Schwarz, Dominik J.

2003-01-01

In the paper by J. Khoury et al., Phys. Rev. D 66, 046005 (2002), it is argued that the expected spectrum of primordial perturbations should be scale invariant in this scenario. Here we show that, contrary to what is claimed in that paper, the expected spectrum depends on an arbitrary choice of matching variable. As no underlying (microphysical) principle exists at the present time that could lift the arbitrariness, we conclude that the ekpyrotic scenario is not yet a predictive model

Off-shell dynamics of the O(3) NLS model beyond Monte Carlo and perturbation theory

International Nuclear Information System (INIS)

Balog, J.; Niedermaier, M.

1997-01-01

The off-shell dynamics of the O(3) non-linear sigma model is probed in terms of spectral densities and two-point functions by means of the form factor approach. The exact form factors of the spin field, Noether current, EM tensor and the topological charge density are computed up to six particles. The corresponding n≤6 particle spectral densities are used to compute the two-point functions, and are argued to deviate at most a few per mille from the exact answer in the entire energy range below 10 3 in units of the mass gap. To cover yet higher energies we propose an extrapolation scheme to arbitrary particle numbers based on a novel scaling hypothesis for the spectral densities. It yields candidate results for the exact two-point functions at all energy scales and allows us to exactly determine the values of two, previously unknown, non-perturbative constants. (orig.)

Investigations of Probe Induced Perturbations in a Hall Thruster

International Nuclear Information System (INIS)

D. Staack; Y. Raitses; N.J. Fisch

2002-01-01

An electrostatic probe used to measure spatial plasma parameters in a Hall thruster generates perturbations of the plasma. These perturbations are examined by varying the probe material, penetration distance, residence time, and the nominal thruster conditions. The study leads us to recommendations for probe design and thruster operating conditions to reduce discharge perturbations, including metal shielding of the probe insulator and operation of the thruster at lower densities

Strong Correlation in Kohn-Sham Density Functional Theory

NARCIS (Netherlands)

Malet, F.; Gori Giorgi, P.

2012-01-01

We use the exact strong-interaction limit of the Hohenberg-Kohn energy density functional to approximate the exchange-correlation energy of the restricted Kohn-Sham scheme. Our approximation corresponds to a highly nonlocal density functional whose functional derivative can be easily constructed,

New Methods in Non-Perturbative QCD

Energy Technology Data Exchange (ETDEWEB)

Unsal, Mithat [North Carolina State Univ., Raleigh, NC (United States)

2017-01-31

In this work, we investigate the properties of quantum chromodynamics (QCD), by using newly developing mathematics and physics formalisms. Almost all of the mass in the visible universe emerges from a quantum chromodynamics (QCD), which has a completely negligible microscopic mass content. An intimately related issue in QCD is the quark confinement problem. Answers to non-perturbative questions in QCD remained largely elusive despite much effort over the years. It is also believed that the usual perturbation theory is inadequate to address these kinds of problems. Perturbation theory gives a divergent asymptotic series (even when the theory is properly renormalized), and there are non-perturbative phenomena which never appear at any order in perturbation theory. Recently, a fascinating bridge between perturbation theory and non-perturbative effects has been found: a formalism called resurgence theory in mathematics tells us that perturbative data and non-perturbative data are intimately related. Translating this to the language of quantum field theory, it turns out that non-perturbative information is present in a coded form in perturbation theory and it can be decoded. We take advantage of this feature, which is particularly useful to understand some unresolved mysteries of QCD from first principles. In particular, we use: a) Circle compactifications which provide a semi-classical window to study confinement and mass gap problems, and calculable prototypes of the deconfinement phase transition; b) Resurgence theory and transseries which provide a unified framework for perturbative and non-perturbative expansion; c) Analytic continuation of path integrals and Lefschetz thimbles which may be useful to address sign problem in QCD at finite density.

Functional renormalization group and Kohn-Sham scheme in density functional theory

Science.gov (United States)

Liang, Haozhao; Niu, Yifei; Hatsuda, Tetsuo

2018-04-01

Deriving accurate energy density functional is one of the central problems in condensed matter physics, nuclear physics, and quantum chemistry. We propose a novel method to deduce the energy density functional by combining the idea of the functional renormalization group and the Kohn-Sham scheme in density functional theory. The key idea is to solve the renormalization group flow for the effective action decomposed into the mean-field part and the correlation part. Also, we propose a simple practical method to quantify the uncertainty associated with the truncation of the correlation part. By taking the φ4 theory in zero dimension as a benchmark, we demonstrate that our method shows extremely fast convergence to the exact result even for the highly strong coupling regime.

PerturbationAnalyzer: a tool for investigating the effects of concentration perturbation on protein interaction networks.

Science.gov (United States)

Li, Fei; Li, Peng; Xu, Wenjian; Peng, Yuxing; Bo, Xiaochen; Wang, Shengqi

2010-01-15

The propagation of perturbations in protein concentration through a protein interaction network (PIN) can shed light on network dynamics and function. In order to facilitate this type of study, PerturbationAnalyzer, which is an open source plugin for Cytoscape, has been developed. PerturbationAnalyzer can be used in manual mode for simulating user-defined perturbations, as well as in batch mode for evaluating network robustness and identifying significant proteins that cause large propagation effects in the PINs when their concentrations are perturbed. Results from PerturbationAnalyzer can be represented in an intuitive and customizable way and can also be exported for further exploration. PerturbationAnalyzer has great potential in mining the design principles of protein networks, and may be a useful tool for identifying drug targets. PerturbationAnalyzer can be accessed from the Cytoscape web site http://www.cytoscape.org/plugins/index.php or http://biotech.bmi.ac.cn/PerturbationAnalyzer. Supplementary data are available at Bioinformatics online.

Density functional theory: Foundations reviewed

Energy Technology Data Exchange (ETDEWEB)

Kryachko, Eugene S., E-mail: eugene.kryachko@ulg.ac.be [Bogolyubov Institute for Theoretical Physics, Kiev, 03680 (Ukraine); Ludeña, Eduardo V., E-mail: popluabe@yahoo.es [Centro de Química, Instituto Venezolano de Investigaciones Científicas, IVIC, Apartado 21827, Caracas 1020-A (Venezuela, Bolivarian Republic of); Prometheus Program, Senescyt (Ecuador); Grupo Ecuatoriano para el Estudio Experimental y Teórico de Nanosistemas, GETNano, USFQ, N104-E, Quito (Ecuador); Escuela Politécnica Superior del Litoral, ESPOL, Guayaquil (Ecuador)

2014-11-10

Guided by the above motto (quotation), we review a broad range of issues lying at the foundations of Density Functional Theory, DFT, a theory which is currently omnipresent in our everyday computational study of atoms and molecules, solids and nano-materials, and which lies at the heart of modern many-body computational technologies. The key goal is to demonstrate that there are definitely the ways to improve DFT. We start by considering DFT in the larger context provided by reduced density matrix theory (RDMT) and natural orbital functional theory (NOFT), and examine the implications that N-representability conditions on the second-order reduced density matrix (2-RDM) have not only on RDMT and NOFT but, also, by extension, on the functionals of DFT. This examination is timely in view of the fact that necessary and sufficient N-representability conditions on the 2-RDM have recently been attained. In the second place, we review some problems appearing in the original formulation of the first Hohenberg–Kohn theorem which is still a subject of some controversy. In this vein we recall Lieb’s comment on this proof and the extension to this proof given by Pino et al. (2009), and in this context examine the conditions that must be met in order that the one-to-one correspondence between ground-state densities and external potentials remains valid for finite subspaces (namely, the subspaces where all Kohn–Sham solutions are obtained in practical applications). We also consider the issue of whether the Kohn–Sham equations can be derived from basic principles or whether they are postulated. We examine this problem in relation to ab initio DFT. The possibility of postulating arbitrary Kohn–Sham-type equations, where the effective potential is by definition some arbitrary mixture of local and non-local terms, is discussed. We also deal with the issue of whether there exists a universal functional, or whether one should advocate instead the construction of problem

Linear scaling of density functional algorithms

International Nuclear Information System (INIS)

Stechel, E.B.; Feibelman, P.J.; Williams, A.R.

1993-01-01

An efficient density functional algorithm (DFA) that scales linearly with system size will revolutionize electronic structure calculations. Density functional calculations are reliable and accurate in determining many condensed matter and molecular ground-state properties. However, because current DFA's, including methods related to that of Car and Parrinello, scale with the cube of the system size, density functional studies are not routinely applied to large systems. Linear scaling is achieved by constructing functions that are both localized and fully occupied, thereby eliminating the need to calculate global eigenfunctions. It is, however, widely believed that exponential localization requires the existence of an energy gap between the occupied and unoccupied states. Despite this, the authors demonstrate that linear scaling can still be achieved for metals. Using a linear scaling algorithm, they have explicitly constructed localized, almost fully occupied orbitals for the quintessential metallic system, jellium. The algorithm is readily generalizable to any system geometry and Hamiltonian. They will discuss the conceptual issues involved, convergence properties and scaling for their new algorithm

Density-Functional formalism

International Nuclear Information System (INIS)

Szasz, L.; Berrios-Pagan, I.; McGinn, G.

1975-01-01

A new Density-Functional formula is constructed for atoms. The kinetic energy of the electron is divided into two parts: the kinetic self-energy and the orthogonalization energy. Calculations were made for the total energies of neutral atoms, positive ions and for the He isoelectronic series. For neutral atoms the results match the Hartree-Fock energies within 1% for atoms with N 36 the results generally match the HF energies within 0.1%. For positive ions the results are fair; for the molecular applications a simplified model is developed in which the kinetic energy consists of the Weizsaecker term plus the Fermi energy reduced by a continuous function. (orig.) [de

Spin orientations of the spin-half Ir(4+) ions in Sr3NiIrO6, Sr2IrO4, and Na2IrO3: Density functional, perturbation theory, and Madelung potential analyses.

Science.gov (United States)

Gordon, Elijah E; Xiang, Hongjun; Köhler, Jürgen; Whangbo, Myung-Hwan

2016-03-21

The spins of the low-spin Ir(4+) (S = 1/2, d(5)) ions at the octahedral sites of the oxides Sr3NiIrO6, Sr2IrO4, and Na2IrO3 exhibit preferred orientations with respect to their IrO6 octahedra. We evaluated the magnetic anisotropies of these S = 1/2 ions on the basis of density functional theory (DFT) calculations including spin-orbit coupling (SOC), and probed their origin by performing perturbation theory analyses with SOC as perturbation within the LS coupling scheme. The observed spin orientations of Sr3NiIrO6 and Sr2IrO4 are correctly predicted by DFT calculations, and are accounted for by the perturbation theory analysis. As for the spin orientation of Na2IrO3, both experimental studies and DFT calculations have not been unequivocal. Our analysis reveals that the Ir(4+) spin orientation of Na2IrO3 should have nonzero components along the c- and a-axis directions. The spin orientations determined by DFT calculations are sensitive to the accuracy of the crystal structures employed, which is explained by perturbation theory analyses when interactions between adjacent Ir(4+) ions are taken into consideration. There are indications implying that the 5d electrons of Na2IrO3 are less strongly localized compared with those of Sr3NiIrO6 and Sr2IrO4. This implication was confirmed by showing that the Madelung potentials of the Ir(4+) ions are less negative in Na2IrO3 than in Sr3NiIrO6 and Sr2IrO4. Most transition-metal S = 1/2 ions do have magnetic anisotropies because the SOC induces interactions among their crystal-field split d-states, and the associated mixing of the states modifies only the orbital parts of the states. This finding cannot be mimicked by a spin Hamiltonian because this model Hamiltonian lacks the orbital degree of freedom, thereby leading to the spin-half syndrome. The spin-orbital entanglement for the 5d spin-half ions Ir(4+) is not as strong as has been assumed.

Density-functional, density-functional tight-binding, and wave-function calculations on biomolecular systems

Czech Academy of Sciences Publication Activity Database

Kubař, Tomáš; Jurečka, Petr; Černý, Jiří; Řezáč, Jan; Otyepka, M.; Valdes, Haydee; Hobza, Pavel

2007-01-01

Roč. 111, č. 26 (2007), s. 5642-5647 ISSN 1089-5639 R&D Projects: GA MŠk LC512; GA AV ČR IAA400550510; GA ČR(CZ) GD203/05/H001; GA ČR GA203/05/0009 Institutional research plan: CEZ:AV0Z40550506 Keywords : density functional theory * empirical dispersion-energy term * non-covalent interactions Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.918, year: 2007

The force distribution probability function for simple fluids by density functional theory.

Science.gov (United States)

Rickayzen, G; Heyes, D M

2013-02-28

Classical density functional theory (DFT) is used to derive a formula for the probability density distribution function, P(F), and probability distribution function, W(F), for simple fluids, where F is the net force on a particle. The final formula for P(F) ∝ exp(-AF(2)), where A depends on the fluid density, the temperature, and the Fourier transform of the pair potential. The form of the DFT theory used is only applicable to bounded potential fluids. When combined with the hypernetted chain closure of the Ornstein-Zernike equation, the DFT theory for W(F) agrees with molecular dynamics computer simulations for the Gaussian and bounded soft sphere at high density. The Gaussian form for P(F) is still accurate at lower densities (but not too low density) for the two potentials, but with a smaller value for the constant, A, than that predicted by the DFT theory.

Second-order perturbations of cosmological fluids: Relativistic effects of pressure, multicomponent, curvature, and rotation

International Nuclear Information System (INIS)

Hwang, Jai-chan; Noh, Hyerim

2007-01-01

We present general relativistic correction terms appearing in Newton's gravity to the second-order perturbations of cosmological fluids. In our previous work we have shown that to the second-order perturbations, the density and velocity perturbation equations of general relativistic zero-pressure, irrotational, single-component fluid in a spatially flat background coincide exactly with the ones known in Newton's theory without using the gravitational potential. We also have shown the effect of gravitational waves to the second order, and pure general relativistic correction terms appearing in the third-order perturbations. Here, we present results of second-order perturbations relaxing all the assumptions made in our previous works. We derive the general relativistic correction terms arising due to (i) pressure, (ii) multicomponent, (iii) background spatial curvature, and (iv) rotation. In the case of multicomponent zero-pressure, irrotational fluids under the flat background, we effectively do not have relativistic correction terms, thus the relativistic equations expressed in terms of density and velocity perturbations again coincide with the Newtonian ones. In the other three cases we generally have pure general relativistic correction terms. In the case of pressure, the relativistic corrections appear even in the level of background and linear perturbation equations. In the presence of background spatial curvature, or rotation, pure relativistic correction terms directly appear in the Newtonian equations of motion of density and velocity perturbations to the second order; to the linear order, without using the gravitational potential (or metric perturbations), we have relativistic/Newtonian correspondences for density and velocity perturbations of a single-component fluid including the rotation even in the presence of background spatial curvature. In the small-scale limit (far inside the horizon), to the second-order, relativistic equations of density and

Instabilities in mimetic matter perturbations

Energy Technology Data Exchange (ETDEWEB)

Firouzjahi, Hassan; Gorji, Mohammad Ali [School of Astronomy, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Mansoori, Seyed Ali Hosseini, E-mail: firouz@ipm.ir, E-mail: gorji@ipm.ir, E-mail: shosseini@shahroodut.ac.ir, E-mail: shossein@ipm.ir [Physics Department, Shahrood University of Technology, P.O. Box 3619995161 Shahrood (Iran, Islamic Republic of)

2017-07-01

We study cosmological perturbations in mimetic matter scenario with a general higher derivative function. We calculate the quadratic action and show that both the kinetic term and the gradient term have the wrong sings. We perform the analysis in both comoving and Newtonian gauges and confirm that the Hamiltonians and the associated instabilities are consistent with each other in both gauges. The existence of instabilities is independent of the specific form of higher derivative function which generates gradients for mimetic field perturbations. It is verified that the ghost instability in mimetic perturbations is not associated with the higher derivative instabilities such as the Ostrogradsky ghost.

Multiple exciton generation in chiral carbon nanotubes: Density functional theory based computation

Science.gov (United States)

Kryjevski, Andrei; Mihaylov, Deyan; Kilina, Svetlana; Kilin, Dmitri

2017-10-01

We use a Boltzmann transport equation (BE) to study time evolution of a photo-excited state in a nanoparticle including phonon-mediated exciton relaxation and the multiple exciton generation (MEG) processes, such as exciton-to-biexciton multiplication and biexciton-to-exciton recombination. BE collision integrals are computed using Kadanoff-Baym-Keldysh many-body perturbation theory based on density functional theory simulations, including exciton effects. We compute internal quantum efficiency (QE), which is the number of excitons generated from an absorbed photon in the course of the relaxation. We apply this approach to chiral single-wall carbon nanotubes (SWCNTs), such as (6,2) and (6,5). We predict efficient MEG in the (6,2) and (6,5) SWCNTs within the solar spectrum range starting at the 2Eg energy threshold and with QE reaching ˜1.6 at about 3Eg, where Eg is the electronic gap.

Versatile Density Functionals for Computational Surface Science

DEFF Research Database (Denmark)

Wellendorff, Jess

Density functional theory (DFT) emerged almost 50 years ago. Since then DFT has established itself as the central electronic structure methodology for simulating atomicscale systems from a few atoms to a few hundred atoms. This success of DFT is due to a very favorable accuracy-to-computational c......Density functional theory (DFT) emerged almost 50 years ago. Since then DFT has established itself as the central electronic structure methodology for simulating atomicscale systems from a few atoms to a few hundred atoms. This success of DFT is due to a very favorable accuracy...... resampling techniques, thereby systematically avoiding problems with overfitting. The first ever density functional presenting both reliable accuracy and convincing error estimation is generated. The methodology is general enough to be applied to more complex functional forms with higher-dimensional fitting...

Divergent Perturbation Series

International Nuclear Information System (INIS)

Suslov, I.M.

2005-01-01

Various perturbation series are factorially divergent. The behavior of their high-order terms can be determined by Lipatov's method, which involves the use of instanton configurations of appropriate functional integrals. When the Lipatov asymptotic form is known and several lowest order terms of the perturbation series are found by direct calculation of diagrams, one can gain insight into the behavior of the remaining terms of the series, which can be resummed to solve various strong-coupling problems in a certain approximation. This approach is demonstrated by determining the Gell-Mann-Low functions in φ 4 theory, QED, and QCD with arbitrary coupling constants. An overview of the mathematical theory of divergent series is presented, and interpretation of perturbation series is discussed. Explicit derivations of the Lipatov asymptotic form are presented for some basic problems in theoretical physics. A solution is proposed to the problem of renormalon contributions, which hampered progress in this field in the late 1970s. Practical perturbation-series summation schemes are described both for a coupling constant of order unity and in the strong-coupling limit. An interpretation of the Borel integral is given for 'non-Borel-summable' series. Higher order corrections to the Lipatov asymptotic form are discussed

Local and linear chemical reactivity response functions at finite temperature in density functional theory

International Nuclear Information System (INIS)

Franco-Pérez, Marco; Ayers, Paul W.; Gázquez, José L.; Vela, Alberto

2015-01-01

We explore the local and nonlocal response functions of the grand canonical potential density functional at nonzero temperature. In analogy to the zero-temperature treatment, local (e.g., the average electron density and the local softness) and nonlocal (e.g., the softness kernel) intrinsic response functions are defined as partial derivatives of the grand canonical potential with respect to its thermodynamic variables (i.e., the chemical potential of the electron reservoir and the external potential generated by the atomic nuclei). To define the local and nonlocal response functions of the electron density (e.g., the Fukui function, the linear density response function, and the dual descriptor), we differentiate with respect to the average electron number and the external potential. The well-known mathematical relationships between the intrinsic response functions and the electron-density responses are generalized to nonzero temperature, and we prove that in the zero-temperature limit, our results recover well-known identities from the density functional theory of chemical reactivity. Specific working equations and numerical results are provided for the 3-state ensemble model

On a finite moment perturbation of linear functionals and the inverse Szegö transformation

Directory of Open Access Journals (Sweden)

Edinson Fuentes

2016-05-01

Full Text Available Given a sequence of moments $\\{c_{n}\\}_{n\\in\\ze}$ associated with an Hermitian linear functional $\\mathcal{L}$ defined in the space of Laurent polynomials, we study a new functional $\\mathcal{L}_{\\Omega}$ which is a perturbation of $\\mathcal{L}$ in such a way that a finite number of moments are perturbed. Necessary and sufficient conditions are given for the regularity of $\\mathcal{L}_{\\Omega}$, and a connection formula between the corresponding families of orthogonal polynomials is obtained. On the other hand, assuming $\\mathcal{L}_{\\Omega}$ is positive definite, the perturbation is analyzed through the inverse Szegö transformation. Resumen. Dada una sucesión de momentos $\\{c_{n}\\}_{n\\in\\ze}$ asociada a un funcional lineal hermitiano $\\mathcal{L}$ definido en el espacio de los polinomios de Laurent, estudiamos un nuevo funcional $\\mathcal{L}_{\\Omega}$ que consiste en una perturbación de $\\mathcal{L}$ de tal forma que se perturba un número finito de momentos de la sucesión. Se encuentran condiciones necesarias y suficientes para la regularidad de $\\mathcal{L}_{\\Omega}$, y se obtiene una fórmula de conexión que relaciona las familias de polinomios ortogonales correspondientes. Por otro lado, suponiendo que $\\mathcal{L}_{\\Omega}$ es definido positivo, se analiza la perturbación mediante de la transformación inversa de Szegö.

Two-body perturbation theory versus first order perturbation theory: A comparison based on the square-well fluid.

Science.gov (United States)

Mercier Franco, Luís Fernando; Castier, Marcelo; Economou, Ioannis G

2017-12-07

We show that the Zwanzig first-order perturbation theory can be obtained directly from a truncated Taylor series expansion of a two-body perturbation theory and that such truncation provides a more accurate prediction of thermodynamic properties than the full two-body perturbation theory. This unexpected result is explained by the quality of the resulting approximation for the fluid radial distribution function. We prove that the first-order and the two-body perturbation theories are based on different approximations for the fluid radial distribution function. To illustrate the calculations, the square-well fluid is adopted. We develop an analytical expression for the two-body perturbed Helmholtz free energy for the square-well fluid. The equation of state obtained using such an expression is compared to the equation of state obtained from the first-order approximation. The vapor-liquid coexistence curve and the supercritical compressibility factor of a square-well fluid are calculated using both equations of state and compared to Monte Carlo simulation data. Finally, we show that the approximation for the fluid radial distribution function given by the first-order perturbation theory provides closer values to the ones calculated via Monte Carlo simulations. This explains why such theory gives a better description of the fluid thermodynamic behavior.

Nonperturbative Quantum Physics from Low-Order Perturbation Theory.

Science.gov (United States)

Mera, Héctor; Pedersen, Thomas G; Nikolić, Branislav K

2015-10-02

The Stark effect in hydrogen and the cubic anharmonic oscillator furnish examples of quantum systems where the perturbation results in a certain ionization probability by tunneling processes. Accordingly, the perturbed ground-state energy is shifted and broadened, thus acquiring an imaginary part which is considered to be a paradigm of nonperturbative behavior. Here we demonstrate how the low order coefficients of a divergent perturbation series can be used to obtain excellent approximations to both real and imaginary parts of the perturbed ground state eigenenergy. The key is to use analytic continuation functions with a built-in singularity structure within the complex plane of the coupling constant, which is tailored by means of Bender-Wu dispersion relations. In the examples discussed the analytic continuation functions are Gauss hypergeometric functions, which take as input fourth order perturbation theory and return excellent approximations to the complex perturbed eigenvalue. These functions are Borel consistent and dramatically outperform widely used Padé and Borel-Padé approaches, even for rather large values of the coupling constant.

Green's functions in quantum chemistry - I. The Σ perturbation method

International Nuclear Information System (INIS)

Sebastian, K.L.

1978-01-01

As an improvement over the Hartree-Fock approximation, a Green's Function method - the Σ perturbation method - is investigated for molecular calculations. The method is applied to the hydrogen molecule and to the π-electron system of ethylene under PPP approximation. It is found that when the algebraic approximation is used, the energy obtained is better than that of the HF approach, but is not as good as that of the configuration-interaction method. The main advantage of this procedure is that it is devoid of the most serious defect of HF method, viz. incorrect dissociation limits. (K.B.)

Calculation of the exchange coupling constants of copper binuclear systems based on spin-flip constricted variational density functional theory.

Science.gov (United States)

Zhekova, Hristina R; Seth, Michael; Ziegler, Tom

2011-11-14

We have recently developed a methodology for the calculation of exchange coupling constants J in weakly interacting polynuclear metal clusters. The method is based on unrestricted and restricted second order spin-flip constricted variational density functional theory (SF-CV(2)-DFT) and is here applied to eight binuclear copper systems. Comparison of the SF-CV(2)-DFT results with experiment and with results obtained from other DFT and wave function based methods has been made. Restricted SF-CV(2)-DFT with the BH&HLYP functional yields consistently J values in excellent agreement with experiment. The results acquired from this scheme are comparable in quality to those obtained by accurate multi-reference wave function methodologies such as difference dedicated configuration interaction and the complete active space with second-order perturbation theory. © 2011 American Institute of Physics

Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin-Barnes Representation

Directory of Open Access Journals (Sweden)

Samuel Friot

2010-10-01

Full Text Available Using a method mixing Mellin-Barnes representation and Borel resummation we show how to obtain hyperasymptotic expansions from the (divergent formal power series which follow from the perturbative evaluation of arbitrary ''N-point'' functions for the simple case of zero-dimensional φ4 field theory. This hyperasymptotic improvement appears from an iterative procedure, based on inverse factorial expansions, and gives birth to interwoven non-perturbative partial sums whose coefficients are related to the perturbative ones by an interesting resurgence phenomenon. It is a non-perturbative improvement in the sense that, for some optimal truncations of the partial sums, the remainder at a given hyperasymptotic level is exponentially suppressed compared to the remainder at the preceding hyperasymptotic level. The Mellin-Barnes representation allows our results to be automatically valid for a wide range of the phase of the complex coupling constant, including Stokes lines. A numerical analysis is performed to emphasize the improved accuracy that this method allows to reach compared to the usual perturbative approach, and the importance of hyperasymptotic optimal truncation schemes.

Gribov ambiguity, perturbation theory, and confinement

International Nuclear Information System (INIS)

Greensite, J.P.

1978-01-01

The generating functional proposed for gauge theories by Bender, Eguchi, and Pagels (BEP) is shown to be equivalent to a truncated form of the functional integral, in which only one field configuration from each gauge-equivalent Gribov set contributes to the functional integration. The standard perturbation technique provides a method of realizing this truncation condition. It is shown that any gauge-covariant quantity (such as the quark N-point functions), evaluated by perturbating around a field configuration gauge-equivalent to A = 0, is related by a gauge transformation to the same quantity evaluated perturbatively around the trivial vacuum. It follows that, contrary to the conclusion of BEP, the existence of degeneracies in the Coulomb gauge-fixing condition (the Gribov ambiguity) is not directly related to the physics of confinement

A Safari Through Density Functional Theory

Science.gov (United States)

Dreizler, Reiner M.; Lüdde, Cora S.

Density functional theory is widely used to treat quantum many body problems in many areas of physics and related fields. A brief survey of this method covering foundations, functionals and applications is presented here.

Perturbation method for experimental determination of neutron spatial distribution in the reactor cell; Metoda perturbacije za eksperimentalno odredjivanje prostorne raspodele neutrona u celiji reaktora

Energy Technology Data Exchange (ETDEWEB)

Takac, S M [Institute of Nuclear Sciences Boris Kidric, Vinca, Beograd (Yugoslavia)

1972-07-01

The method is based on perturbation of the reactor cell from a few up to few tens of percent. Measurements were performed for square lattice calls of zero power reactors ANNA, NORA and RB, with metal uranium and uranium oxide fuel elements, water, heavy water and graphite moderators. Character and functional dependence of perturbations were obtained from the experimental results. Zero perturbation was determined by extrapolation thus obtaining the real physical neutron flux distribution in the reactor cell. Simple diffusion theory for partial plate cell perturbation was developed for verification of the perturbation method. The results of these calculation proved that introducing the perturbation sample in the fuel results in flattening the thermal neutron density dependent on the amplitude of the applied perturbation. Extrapolation applied for perturbed distributions was found to be justified.

Second-Order Moller-Plesset Perturbation Theory for Molecular Dirac-Hartree-Fock Wave Functions

Science.gov (United States)

Dyall, Kenneth G.; Arnold, James O. (Technical Monitor)

1994-01-01

Moller-Plesset perturbation theory is developed to second order for a selection of Kramers restricted Dirac-Hartree-Fock closed and open-shell reference wave functions. The open-shell wave functions considered are limited to those with no more than two electrons in open shells, but include the case of a two-configuration SCF reference. Denominator shifts are included in the style of Davidson's OPT2 method. An implementation which uses unordered integrals with labels is presented, and results are given for a few test cases.

Comparison of exact-exchange calculations for solids in current-spin-density- and spin-density-functional theory

DEFF Research Database (Denmark)

Sharma, S.; Pittalis, S.; Kurth, S.

2007-01-01

The relative merits of current-spin-density- and spin-density-functional theory are investigated for solids treated within the exact-exchange-only approximation. Spin-orbit splittings and orbital magnetic moments are determined at zero external magnetic field. We find that for magnetic (Fe, Co......, and Ni) and nonmagnetic (Si and Ge) solids, the exact-exchange current-spin-density functional approach does not significantly improve the accuracy of the corresponding spin-density functional results....

Dynamical density functional theory for dense atomic liquids

International Nuclear Information System (INIS)

Archer, A J

2006-01-01

Starting from Newton's equations of motion, we derive a dynamical density functional theory (DDFT) applicable to atomic liquids. The theory has the feature that it requires as input the Helmholtz free energy functional from equilibrium density functional theory. This means that, given a reliable equilibrium free energy functional, the correct equilibrium fluid density profile is guaranteed. We show that when the isothermal compressibility is small, the DDFT generates the correct value for the speed of sound in a dense liquid. We also interpret the theory as a dynamical equation for a coarse grained fluid density and show that the theory can be used (making further approximations) to derive the standard mode coupling theory that is used to describe the glass transition. The present theory should provide a useful starting point for describing the dynamics of inhomogeneous atomic fluids

Higher order alchemical derivatives from coupled perturbed self-consistent field theory.

Science.gov (United States)

Lesiuk, Michał; Balawender, Robert; Zachara, Janusz

2012-01-21

We present an analytical approach to treat higher order derivatives of Hartree-Fock (HF) and Kohn-Sham (KS) density functional theory energy in the Born-Oppenheimer approximation with respect to the nuclear charge distribution (so-called alchemical derivatives). Modified coupled perturbed self-consistent field theory is used to calculate molecular systems response to the applied perturbation. Working equations for the second and the third derivatives of HF/KS energy are derived. Similarly, analytical forms of the first and second derivatives of orbital energies are reported. The second derivative of Kohn-Sham energy and up to the third derivative of Hartree-Fock energy with respect to the nuclear charge distribution were calculated. Some issues of practical calculations, in particular the dependence of the basis set and Becke weighting functions on the perturbation, are considered. For selected series of isoelectronic molecules values of available alchemical derivatives were computed and Taylor series expansion was used to predict energies of the "surrounding" molecules. Predicted values of energies are in unexpectedly good agreement with the ones computed using HF/KS methods. Presented method allows one to predict orbital energies with the error less than 1% or even smaller for valence orbitals. © 2012 American Institute of Physics

Constructive definition of functional derivatives in density-functional theory

International Nuclear Information System (INIS)

Luo Ji

2006-01-01

It is shown that the functional derivatives in density-functional theory (DFT) can be explicitly defined within the domain of electron densities restricted by the electron number, and a constructive definition of such restricted derivatives is suggested. With this definition, Kohn-Sham (KS) equations can be established for an N-electron system without extending the functional domain and introducing a Lagrange multiplier. This may clarify some of the fundamental questions raised by Nesbet (1998 Phys. Rev. A 58 R12). The definition naturally leads to the fact that the KS effective potential is determined only to within an additive constant, thus the KS levels can shift freely and the relation between the highest occupied molecular orbital (HOMO) energy and the ionization potential of the system depends on the choice of the constant. On the other hand, if the domain of functionals is indeed extended beyond the electron number restriction, conclusions depend on whether the extended functionals have unrestricted derivatives or not. It is shown that the ensemble extension of DFT to open systems of mixed states (Perdew et al 1982 Phys. Rev. Lett. 49 1691) leads to an energy functional which has no unrestricted derivative at integer electron numbers. Hence after this extension, the relation between the HOMO energy and the ionization potential for an N-electron system is still uncertain. Besides, there are different extensions of the energy functional to a domain of densities unrestricted by the integer electron number, resulting in different unrestricted derivatives and electron systems with different chemical potentials. Even for the exact exchange-correlation potential, there is still an undetermined constant, whether it is a restricted or unrestricted derivative

Density functional theory in quantum chemistry

CERN Document Server

Tsuneda, Takao

2014-01-01

This book examines density functional theory based on the foundation of quantum chemistry. Unconventional in approach, it reviews basic concepts, then describes the physical meanings of state-of-the-art exchange-correlation functionals and their corrections.

Comment on 'Kinetic energy as a density functional'

International Nuclear Information System (INIS)

Holas, A.; March, N.H.

2002-01-01

In a recent paper, Nesbet [Phys. Rev. A 65, 010502(R) (2001)] has proposed dropping ''the widespread but unjustified assumption that the existence of a ground-state density functional for the kinetic energy, T s [ρ], of an N-electron system implies the existence of a density-functional derivative, δT s [ρ]/δρ(r), equivalent to a local potential function,'' because, according to his arguments, this derivative 'has the mathematical character of a linear operator that acts on orbital wave functions'. Our Comment demonstrates that the statement called by Nesbet an 'unjustified assumption' happens, in fact, to be a rigorously proven theorem. Therefore, his previous conclusions stemming from his different view of this derivative, which undermined the foundations of density-functional theory, can be discounted

Neutronic density perturbation by probes

International Nuclear Information System (INIS)

Vigon, M. A.; Diez, L.

1956-01-01

The introduction of absorbent materials of neutrons in diffuser media, produces local disturbances of neutronic density. The disturbance depends especially on the nature and size of the absorbent. Approximated equations which relates te disturbance and the distance to the absorbent in the case of thin disks have been drawn. The experimental comprobation has been carried out in two especial cases. In both cases the experimental results are in agreement with the calculated values from these equations. (Author)

SYNTHESIS, CHARACTERIZATION AND DENSITY FUNCTIONAL ...

African Journals Online (AJOL)

Preferred Customer

We synthesized a number of aniline derivatives containing acyl groups to compare their barriers of rotation around ... KEY WORDS: Monoacyl aniline, Synthesis, Density functional theory, Rotation barrier. INTRODUCTION. Developments in ...

Application of perturbation theory to lattice calculations based on method of cyclic characteristics

Science.gov (United States)

Assawaroongruengchot, Monchai

computing time when both direct and adjoint solutions are required. A problem that arises for the generalized adjoint problem is that the direct use of the negative external generalized adjoint sources in the adjoint solution algorithm results in negative generalized adjoint functions. A coupled flux biasing/decontamination scheme is applied to make the generalized adjoint functions positive using the adjoint functions in such a way that it can be used for the multigroup rebalance technique. Next we consider the application of the perturbation theory to the reactor problems. Since the coolant void reactivity (CVR) is a important factor in reactor safety analysis, we have decided to select this parameter for optimization studies. We consider the optimization and adjoint sensitivity techniques for the adjustments of CVR at beginning of burnup cycle (BOC) and k eff at end of burnup cycle (EOC) for a 2D Advanced CANDU Reactor (ACR) lattice. The sensitivity coefficients are evaluated using the perturbation theory based on the integral transport equations. Three sets of parameters for CVR-BOC and keff-EOC adjustments are studied: (1) Dysprosium density in the central pin with Uranium enrichment in the outer fuel rings, (2) Dysprosium density and Uranium enrichment both in the central pin, and (3) the same parameters as in the first case but the objective is to obtain a negative checkerboard CVR at beginning of cycle (CBCVR-BOC). To approximate the sensitivity coefficient at EOC, we perform constant-power burnup/depletion calculations for 600 full power days (FPD) using a slightly perturbed nuclear library and the unperturbed neutron fluxes to estimate the variation of nuclide densities at EOC. Sensitivity analyses of CVR and eigenvalue are included in the study. In addition the optimization and adjoint sensitivity techniques are applied to the CBCVR-BOC and keff-EOC adjustment of the ACR lattices with Gadolinium in the central pin. Finally we apply these techniques to the CVR

Application of perturbation theory to lattice calculations based on method of cyclic characteristics

Energy Technology Data Exchange (ETDEWEB)

Assawaroongruengchot, M

2007-07-01

computing time when both direct and adjoint solutions are required. A problem that arises for the generalized adjoint problem is that the direct use of the negative external generalized adjoint sources in the adjoint solution algorithm results in negative generalized adjoint functions. A coupled flux biasing/decontamination scheme is applied to make the generalized adjoint functions positive using the adjoint functions in such a way that it can be used for the multigroup rebalance technique. Next we consider the application of the perturbation theory to the reactor problems. Since the coolant void reactivity (CVR) is a important factor in reactor safety analysis, we have decided to select this parameter for optimization studies. We consider the optimization and adjoint sensitivity techniques for the adjustments of CVR at beginning of burnup cycle (BOC) and k{sub eff} at end of burnup cycle (EOC) for a 2D Advanced CANDU Reactor (ACR) lattice. The sensitivity coefficients are evaluated using the perturbation theory based on the integral transport equations. Three sets of parameters for CVR-BOC and k{sub eff}-EOC adjustments are studied: (1) Dysprosium density in the central pin with Uranium enrichment in the outer fuel rings, (2) Dysprosium density and Uranium enrichment both in the central pin, and (3) the same parameters as in the first case but the objective is to obtain a negative checkerboard CVR at beginning of cycle (CBCVR-BOC). To approximate the sensitivity coefficient at EOC, we perform constant-power burnup/depletion calculations for 600 full power days (FPD) using a slightly perturbed nuclear library and the unperturbed neutron fluxes to estimate the variation of nuclide densities at EOC. Sensitivity analyses of CVR and eigenvalue are included in the study. In addition the optimization and adjoint sensitivity techniques are applied to the CBCVR-BOC and k{sub eff}-EOC adjustment of the ACR lattices with Gadolinium in the central pin. Finally we apply these

Application of perturbation theory to lattice calculations based on method of cyclic characteristics

International Nuclear Information System (INIS)

Assawaroongruengchot, M.

2007-01-01

computing time when both direct and adjoint solutions are required. A problem that arises for the generalized adjoint problem is that the direct use of the negative external generalized adjoint sources in the adjoint solution algorithm results in negative generalized adjoint functions. A coupled flux biasing/decontamination scheme is applied to make the generalized adjoint functions positive using the adjoint functions in such a way that it can be used for the multigroup rebalance technique. Next we consider the application of the perturbation theory to the reactor problems. Since the coolant void reactivity (CVR) is a important factor in reactor safety analysis, we have decided to select this parameter for optimization studies. We consider the optimization and adjoint sensitivity techniques for the adjustments of CVR at beginning of burnup cycle (BOC) and k eff at end of burnup cycle (EOC) for a 2D Advanced CANDU Reactor (ACR) lattice. The sensitivity coefficients are evaluated using the perturbation theory based on the integral transport equations. Three sets of parameters for CVR-BOC and k eff -EOC adjustments are studied: (1) Dysprosium density in the central pin with Uranium enrichment in the outer fuel rings, (2) Dysprosium density and Uranium enrichment both in the central pin, and (3) the same parameters as in the first case but the objective is to obtain a negative checkerboard CVR at beginning of cycle (CBCVR-BOC). To approximate the sensitivity coefficient at EOC, we perform constant-power burnup/depletion calculations for 600 full power days (FPD) using a slightly perturbed nuclear library and the unperturbed neutron fluxes to estimate the variation of nuclide densities at EOC. Sensitivity analyses of CVR and eigenvalue are included in the study. In addition the optimization and adjoint sensitivity techniques are applied to the CBCVR-BOC and k eff -EOC adjustment of the ACR lattices with Gadolinium in the central pin. Finally we apply these techniques to the CVR

Perturbation of a Schwarzschild Black Hole Due to a Rotating Thin Disk

Energy Technology Data Exchange (ETDEWEB)

Čížek, P.; Semerák, O., E-mail: oldrich.semerak@mff.cuni.cz [Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University, Prague (Czech Republic)

2017-09-01

Will, in 1974, treated the perturbation of a Schwarzschild black hole due to a slowly rotating, light, concentric thin ring by solving the perturbation equations in terms of a multipole expansion of the mass-and-rotation perturbation series. In the Schwarzschild background, his approach can be generalized to perturbation by a thin disk (which is more relevant astrophysically), but, due to rather bad convergence properties, the resulting expansions are not suitable for specific (numerical) computations. However, we show that Green’s functions, represented by Will’s result, can be expressed in closed form (without multipole expansion), which is more useful. In particular, they can be integrated out over the source (a thin disk in our case) to yield good converging series both for the gravitational potential and for the dragging angular velocity. The procedure is demonstrated, in the first perturbation order, on the simplest case of a constant-density disk, including the physical interpretation of the results in terms of a one-component perfect fluid or a two-component dust in a circular orbit about the central black hole. Free parameters are chosen in such a way that the resulting black hole has zero angular momentum but non-zero angular velocity, as it is just carried along by the dragging effect of the disk.

Density functional approach to the many-body problem : Key concepts and exact functionals

NARCIS (Netherlands)

van Leeuwen, Robert

2003-01-01

We give an overview of the fundamental concepts of density functional theory. We give a careful discussion of the several density functionals and their differentiability properties. We show that for nondegenerate ground states we can calculate the necessary functional derivatives by means of linear

MCNP perturbation technique for criticality analysis

International Nuclear Information System (INIS)

McKinney, G.W.; Iverson, J.L.

1995-01-01

The differential operator perturbation technique has been incorporated into the Monte Carlo N-Particle transport code MCNP and will become a standard feature of future releases. This feature includes first and/or second order terms of the Taylor Series expansion for response perturbations related to cross-section data (i.e., density, composition, etc.). Criticality analyses can benefit from this technique in that predicted changes in the track-length tally estimator of K eff may be obtained for multiple perturbations in a single run. A key advantage of this method is that a precise estimate of a small change in response (i.e., < 1%) is easily obtained. This technique can also offer acceptable accuracy, to within a few percent, for up to 20-30% changes in a response

Extended screened exchange functional derived from transcorrelated density functional theory.

Science.gov (United States)

Umezawa, Naoto

2017-09-14

We propose a new formulation of the correlation energy functional derived from the transcorrelated method in use in density functional theory (TC-DFT). An effective Hamiltonian, H TC , is introduced by a similarity transformation of a many-body Hamiltonian, H, with respect to a complex function F: H TC =1FHF. It is proved that an expectation value of H TC for a normalized single Slater determinant, D n , corresponds to the total energy: E[n] = ⟨Ψ n |H|Ψ n ⟩/⟨Ψ n |Ψ n ⟩ = ⟨D n |H TC |D n ⟩ under the two assumptions: (1) The electron density nr associated with a trial wave function Ψ n = D n F is v-representable and (2) Ψ n and D n give rise to the same electron density nr. This formulation, therefore, provides an alternative expression of the total energy that is useful for the development of novel correlation energy functionals. By substituting a specific function for F, we successfully derived a model correlation energy functional, which resembles the functional form of the screened exchange method. The proposed functional, named the extended screened exchange (ESX) functional, is described within two-body integrals and is parametrized for a numerically exact correlation energy of the homogeneous electron gas. The ESX functional does not contain any ingredients of (semi-)local functionals and thus is totally free from self-interactions. The computational cost for solving the self-consistent-field equation is comparable to that of the Hartree-Fock method. We apply the ESX functional to electronic structure calculations for a solid silicon, H - ion, and small atoms. The results demonstrate that the TC-DFT formulation is promising for the systematic improvement of the correlation energy functional.

Primordial black holes and uncertainties in the choice of the window function

Science.gov (United States)

Ando, Kenta; Inomata, Keisuke; Kawasaki, Masahiro

2018-05-01

Primordial black holes (PBHs) can be produced by the perturbations that exit the horizon during the inflationary phase. While inflation models predict the power spectrum of the perturbations in Fourier space, the PBH abundance depends on the probability distribution function of density perturbations in real space. To estimate the PBH abundance in a given inflation model, we must relate the power spectrum in Fourier space to the probability density function in real space by coarse graining the perturbations with a window function. However, there are uncertainties on what window function should be used, which could change the relation between the PBH abundance and the power spectrum. This is particularly important in considering PBHs with mass 30 M⊙, which account for the LIGO events because the required power spectrum is severely constrained by the observations. In this paper, we investigate how large an influence the uncertainties on the choice of a window function has over the power spectrum required for LIGO PBHs. As a result, it is found that the uncertainties significantly affect the prediction for the stochastic gravitational waves induced by the second-order effect of the perturbations. In particular, the pulsar timing array constraints on the produced gravitational waves could disappear for the real-space top-hat window function.

Impact of rotating resonant magnetic perturbation fields on plasma edge electron density and temperature

International Nuclear Information System (INIS)

Stoschus, H.; Schmitz, O.; Frerichs, H.; Reiser, D.; Unterberg, B.; Lehnen, M.; Reiter, D.; Samm, U.; Jakubowski, M.W.

2012-01-01

Rotating resonant magnetic perturbation (RMP) fields impose a characteristic modulation to the edge electron density n e (r, t) and temperature T e (r, t) fields, which depends on the relative rotation f rel between external RMP field and plasma fluid. The n e (r, t) and T e (r, t) fields measured in the edge (r/a = 0.9–1.05) of TEXTOR L-mode plasmas are in close correlation with the local magnetic vacuum topology for low relative rotation f rel = −0.2 kHz. In comparison with the 3D neutral and plasma transport code EMC3-Eirene, this provides substantial experimental evidence that for low relative rotation level and high resonant field amplitudes (normalized radial field strength B r 4/1 /B t =2×10 -3 ), a stochastic edge with a remnant island chain dominated by diffusive transport exists. Radially outside a helical scrape-off layer, the so-called laminar zone embedded into a stochastic domain is found to exist. In contrast for high relative rotation of f rel = 1.8 kHz, the measured modulation of n e is shifted by π/2 toroidally with respect to the modelled vacuum topology. A pronounced flattening in T e (r) and a reduction in n e (r) is measured at the resonant flux surface and represents a clear signature for a magnetic island, which is phase shifted with respect to the vacuum island position. A correlated shift of the laminar zone radially outwards at the very plasma edge is observed suggesting that the actual near-field structure at the perturbation source is determined by the plasma response as well. (paper)

Dynamic density functional theory with hydrodynamic interactions: Theoretical development and application in the study of phase separation in gas-liquid systems

International Nuclear Information System (INIS)

Kikkinides, E. S.; Monson, P. A.

2015-01-01

Building on recent developments in dynamic density functional theory, we have developed a version of the theory that includes hydrodynamic interactions. This is achieved by combining the continuity and momentum equations eliminating velocity fields, so the resulting model equation contains only terms related to the fluid density and its time and spatial derivatives. The new model satisfies simultaneously continuity and momentum equations under the assumptions of constant dynamic or kinematic viscosity and small velocities and/or density gradients. We present applications of the theory to spinodal decomposition of subcritical temperatures for one-dimensional and three-dimensional density perturbations for both a van der Waals fluid and for a lattice gas model in mean field theory. In the latter case, the theory provides a hydrodynamic extension to the recently studied dynamic mean field theory. We find that the theory correctly describes the transition from diffusive phase separation at short times to hydrodynamic behaviour at long times

Quantum Crystallography: Density Matrix-Density Functional Theory and the X-Ray Diffraction Experiment

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Soirat, Arnaud J. A.

Density Matrix Theory is a Quantum Mechanical formalism in which the wavefunction is eliminated and its role taken over by reduced density matrices. The interest of this is that, it allows one, in principle, to calculate any electronic property of a physical system, without having to solve the Schrodinger equation, using only two entities much simpler than an N-body wavefunction: first and second -order reduced density matrices. In practice, though, this very promising possibility faces the tremendous theoretical problem of N-representability, which has been solved for the former, but, until now, voids any hope of theoretically determining the latter. However, it has been shown that single determinant reduced density matrices of any order may be recovered from coherent X-ray diffraction data, if one provides a proper Quantum Mechanical description of the Crystallography experiment. A deeper investigation of this method is the purpose of this work, where we, first, further study the calculation of X-ray reduced density matrices N-representable by a single Slater determinant. In this context, we independently derive necessary and sufficient conditions for the uniqueness of the method. We then show how to account for electron correlation in this model. For the first time, indeed, we derive highly accurate, yet practical, density matrices approximately N-representable by correlated-determinant wavefunctions. The interest of such a result lies in the Quantum Mechanical validity of these density matrices, their property of being entirely obtainable from X-ray coherent diffraction data, their very high accuracy conferred by this known property of the N-representing wavefunction, as well as their definition as explicit functionals of the density. All of these properties are finally used in both a theoretical and a numerical application: in the former, we show that these density matrices may be used in the context of Density Functional Theory to highly accurately determine

Density functional theory of nuclei

International Nuclear Information System (INIS)

Terasaki, Jun

2008-01-01

The density functional theory of nuclei has come to draw attention of scientists in the field of nuclear structure because the theory is expected to provide reliable numerical data in wide range on the nuclear chart. This article is organized to present an overview of the theory to the people engaged in the theory of other fields as well as those people in the nuclear physics experiments. At first, the outline of the density functional theory widely used in the electronic systems (condensed matter, atoms, and molecules) was described starting from the Kohn-Sham equation derived on the variational principle. Then the theory used in the field of nuclear physics was presented. Hartree-Fock and Hartree-Fock-Bogolyubov approximation by using Skyrme interaction was explained. Comparison of the results of calculations and experiments of binding energies and ground state mean square charge radii of some magic number nuclei were shown. The similarity and dissimilarity between the two streams were summarized. Finally the activities of the international project of Universal Nuclear Energy Density Functional (UNEDF) which was started recently lead by US scientist was reported. This project is programmed for five years. One of the applications of the project is the calculation of the neutron capture cross section of nuclei on the r-process, which is absolutely necessary for the nucleosynthesis research. (S. Funahashi)

Perturbation expansions of stochastic wavefunctions for open quantum systems

Science.gov (United States)

Ke, Yaling; Zhao, Yi

2017-11-01

Based on the stochastic unravelling of the reduced density operator in the Feynman path integral formalism for an open quantum system in touch with harmonic environments, a new non-Markovian stochastic Schrödinger equation (NMSSE) has been established that allows for the systematic perturbation expansion in the system-bath coupling to arbitrary order. This NMSSE can be transformed in a facile manner into the other two NMSSEs, i.e., non-Markovian quantum state diffusion and time-dependent wavepacket diffusion method. Benchmarked by numerically exact results, we have conducted a comparative study of the proposed method in its lowest order approximation, with perturbative quantum master equations in the symmetric spin-boson model and the realistic Fenna-Matthews-Olson complex. It is found that our method outperforms the second-order time-convolutionless quantum master equation in the whole parameter regime and even far better than the fourth-order in the slow bath and high temperature cases. Besides, the method is applicable on an equal footing for any kind of spectral density function and is expected to be a powerful tool to explore the quantum dynamics of large-scale systems, benefiting from the wavefunction framework and the time-local appearance within a single stochastic trajectory.

Fast dynamics perturbation analysis for prediction of protein functional sites

Directory of Open Access Journals (Sweden)

Cohn Judith D

2008-01-01

Full Text Available Abstract Background We present a fast version of the dynamics perturbation analysis (DPA algorithm to predict functional sites in protein structures. The original DPA algorithm finds regions in proteins where interactions cause a large change in the protein conformational distribution, as measured using the relative entropy Dx. Such regions are associated with functional sites. Results The Fast DPA algorithm, which accelerates DPA calculations, is motivated by an empirical observation that Dx in a normal-modes model is highly correlated with an entropic term that only depends on the eigenvalues of the normal modes. The eigenvalues are accurately estimated using first-order perturbation theory, resulting in a N-fold reduction in the overall computational requirements of the algorithm, where N is the number of residues in the protein. The performance of the original and Fast DPA algorithms was compared using protein structures from a standard small-molecule docking test set. For nominal implementations of each algorithm, top-ranked Fast DPA predictions overlapped the true binding site 94% of the time, compared to 87% of the time for original DPA. In addition, per-protein recall statistics (fraction of binding-site residues that are among predicted residues were slightly better for Fast DPA. On the other hand, per-protein precision statistics (fraction of predicted residues that are among binding-site residues were slightly better using original DPA. Overall, the performance of Fast DPA in predicting ligand-binding-site residues was comparable to that of the original DPA algorithm. Conclusion Compared to the original DPA algorithm, the decreased run time with comparable performance makes Fast DPA well-suited for implementation on a web server and for high-throughput analysis.

Adiabaticity and gravity theory independent conservation laws for cosmological perturbations

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Romano, Antonio Enea; Mooij, Sander; Sasaki, Misao

2016-04-01

We carefully study the implications of adiabaticity for the behavior of cosmological perturbations. There are essentially three similar but different definitions of non-adiabaticity: one is appropriate for a thermodynamic fluid δPnad, another is for a general matter field δPc,nad, and the last one is valid only on superhorizon scales. The first two definitions coincide if cs2 = cw2 where cs is the propagation speed of the perturbation, while cw2 = P ˙ / ρ ˙ . Assuming the adiabaticity in the general sense, δPc,nad = 0, we derive a relation between the lapse function in the comoving slicing Ac and δPnad valid for arbitrary matter field in any theory of gravity, by using only momentum conservation. The relation implies that as long as cs ≠cw, the uniform density, comoving and the proper-time slicings coincide approximately for any gravity theory and for any matter field if δPnad = 0 approximately. In the case of general relativity this gives the equivalence between the comoving curvature perturbation Rc and the uniform density curvature perturbation ζ on superhorizon scales, and their conservation. This is realized on superhorizon scales in standard slow-roll inflation. We then consider an example in which cw =cs, where δPnad = δPc,nad = 0 exactly, but the equivalence between Rc and ζ no longer holds. Namely we consider the so-called ultra slow-roll inflation. In this case both Rc and ζ are not conserved. In particular, as for ζ, we find that it is crucial to take into account the next-to-leading order term in ζ's spatial gradient expansion to show its non-conservation, even on superhorizon scales. This is an example of the fact that adiabaticity (in the thermodynamic sense) is not always enough to ensure the conservation of Rc or ζ.

Optimal Bandwidth Selection for Kernel Density Functionals Estimation

Directory of Open Access Journals (Sweden)

Su Chen

2015-01-01

Full Text Available The choice of bandwidth is crucial to the kernel density estimation (KDE and kernel based regression. Various bandwidth selection methods for KDE and local least square regression have been developed in the past decade. It has been known that scale and location parameters are proportional to density functionals ∫γ(xf2(xdx with appropriate choice of γ(x and furthermore equality of scale and location tests can be transformed to comparisons of the density functionals among populations. ∫γ(xf2(xdx can be estimated nonparametrically via kernel density functionals estimation (KDFE. However, the optimal bandwidth selection for KDFE of ∫γ(xf2(xdx has not been examined. We propose a method to select the optimal bandwidth for the KDFE. The idea underlying this method is to search for the optimal bandwidth by minimizing the mean square error (MSE of the KDFE. Two main practical bandwidth selection techniques for the KDFE of ∫γ(xf2(xdx are provided: Normal scale bandwidth selection (namely, “Rule of Thumb” and direct plug-in bandwidth selection. Simulation studies display that our proposed bandwidth selection methods are superior to existing density estimation bandwidth selection methods in estimating density functionals.

Generalized perturbation series

International Nuclear Information System (INIS)

Baird, L.C.; Stinchcomb, G.

1973-01-01

An approximate solution of the Green's function equation may be used to generate an exact solution of the Schroedinger equation. This is accomplished through an iterative procedure. The procedure is equivalent to a perturbation expansion if the approximate Green's function is exact with respect to some reference potential

Analytic continuation in perturbative QCD

International Nuclear Information System (INIS)

Caprini, Irinel

2002-01-01

We discuss some attempts to improve standard perturbative expansion in QCD by using the analytic continuation in the momentum and the Borel complex planes. We first analyse the momentum-plane analyticity properties of the Borel-summed Green functions in perturbative QCD and the connection between the Landau singularities and the infrared renormalons. By using the analytic continuation in the Borel complex plane, we propose a new perturbative series replacing the standard expansion in powers of the normalized coupling constant a. The new expansion functions have branch point and essential singularities at the origin of the complex a-plane and divergent Taylor expansions in powers of a. On the other hand the modified expansion of the QCD correlators is convergent under rather conservative conditions. (author)

Significance of constraints associated with Green's functions in Hamiltonian perturbation theory

International Nuclear Information System (INIS)

Maharana, L.; Muller-Kirsten, H.J.W.; Wiedemann, A.

1987-01-01

In many formulations of Hamiltonian perturbation theory a Green's function becomes undefined when some parameter is allowed to vanish. Here various examples are discussed to illustrate this phenomenon, and it is shown that they are all realizations of a general theorem. The cases considered are examples in classical mechanics, quantum mechanics, electrodynamics and field theory. The prime object is to illustrate the unity of the examples and thus to make the application of the procedure to field theory models of current interest more transparent. One example that it is referred to is the skyrmion model

Distribution function approach to redshift space distortions. Part V: perturbation theory applied to dark matter halos

Energy Technology Data Exchange (ETDEWEB)

Vlah, Zvonimir; Seljak, Uroš [Institute for Theoretical Physics, University of Zürich, Zürich (Switzerland); Okumura, Teppei [Institute for the Early Universe, Ewha Womans University, Seoul, S. Korea (Korea, Republic of); Desjacques, Vincent, E-mail: zvlah@physik.uzh.ch, E-mail: seljak@physik.uzh.ch, E-mail: teppei@ewha.ac.kr, E-mail: Vincent.Desjacques@unige.ch [Département de Physique Théorique and Center for Astroparticle Physics (CAP) Université de Genéve, Genéve (Switzerland)

2013-10-01

Numerical simulations show that redshift space distortions (RSD) introduce strong scale dependence in the power spectra of halos, with ten percent deviations relative to linear theory predictions even on relatively large scales (k < 0.1h/Mpc) and even in the absence of satellites (which induce Fingers-of-God, FoG, effects). If unmodeled these effects prevent one from extracting cosmological information from RSD surveys. In this paper we use Eulerian perturbation theory (PT) and Eulerian halo biasing model and apply it to the distribution function approach to RSD, in which RSD is decomposed into several correlators of density weighted velocity moments. We model each of these correlators using PT and compare the results to simulations over a wide range of halo masses and redshifts. We find that with an introduction of a physically motivated halo biasing, and using dark matter power spectra from simulations, we can reproduce the simulation results at a percent level on scales up to k ∼ 0.15h/Mpc at z = 0, without the need to have free FoG parameters in the model.

Photon density of states for deformed surfaces

International Nuclear Information System (INIS)

Emig, T

2006-01-01

A new approach to the Helmholtz spectrum for arbitrarily shaped boundaries and a rather general class of boundary conditions is introduced. We derive the boundary induced change of the density of states in terms of the free Green's function from which we obtain both perturbative and non-perturbative results for the Casimir interaction between deformed surfaces. As an example, we compute the lateral electrodynamic Casimir force between two corrugated surfaces over a wide parameter range. Universal behaviour, fixed only by the largest wavelength component of the surface shape, is identified at large surface separations. This complements known short distance expansions which are also reproduced

Perturbative QCD predictions for the small x behaviour of unpolarized and polarized deep inelastic scattering structure functions

International Nuclear Information System (INIS)

Kwiecinski, J.

1996-01-01

The perturbative QCD predictions for the small x behaviour of the nucleon structure functions F 2L (x,Q 2 ) and g 1 (x,Q 2 ) are summarized. The importance of the double logarithmic terms for the small x behaviour of the spin structure function g 1 (x,Q 2 ) is emphasized. These terms correspond to the contributions containing the leading powers of α s ln 2 (1/x) at each order of the perturbative expansion. In the non-singlet case they can be approximately accounted for by the ladder diagrams with quark (antiquark) exchange. We solve the corresponding integral equation with the running coupling effects taken into account and present estimate of the effective slope controlling the small x behaviour of the non-singlet spin structure function g 1 (x,Q 2 ) of a nucleon. (author)

Fast Computation of Solvation Free Energies with Molecular Density Functional Theory: Thermodynamic-Ensemble Partial Molar Volume Corrections.

Science.gov (United States)

Sergiievskyi, Volodymyr P; Jeanmairet, Guillaume; Levesque, Maximilien; Borgis, Daniel

2014-06-05

Molecular density functional theory (MDFT) offers an efficient implicit-solvent method to estimate molecule solvation free-energies, whereas conserving a fully molecular representation of the solvent. Even within a second-order approximation for the free-energy functional, the so-called homogeneous reference fluid approximation, we show that the hydration free-energies computed for a data set of 500 organic compounds are of similar quality as those obtained from molecular dynamics free-energy perturbation simulations, with a computer cost reduced by 2-3 orders of magnitude. This requires to introduce the proper partial volume correction to transform the results from the grand canonical to the isobaric-isotherm ensemble that is pertinent to experiments. We show that this correction can be extended to 3D-RISM calculations, giving a sound theoretical justification to empirical partial molar volume corrections that have been proposed recently.

Electromiography comparison of distal and proximal lower limb muscle activity patterns during external perturbation in subjects with and without functional ankle instability.

Science.gov (United States)

Kazemi, Khadijeh; Arab, Amir Massoud; Abdollahi, Iraj; López-López, Daniel; Calvo-Lobo, César

2017-10-01

Ankle sprain is one of the most common injuries among athletes and the general population. Most ankle injuries commonly affect the lateral ligament complex. Changes in postural sway and hip abductor muscle strength may be generated after inversion ankle sprain. Therefore, the consequences of ankle injury may affect proximal structures of the lower limb. The aim is to describe and compare the activity patterns of distal and proximal lower limb muscles following external perturbation in individuals with and without functional ankle instability. The sample consisted of 16 women with functional ankle instability and 18 healthy women were recruited to participate in this research. The external perturbation via body jacket using surface electromyography, amplitude and onset of muscle activity of gluteus maximums, gluteus medius, tibialis anterior, and peroneus longus was recorded and analyzed during external perturbation. There were differences between the onset of muscles activity due to perturbation direction in the two groups (healthy and functional ankle instability). In the healthy group, there were statistically significant differences in amplitude of proximal muscle activity with distal muscle activity during front perturbation with eyes open and closed. In the functional ankle instability group; there were statistically significant differences in amplitude of proximal muscle activity with distal muscle activity during perturbation of the front and back with eyes open. There were statistically significant differences in the onset of muscle activity and amplitude of muscle activity, with-in and between groups (Pankle instability, activation patterns of the lower limb proximal muscles may be altered. Copyright © 2017 Elsevier B.V. All rights reserved.

Modification of response functions of cat visual cortical cells by spatially congruent perturbing stimuli.

Science.gov (United States)

Kabara, J F; Bonds, A B

2001-12-01

Responses of cat striate cortical cells to a drifting sinusoidal grating were modified by the superimposition of a second, perturbing grating (PG) that did not excite the cell when presented alone. One consequence of the presence of a PG was a shift in the tuning curves. The orientation tuning of all 41 cells exposed to a PG and the spatial frequency tuning of 83% of the 23 cells exposed to a PG showed statistically significant dislocations of both the response function peak and center of mass from their single grating values. As found in earlier reports, the presence of PGs suppressed responsiveness. However, reductions measured at the single grating optimum orientation or spatial frequency were on average 1.3 times greater than the suppression found at the peak of the response function modified by the presence of the PG. Much of the loss in response seen at the single grating optimum is thus a result of a shift in the tuning function rather than outright suppression. On average orientation shifts were repulsive and proportional (approximately 0.10 deg/deg) to the angle between the perturbing stimulus and the optimum single grating orientation. Shifts in the spatial frequency response function were both attractive and repulsive, resulting in an overall average of zero. For both simple and complex cells, PGs generally broadened orientation response function bandwidths. Similarly, complex cell spatial frequency response function bandwidths broadened. Simple cell spatial frequency response functions usually did not change, and those that did broadened only 4% on average. These data support the hypothesis that additional sinusoidal components in compound stimuli retune cells' response functions for orientation and spatial frequency.

Prospects of inflation with perturbed throat geometry

International Nuclear Information System (INIS)

Ali, Amna; Chingangbam, R.; Panda, Sudhakar; Sami, M.

2009-01-01

We study brane inflation in a warped deformed conifold background that includes general possible corrections to the throat geometry sourced by coupling to the bulk of a compact Calabi-Yau space. We focus specifically, on the perturbation by chiral operator of dimension 3/2 in the CFT. We find that the effective potential in this case can give rise to required number of e-foldings and the spectral index n S consistent with observation. The tensor to scalar ratio of perturbations is generally very low in this scenario. The COBE normalization, however, poses certain difficulties which can be circumvented provided model parameters are properly fine tuned. We find the numerical values of parameters which can give rise to enough inflation, observationally consistent values of density perturbations, scalar to tensor ratio of perturbations and the spectral index n S .

Comments on the locality in density-functional theory

International Nuclear Information System (INIS)

Lindgren, Ingvar; Salomonson, Sten

2003-01-01

The 'locality hypothesis' in density-functional theory (DFT), implying that the functional derivative is equivalent to a multiplicative local function, forms the basis of models of Kohn-Sham type. This has been generally accepted by the community since the advent of the model, and has later been formally proved for a large class of functionals. The hypothesis has recently been questioned by Nesbet [Phys. Rev. A 58, R12 (1998) and Phys. Rev. A 65, 010502 (2001)], who claims that it fails for the kinetic-energy functional for a system with more than two noninteracting electrons with a nondegenerate ground state. This conclusion has been questioned by Gal [Phys. Rev. A 62, 044501 (2000)] and by Holas and March [Phys. Rev. A 64, 016501 (2001)]. We claim that the arguments of Nesbet are incorrect, since the orbital functional used for the kinetic energy is not a unique functional of the total density in the domain of unnormalized orbitals. We have demonstrated that with a proper definition of the kinetic energy, which is a unique density functional also in the unnormalized region, the derivative can be represented by a single local multiplicative function for all v-representable densities. Therefore, we consider the controversy connected with the issue raised by Nesbet as resolved. We believe that the proof of the differentiability given here can be extended to larger groups of DFT functionals, and works along these lines are in progress

Target mass corrections to electroweak structure functions and perturbative neutrino cross sections

International Nuclear Information System (INIS)

Kretzer, S.; Reno, M.H.

2004-01-01

We provide a complete and consistent framework to include subasymptotic perturbative as well as mass corrections to the leading twist (τ=2) evaluation of charged and neutral current weak structure functions and the perturbative neutrino cross sections. We reexamine previous calculations in a modern language and fill in the gaps that we find missing for a complete and ready-to-use 'NLO ξ-scaling' formulary. In particular, as a new result we formulate the mixing of the partonic and hadronic structure function tensor basis in the operator approach to deep inelastic scattering. As an underlying framework we follow the operator product expansion in the manner of Georgi and Politzer that allows the inclusion of target mass corrections at arbitrary order in QCD and we provide explicit analytical and numerical results at NLO. We compare this approach with a simpler collinear parton model approach to ξ scaling. Along with target mass corrections we include heavy quark mass effects as a calculable leading twist power suppressed correction. The complete corrections have been implemented into a Monte Carlo integration program to evaluate structure functions and/or integrated cross sections. As applications, we compare the operator approach with the collinear approximation numerically and we investigate the NLO and mass corrections to observables that are related to the extraction of the weak mixing angle from a Paschos-Wolfenstein-like relation in neutrino-iron scattering. We expect that the interpretation of neutrino scattering events in terms of oscillation physics and electroweak precision physics will benefit from our results

Trivial constraints on orbital-free kinetic energy density functionals

Science.gov (United States)

Luo, Kai; Trickey, S. B.

2018-03-01

Approximate kinetic energy density functionals (KEDFs) are central to orbital-free density functional theory. Limitations on the spatial derivative dependencies of KEDFs have been claimed from differential virial theorems. We identify a central defect in the argument: the relationships are not true for an arbitrary density but hold only for the minimizing density and corresponding chemical potential. Contrary to the claims therefore, the relationships are not constraints and provide no independent information about the spatial derivative dependencies of approximate KEDFs. A simple argument also shows that validity for arbitrary v-representable densities is not restored by appeal to the density-potential bijection.

Primordial inhomogeneities in the expanding universe. I - Density and velocity distributions of galaxies in the vicinities of rich clusters

Science.gov (United States)

Silk, J.; Wilson, M. L.

1979-01-01

The density profiles and Hubble flow deviations in the vicinities of rich galaxy clusters are derived for a variety of models of initial density and velocity perturbations at the recombination epoch. The galaxy correlation function, measured with respect to the Abell clusters, is used to normalize the theoretical models. The angular scales of the required primordial inhomogeneities are calculated. It is found that the resulting density profiles around rich clusters are surprisingly insensitive to the shape of the initial perturbations and also to the cosmological density parameter, Omega. However, it is shown that the distribution of galaxy radial velocities can provide a possible means of deriving Omega.

Self-consistent embedding of density-matrix renormalization group wavefunctions in a density functional environment.

Science.gov (United States)

Dresselhaus, Thomas; Neugebauer, Johannes; Knecht, Stefan; Keller, Sebastian; Ma, Yingjin; Reiher, Markus

2015-01-28

We present the first implementation of a density matrix renormalization group algorithm embedded in an environment described by density functional theory. The frozen density embedding scheme is used with a freeze-and-thaw strategy for a self-consistent polarization of the orbital-optimized wavefunction and the environmental densities with respect to each other.

Time-dependent density functional theory of open quantum systems in the linear-response regime.

Science.gov (United States)

Tempel, David G; Watson, Mark A; Olivares-Amaya, Roberto; Aspuru-Guzik, Alán

2011-02-21

Time-dependent density functional theory (TDDFT) has recently been extended to describe many-body open quantum systems evolving under nonunitary dynamics according to a quantum master equation. In the master equation approach, electronic excitation spectra are broadened and shifted due to relaxation and dephasing of the electronic degrees of freedom by the surrounding environment. In this paper, we develop a formulation of TDDFT linear-response theory (LR-TDDFT) for many-body electronic systems evolving under a master equation, yielding broadened excitation spectra. This is done by mapping an interacting open quantum system onto a noninteracting open Kohn-Sham system yielding the correct nonequilibrium density evolution. A pseudoeigenvalue equation analogous to the Casida equations of the usual LR-TDDFT is derived for the Redfield master equation, yielding complex energies and Lamb shifts. As a simple demonstration, we calculate the spectrum of a C(2 +) atom including natural linewidths, by treating the electromagnetic field vacuum as a photon bath. The performance of an adiabatic exchange-correlation kernel is analyzed and a first-order frequency-dependent correction to the bare Kohn-Sham linewidth based on the Görling-Levy perturbation theory is calculated.

Rydberg energies using excited state density functional theory

International Nuclear Information System (INIS)

Cheng, C.-L.; Wu Qin; Van Voorhis, Troy

2008-01-01

We utilize excited state density functional theory (eDFT) to study Rydberg states in atoms. We show both analytically and numerically that semilocal functionals can give quite reasonable Rydberg energies from eDFT, even in cases where time dependent density functional theory (TDDFT) fails catastrophically. We trace these findings to the fact that in eDFT the Kohn-Sham potential for each state is computed using the appropriate excited state density. Unlike the ground state potential, which typically falls off exponentially, the sequence of excited state potentials has a component that falls off polynomially with distance, leading to a Rydberg-type series. We also address the rigorous basis of eDFT for these systems. Perdew and Levy have shown using the constrained search formalism that every stationary density corresponds, in principle, to an exact stationary state of the full many-body Hamiltonian. In the present context, this means that the excited state DFT solutions are rigorous as long as they deliver the minimum noninteracting kinetic energy for the given density. We use optimized effective potential techniques to show that, in some cases, the eDFT Rydberg solutions appear to deliver the minimum kinetic energy because the associated density is not pure state v-representable. We thus find that eDFT plays a complementary role to constrained DFT: The former works only if the excited state density is not the ground state of some potential while the latter applies only when the density is a ground state density.

Very high order lattice perturbation theory for Wilson loops

International Nuclear Information System (INIS)

Horsley, R.

2010-10-01

We calculate perturbativeWilson loops of various sizes up to loop order n=20 at different lattice sizes for pure plaquette and tree-level improved Symanzik gauge theories using the technique of Numerical Stochastic Perturbation Theory. This allows us to investigate the behavior of the perturbative series at high orders. We observe differences in the behavior of perturbative coefficients as a function of the loop order. Up to n=20 we do not see evidence for the often assumed factorial growth of the coefficients. Based on the observed behavior we sum this series in a model with hypergeometric functions. Alternatively we estimate the series in boosted perturbation theory. Subtracting the estimated perturbative series for the average plaquette from the non-perturbative Monte Carlo result we estimate the gluon condensate. (orig.)

An integral for second-order multiple scattering perturbation theory

International Nuclear Information System (INIS)

Hoffman, G.G.

1997-01-01

This paper presents the closed form evaluation of a six-dimensional integral. The integral arises in the application to many-electron systems of a multiple scattering perturbation expansion at second order when formulated in fourier space. The resulting function can be used for the calculation of both the electron density and the effective one-electron potential in an SCF calculations. The closed form expression derived here greatly facilitates these calculations. In addition, the evaluated integral can be used for the computation of second-order corrections to the open-quotes optimized Thomas-Fermi theory.close quotes 10 refs., 2 figs

Solution of Point Reactor Neutron Kinetics Equations with Temperature Feedback by Singularly Perturbed Method

Directory of Open Access Journals (Sweden)

Wenzhen Chen

2013-01-01

Full Text Available The singularly perturbed method (SPM is proposed to obtain the analytical solution for the delayed supercritical process of nuclear reactor with temperature feedback and small step reactivity inserted. The relation between the reactivity and time is derived. Also, the neutron density (or power and the average density of delayed neutron precursors as the function of reactivity are presented. The variations of neutron density (or power and temperature with time are calculated and plotted and compared with those by accurate solution and other analytical methods. It is shown that the results by the SPM are valid and accurate in the large range and the SPM is simpler than those in the previous literature.

PREFACE: Classical density functional theory methods in soft and hard matter Classical density functional theory methods in soft and hard matter

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Haataja, Mikko; Gránásy, László; Löwen, Hartmut

2010-08-01

, about a half of which are related to the theoretical materials science community and the other half came from the soft-matter community. We begin by discussing papers related to PFC. Diverse subjects related to the phase-field crystal model include exciting topics such as predicting/controlling the equilibrium phase behavior [19, 18, 17] and kinetics of epitaxial island formation on nano-membranes [20]. Moreover, phase-field crystal modeling has proved to be very successful in simulating homogeneous and heterogeneous crystal nucleation and growth, and several aspects of these phenomena are discussed in this issue [18, 21]. Finally, it is shown how to incorporate additional orientational degrees of freedom within the PFC approach to model liquid crystals [22]. On the DFT side, the other papers in this special issue deal with problems associated with advanced DFT techniques and applications. The existence of a structural instability in sub-critical crystalline fluctuations in a supercooled liquid within a square-gradient theory is discussed in [23]. Fundamental measure theory for hard-body systems is improved by discussing a correction term in detail, as discussed in [24]. A mean-field-like density functional for charges is applied to the effective interaction between charged colloids obtained within a cell model [25]. The remaining articles provide fundamental insight into how to supplement DDFT-type methods with hydrodynamics [26, 27], highlight the role of the projection operator technique in deriving dynamical density functional theories [28], and demonstrate how perturbation methods can be employed to compute the properties of solid-liquid interfaces [29]. This particular collection of papers demonstrates rather convincingly the significant potential that classical density functional techniques possess in modeling complex systems built of either soft or hard matter (or combinations thereof). While the PFC approach offers a simple and appealing means to simulate

Construction of nonsingular pre-big-bang and ekpyrotic cosmologies and the resulting density perturbations

International Nuclear Information System (INIS)

Tsujikawa, Shinji; Brandenberger, Robert; Finelli, Fabio

2002-01-01

We consider the construction of nonsingular pre-big-bang and ekpyrotic type cosmological models realized by the addition to the action of specific higher-order terms stemming from quantum corrections. We study models involving general relativity coupled to a single scalar field with a potential motivated by the ekpyrotic scenario. We find that the inclusion of the string loop and quantum correction terms in the string frame makes it possible to obtain solutions of the variational equations which are nonsingular and bouncing in the Einstein frame, even when a negative exponential potential is present, as is the case in the ekpyrotic scenario. This allows us to discuss the evolution of cosmological perturbations without the need to invoke matching conditions between two Einstein universes, one representing the contracting branch, the second the expanding branch. We analyze the spectra of perturbations produced during the bouncing phase and find that the spectrum of curvature fluctuations in the model proposed originally to implement the ekpyrotic scenario has a large blue tilt (n R =3). Except for instabilities introduced on small scales, the result agrees with what is obtained by imposing continuity of the induced metric and of the extrinsic curvature across a constant scalar field (up to k 2 corrections equal to the constant energy density) matching surface between the contracting and the expanding Einstein universes. We also discuss nonsingular cosmological solutions obtained when a Gauss-Bonnet term with a coefficient suitably dependent on the scalar matter field is added to the action in the Einstein frame with a potential for the scalar field present. In this scenario, nonsingular solutions are found which start in an asymptotically flat state, undergo a period of superexponential inflation, and end with a graceful exit. The spectrum of fluctuations is also calculated in this case

Covariant Density Functionals: time-odd channel investigated

International Nuclear Information System (INIS)

Afanasjev, A. V.; Abusara, H.

2009-01-01

The description of exotic nuclear systems and phenomena requires a detailed understanding of all channels of density functional theories. The role of time-odd mean fields, their evidence in experiment, and an accurate description of these fields are subject of current interest. Recent studies advanced the understanding of these fields in energy density functional theories based on the Skyrme force [1,2]. Time-odd mean fields are related to nuclear magnetism in covariant density functional (CDF) theories [3]. They arise from space-like components of vector mesons and Lorentz invariance requires that their coupling strengths are identical to that of time-like components. There were only few limited efforts to understand the role of time-odd mean fields in covariant density functional theory [4,5]. For example, the microscopic role of nuclear magnetism and its impact on rotational properties of nuclei has been studied in Ref. [5]. It is known that time-odd mean fields modify the angular momentum content of the single-particle orbitals and thus the moments of inertia, effective alignments, alignment gains at the band crossings and other physical observables. We aim on more detailed and systematic understanding of the role of time-odd mean fields in covariant density functional theory. This investigation covers both rotating and non-rotating systems. It is shown that contrary to the Skyrme energy density functionals time-odd mean fields of CDF theory always provide additional binding in the systems with broken time-reversal symmetry (rotating nuclei, odd mass nuclei). This additional binding increases with spin and has its maximum exactly at the terminating state [6], where it can reach several MeV. The impact of time-odd mean fields on the properties of rotating systems has been studied in a systematic way (as a function of particle number and deformation) across the nuclear chart [7]. In addition, this contribution extends these studies to non-rotating systems such as

Survival of the most transferable at the top of Jacob's ladder: Defining and testing the ωB97M(2) double hybrid density functional

Science.gov (United States)

Mardirossian, Narbe; Head-Gordon, Martin

2018-06-01

A meta-generalized gradient approximation, range-separated double hybrid (DH) density functional with VV10 non-local correlation is presented. The final 14-parameter functional form is determined by screening trillions of candidate fits through a combination of best subset selection, forward stepwise selection, and random sample consensus (RANSAC) outlier detection. The MGCDB84 database of 4986 data points is employed in this work, containing a training set of 870 data points, a validation set of 2964 data points, and a test set of 1152 data points. Following an xDH approach, orbitals from the ωB97M-V density functional are used to compute the second-order perturbation theory correction. The resulting functional, ωB97M(2), is benchmarked against a variety of leading double hybrid density functionals, including B2PLYP-D3(BJ), B2GPPLYP-D3(BJ), ωB97X-2(TQZ), XYG3, PTPSS-D3(0), XYGJ-OS, DSD-PBEP86-D3(BJ), and DSD-PBEPBE-D3(BJ). Encouragingly, the overall performance of ωB97M(2) on nearly 5000 data points clearly surpasses that of all of the tested density functionals. As a Rung 5 density functional, ωB97M(2) completes our family of combinatorially optimized functionals, complementing B97M-V on Rung 3, and ωB97X-V and ωB97M-V on Rung 4. The results suggest that ωB97M(2) has the potential to serve as a powerful predictive tool for accurate and efficient electronic structure calculations of main-group chemistry.

Graphene-induced band gap renormalization in polythiophene: a many-body perturbation study

Science.gov (United States)

Marsusi, F.; Fedorov, I. A.; Gerivani, S.

2018-01-01

Density functional theory and many-body perturbation theory at the G0W0 level are employed to study the electronic properties of polythiophene (PT) adsorbed on the graphene surface. Analysis of the charge density difference shows that substrate-adsorbate interaction leads to a strong physisorption and interfacial electric dipole moment formation. The electrostatic potential displays a  -0.19 eV shift in the graphene work function from its initial value of 4.53 eV, as the result of the interaction. The LDA band gap of the polymer does not show any change. However, the band structure exhibits weak orbital hybridizations resulting from slight overlapping between the polymer and graphene states wave functions. The interfacial polarization effects on the band gap and levels alignment are investigated at the G0W0 level and show a notable reduction of PT band gap compared to that of the isolated chain.

Orthogonal bases of radial functions for charge density refinements

International Nuclear Information System (INIS)

Restori, R.

1990-01-01

Charge density determination from X-ray measurements necessitates the evaluation of the Fourier-Bessel transforms of the radial functions used to expand the charge density. Analytical expressions are given here for four sets of orthogonal functions which can substitute for the 'traditional exponential functions' set in least-squares refinements. (orig.)

Gaussian-3 theory using density functional geometries and zero-point energies

International Nuclear Information System (INIS)

Baboul, A.G.; Curtiss, L.A.; Redfern, P.C.; Raghavachari, K.

1999-01-01

A variation of Gaussian-3 (G3) theory is presented in which the geometries and zero-point energies are obtained from B3LYP density functional theory [B3LYP/6-31G(d)] instead of geometries from second-order perturbation theory [MP2(FU)/6-31G(d)] and zero-point energies from Hartree - Fock theory [HF/6-31G(d)]. This variation, referred to as G3//B3LYP, is assessed on 299 energies (enthalpies of formation, ionization potentials, electron affinities, proton affinities) from the G2/97 test set [J. Chem. Phys. 109, 42 (1998)]. The G3//B3LYP average absolute deviation from experiment for the 299 energies is 0.99 kcal/mol compared to 1.01 kcal/mol for G3 theory. Generally, the results from the two methods are similar, with some exceptions. G3//B3LYP theory gives significantly improved results for several cases for which MP2 theory is deficient for optimized geometries, such as CN and O 2 + . However, G3//B3LYP does poorly for ionization potentials that involve a Jahn - Teller distortion in the cation (CH 4 + , BF 3 + , BCl 3 + ) because of the B3LYP/6-31G(d) geometries. The G3(MP2) method is also modified to use B3LYP/6-31G(d) geometries and zero-point energies. This variation, referred to as G3(MP2)//B3LYP, has an average absolute deviation of 1.25 kcal/mol compared to 1.30 kcal/mol for G3(MP2) theory. Thus, use of density functional geometries and zero-point energies in G3 and G3(MP2) theories is a useful alternative to MP2 geometries and HF zero-point energies. copyright 1999 American Institute of Physics

Rayleigh-Taylor stability for a shock wave-density discontinuity interaction

International Nuclear Information System (INIS)

Fraley, G.S.

1981-01-01

Shells in inertial fusion targets are typically accelerated and decelerated by two or three shocks followed by continuous acceleration. The analytic solution for perturbation growth of a shock wave striking a density discontinuity in an inviscid fluid is investigated. The Laplace transform of the solution results in a functional equation, which has a simple solution for weak shock waves. The solution for strong shock waves may be given by a power series. It is assumed that the equation of state is given by a gamma law. The four independent parameters of the solution are the gamma values on each side of the material interface, the density ratio at the interface, and the shock strength. The asymptotic behavior (for large distances and times) of the perturbation velocity is given. For strong shocks the decay of the perturbation away from the interface is much weaker than the exponential decay of an incompressible fluid. The asymptotic value is given by a constant term and a number of slowly decaying discreet frequencies. The number of frequencies is roughly proportional to the logarithm of the density discontinuity divided by that of the shock strength. The asymptotic velocity at the interface is tabulated for representative values of the independent parameters. For weak shocks the solution is compared with results for an incompressible fluid. The range of density ratios with possible zero asymptotic velocities is given

Analysis of perturbations of moments associated with orthogonality linear functionals through the Szegö transformation

Directory of Open Access Journals (Sweden)

Edinson Fuentes

2015-06-01

Full Text Available In this paper, we consider perturbations to a sequence of moments associated with an orthogonality linear functional that is represented by a positive measure supported in [−1, 1]. In particular, given a perturbation to such a measure on the real line, we analyze the perturbation obtained on the corresponding measure on the unit circle, when both measures are related through the Szeg´´o transformation. A similar perturbation is analyzed through the inverse Szeg´´o transformation. In both cases, we show that the applied perturbation can be expressed in terms of the singular part of the measures, and also in terms of the corresponding sequences of moments. Resumen. En el presente trabajo, analizamos las perturbaciones a una sucesión de momentos asociada a un funcional lineal de ortogonalidad que se representa por una medida positiva con soporte en [−1, 1]. En particular, dada una cierta perturbación a dicha medida en la recta real, analizamos la perturbación obtenida en la correspondiente medida en la circunferencia unidad, cuando dichas medidas están relacionadas por la transformación de Szeg´´o. También se analiza una perturbación similar a través de la transformación inversa de Szeg´´o. En ambos casos, se muestra que la perturbación aplicada puede ser expresada en términos de la parte singular de las medidas, y también a través de las correspondientes sucesiones de momentos.

Time-dependent density-functional tight-binding method with the third-order expansion of electron density.

Science.gov (United States)

Nishimoto, Yoshio

2015-09-07

We develop a formalism for the calculation of excitation energies and excited state gradients for the self-consistent-charge density-functional tight-binding method with the third-order contributions of a Taylor series of the density functional theory energy with respect to the fluctuation of electron density (time-dependent density-functional tight-binding (TD-DFTB3)). The formulation of the excitation energy is based on the existing time-dependent density functional theory and the older TD-DFTB2 formulae. The analytical gradient is computed by solving Z-vector equations, and it requires one to calculate the third-order derivative of the total energy with respect to density matrix elements due to the inclusion of the third-order contributions. The comparison of adiabatic excitation energies for selected small and medium-size molecules using the TD-DFTB2 and TD-DFTB3 methods shows that the inclusion of the third-order contributions does not affect excitation energies significantly. A different set of parameters, which are optimized for DFTB3, slightly improves the prediction of adiabatic excitation energies statistically. The application of TD-DFTB for the prediction of absorption and fluorescence energies of cresyl violet demonstrates that TD-DFTB3 reproduced the experimental fluorescence energy quite well.

Energy vs. density on paths toward exact density functionals

DEFF Research Database (Denmark)

Kepp, Kasper Planeta

2018-01-01

Recently, the progression toward more exact density functional theory has been questioned, implying a need for more formal ways to systematically measure progress, i.e. a “path”. Here I use the Hohenberg-Kohn theorems and the definition of normality by Burke et al. to define a path toward exactness...

High-order perturbations of a spherical collapsing star

International Nuclear Information System (INIS)

Brizuela, David; Martin-Garcia, Jose M.; Sperhake, Ulrich; Kokkotas, Kostas D.

2010-01-01

A formalism to deal with high-order perturbations of a general spherical background was developed in earlier work [D. Brizuela, J. M. Martin-Garcia, and G. A. Mena Marugan, Phys. Rev. D 74, 044039 (2006); D. Brizuela, J. M. Martin-Garcia, and G. A. Mena Marugan, Phys. Rev. D 76, 024004 (2007)]. In this paper, we apply it to the particular case of a perfect fluid background. We have expressed the perturbations of the energy-momentum tensor at any order in terms of the perturbed fluid's pressure, density, and velocity. In general, these expressions are not linear and have sources depending on lower-order perturbations. For the second-order case we make the explicit decomposition of these sources in tensor spherical harmonics. Then, a general procedure is given to evolve the perturbative equations of motions of the perfect fluid for any value of the harmonic label. Finally, with the problem of a spherical collapsing star in mind, we discuss the high-order perturbative matching conditions across a timelike surface, in particular, the surface separating the perfect fluid interior from the exterior vacuum.

A systematic comparison of different approaches of density functional theory for the study of electrical double layers

International Nuclear Information System (INIS)

Yang, Guomin; Liu, Longcheng

2015-01-01

Based on the best available knowledge of density functional theory (DFT), the reference-fluid perturbation method is here extended to yield different approaches that well account for the cross correlations between the Columbic interaction and the hard-sphere exclusion in an inhomogeneous ionic hard-sphere fluid. In order to quantitatively evaluate the advantage and disadvantage of different approaches in describing the interfacial properties of electrical double layers, this study makes a systematic comparison against Monte Carlo simulations over a wide range of conditions. The results suggest that the accuracy of the DFT approaches is well correlated to a coupling parameter that describes the coupling strength of electrical double layers by accounting for the steric effect and that can be used to classify the systems into two regimes. In the weak-coupling regime, the approaches based on the bulk-fluid perturbation method are shown to be more accurate than the counterparts based on the reference-fluid perturbation method, whereas they exhibit the opposite behavior in the strong-coupling regime. More importantly, the analysis indicates that, with a suitable choice of the reference fluid, the weighted correlation approximation (WCA) to DFT gives the best account of the coupling effect of the electrostatic-excluded volume correlations. As a result, a piecewise WCA approach can be developed that is robust enough to describe the structural and thermodynamic properties of electrical double layers over both weak- and strong-coupling regimes

Block correlated second order perturbation theory with a generalized valence bond reference function

International Nuclear Information System (INIS)

Xu, Enhua; Li, Shuhua

2013-01-01

The block correlated second-order perturbation theory with a generalized valence bond (GVB) reference (GVB-BCPT2) is proposed. In this approach, each geminal in the GVB reference is considered as a “multi-orbital” block (a subset of spin orbitals), and each occupied or virtual spin orbital is also taken as a single block. The zeroth-order Hamiltonian is set to be the summation of the individual Hamiltonians of all blocks (with explicit two-electron operators within each geminal) so that the GVB reference function and all excited configuration functions are its eigenfunctions. The GVB-BCPT2 energy can be directly obtained without iteration, just like the second order Møller–Plesset perturbation method (MP2), both of which are size consistent. We have applied this GVB-BCPT2 method to investigate the equilibrium distances and spectroscopic constants of 7 diatomic molecules, conformational energy differences of 8 small molecules, and bond-breaking potential energy profiles in 3 systems. GVB-BCPT2 is demonstrated to have noticeably better performance than MP2 for systems with significant multi-reference character, and provide reasonably accurate results for some systems with large active spaces, which are beyond the capability of all CASSCF-based methods

Block correlated second order perturbation theory with a generalized valence bond reference function.

Science.gov (United States)

Xu, Enhua; Li, Shuhua

2013-11-07

The block correlated second-order perturbation theory with a generalized valence bond (GVB) reference (GVB-BCPT2) is proposed. In this approach, each geminal in the GVB reference is considered as a "multi-orbital" block (a subset of spin orbitals), and each occupied or virtual spin orbital is also taken as a single block. The zeroth-order Hamiltonian is set to be the summation of the individual Hamiltonians of all blocks (with explicit two-electron operators within each geminal) so that the GVB reference function and all excited configuration functions are its eigenfunctions. The GVB-BCPT2 energy can be directly obtained without iteration, just like the second order Mo̸ller-Plesset perturbation method (MP2), both of which are size consistent. We have applied this GVB-BCPT2 method to investigate the equilibrium distances and spectroscopic constants of 7 diatomic molecules, conformational energy differences of 8 small molecules, and bond-breaking potential energy profiles in 3 systems. GVB-BCPT2 is demonstrated to have noticeably better performance than MP2 for systems with significant multi-reference character, and provide reasonably accurate results for some systems with large active spaces, which are beyond the capability of all CASSCF-based methods.

Multicomponent density-functional theory for time-dependent systems

NARCIS (Netherlands)

Butriy, O.; Ebadi, H.; de Boeij, P. L.; van Leeuwen, R.; Gross, E. K. U.

2007-01-01

We derive the basic formalism of density functional theory for time-dependent electron-nuclear systems. The basic variables of this theory are the electron density in body-fixed frame coordinates and the diagonal of the nuclear N-body density matrix. The body-fixed frame transformation is carried

Improved Density Functional Tight Binding Potentials for Metalloid Aluminum Clusters

Science.gov (United States)

2016-06-01

unlimited IMPROVED DENSITY-FUNCTIONAL TIGHT BINDING POTENTIALS FOR METALLOID ALUMINUM CLUSTERS by Joon H. Kim June 2016 Thesis Advisor...DATES COVERED Master’s thesis 4. TITLE AND SUBTITLE IMPROVED DENSITY-FUNCTIONAL TIGHT BINDING POTENTIALS FOR METALLOID ALUMINUM CLUSTERS 5. FUNDING...repulsive potentials for use in density-functional tight binding (DFTB) simulations of low-valence aluminum metalloid clusters . These systems are under

A perturbative approach to neutron stars in f(T, T)-gravity

Energy Technology Data Exchange (ETDEWEB)

Pace, Mark; Said, Jackson Levi [University of Malta, Department of Physics, Msida (Malta); University of Malta, Institute of Space Sciences and Astronomy, Msida (Malta)

2017-05-15

We derive a Tolman-Oppenheimer-Volkoff equation in neutron star systems within the modified f(T, T)-gravity class of models using a perturbative approach. In our approach f(T, T)-gravity is considered to be a static spherically symmetric space-time. In this instance the metric is built from a more fundamental vierbein which can be used to relate inertial and global coordinates. A linear function f = T(r) + T(r) + χh(T, T) + O(χ{sup 2}) is taken as the Lagrangian density for the gravitational action. Finally we impose the polytropic equation of state of neutron star upon the derived equations in order to derive the mass profile and mass-central density relations of the neutron star in f(T, T)-gravity. (orig.)

Mitigate the tent-induced perturbation in ignition capsules by supersonic radiation propagation

Science.gov (United States)

Dai, Zhensheng; Gu, Jianfa; Zheng, Wudi

2017-10-01

In the inertial confinement fusion (ICF) scheme, to trap the alpha particle products of the D-T reaction, the capsules needs to be imploded and compressed with high symmetry In the laser indirect drive scheme, the capsules are held at the center of high-Z hohlraums by thin membranes (tents). However, the tents are recognized as one of the most important contributors to hot spot asymmetries, areal density perturbations and reduced performance. To improve the capsule implosion performance, various alternatives such as the micro-scale rods, a larger fill-tube and a low-density foam layer around the capsule have been presented. Our simulations show that the radiation propagates supersonically in the low-density foam layer and starts to ablate the capsule before the perturbations induced by the tents reach the ablating fronts. The tent induced perturbations are remarkably weakened when they are propagating in the blow-off plasma.

A density functional approach to ferrogels

Science.gov (United States)

Cremer, P.; Heinen, M.; Menzel, A. M.; Löwen, H.

2017-07-01

Ferrogels consist of magnetic colloidal particles embedded in an elastic polymer matrix. As a consequence, their structural and rheological properties are governed by a competition between magnetic particle-particle interactions and mechanical matrix elasticity. Typically, the particles are permanently fixed within the matrix, which makes them distinguishable by their positions. Over time, particle neighbors do not change due to the fixation by the matrix. Here we present a classical density functional approach for such ferrogels. We map the elastic matrix-induced interactions between neighboring colloidal particles distinguishable by their positions onto effective pairwise interactions between indistinguishable particles similar to a ‘pairwise pseudopotential’. Using Monte-Carlo computer simulations, we demonstrate for one-dimensional dipole-spring models of ferrogels that this mapping is justified. We then use the pseudopotential as an input into classical density functional theory of inhomogeneous fluids and predict the bulk elastic modulus of the ferrogel under various conditions. In addition, we propose the use of an ‘external pseudopotential’ when one switches from the viewpoint of a one-dimensional dipole-spring object to a one-dimensional chain embedded in an infinitely extended bulk matrix. Our mapping approach paves the way to describe various inhomogeneous situations of ferrogels using classical density functional concepts of inhomogeneous fluids.

Recent developments in LIBXC - A comprehensive library of functionals for density functional theory

Science.gov (United States)

Lehtola, Susi; Steigemann, Conrad; Oliveira, Micael J. T.; Marques, Miguel A. L.

2018-01-01

LIBXC is a library of exchange-correlation functionals for density-functional theory. We are concerned with semi-local functionals (or the semi-local part of hybrid functionals), namely local-density approximations, generalized-gradient approximations, and meta-generalized-gradient approximations. Currently we include around 400 functionals for the exchange, correlation, and the kinetic energy, spanning more than 50 years of research. Moreover, LIBXC is by now used by more than 20 codes, not only from the atomic, molecular, and solid-state physics, but also from the quantum chemistry communities.

On the evolution of the density probability density function in strongly self-gravitating systems

International Nuclear Information System (INIS)

Girichidis, Philipp; Konstandin, Lukas; Klessen, Ralf S.; Whitworth, Anthony P.

2014-01-01

The time evolution of the probability density function (PDF) of the mass density is formulated and solved for systems in free-fall using a simple approximate function for the collapse of a sphere. We demonstrate that a pressure-free collapse results in a power-law tail on the high-density side of the PDF. The slope quickly asymptotes to the functional form P V (ρ)∝ρ –1.54 for the (volume-weighted) PDF and P M (ρ)∝ρ –0.54 for the corresponding mass-weighted distribution. From the simple approximation of the PDF we derive analytic descriptions for mass accretion, finding that dynamically quiet systems with narrow density PDFs lead to retarded star formation and low star formation rates (SFRs). Conversely, strong turbulent motions that broaden the PDF accelerate the collapse causing a bursting mode of star formation. Finally, we compare our theoretical work with observations. The measured SFRs are consistent with our model during the early phases of the collapse. Comparison of observed column density PDFs with those derived from our model suggests that observed star-forming cores are roughly in free-fall.

Enforcing conservation laws in nonequilibrium cluster perturbation theory

Science.gov (United States)

Gramsch, Christian; Potthoff, Michael

2017-05-01

Using the recently introduced time-local formulation of the nonequilibrium cluster perturbation theory (CPT), we construct a generalization of the approach such that macroscopic conservation laws are respected. This is achieved by exploiting the freedom for the choice of the starting point of the all-order perturbation theory in the intercluster hopping. The proposed conserving CPT is a self-consistent propagation scheme which respects the conservation of energy, particle number, and spin, which treats short-range correlations exactly up to the linear scale of the cluster, and which represents a mean-field-like approach on length scales beyond the cluster size. Using Green's functions, conservation laws are formulated as local constraints on the local spin-dependent particle and the doublon density. We consider them as conditional equations to self-consistently fix the time-dependent intracluster one-particle parameters. Thanks to the intrinsic causality of the CPT, this can be set up as a step-by-step time propagation scheme with a computational effort scaling linearly with the maximum propagation time and exponentially in the cluster size. As a proof of concept, we consider the dynamics of the two-dimensional, particle-hole-symmetric Hubbard model following a weak interaction quench by simply employing two-site clusters only. Conservation laws are satisfied by construction. We demonstrate that enforcing them has strong impact on the dynamics. While the doublon density is strongly oscillating within plain CPT, a monotonic relaxation is observed within the conserving CPT.

Functional development in density functional theory for superconductors

Energy Technology Data Exchange (ETDEWEB)

Sanna, Antonio; Gross, E.K.U.; Essenberger, Frank [Max Planck Institute of Microstructure Physics, Halle (Saale) (Germany)

2015-07-01

Density functional theory for superconductors (SCDFT) is a fully parameter-free approach to superconductivity that allows for accurate predictions of critical temperature and properties of superconductors. We report on the most recent extensions of the method, in particular the development of new functionals to: (1) incorporate in a correct fashion Migdal's theorem; (2) compute the excitation spectrum; (3) include spin-fluctuation mediated pairing Applications and predictions are shown for a set of materials, including conventional and unconventional superconductors.

On soft limits of large-scale structure correlation functions

International Nuclear Information System (INIS)

Sagunski, Laura

2016-08-01

Large-scale structure surveys have the potential to become the leading probe for precision cosmology in the next decade. To extract valuable information on the cosmological evolution of the Universe from the observational data, it is of major importance to derive accurate theoretical predictions for the statistical large-scale structure observables, such as the power spectrum and the bispectrum of (dark) matter density perturbations. Hence, one of the greatest challenges of modern cosmology is to theoretically understand the non-linear dynamics of large-scale structure formation in the Universe from first principles. While analytic approaches to describe the large-scale structure formation are usually based on the framework of non-relativistic cosmological perturbation theory, we pursue another road in this thesis and develop methods to derive generic, non-perturbative statements about large-scale structure correlation functions. We study unequal- and equal-time correlation functions of density and velocity perturbations in the limit where one of their wavenumbers becomes small, that is, in the soft limit. In the soft limit, it is possible to link (N+1)-point and N-point correlation functions to non-perturbative 'consistency conditions'. These provide in turn a powerful tool to test fundamental aspects of the underlying theory at hand. In this work, we first rederive the (resummed) consistency conditions at unequal times by using the so-called eikonal approximation. The main appeal of the unequal-time consistency conditions is that they are solely based on symmetry arguments and thus are universal. Proceeding from this, we direct our attention to consistency conditions at equal times, which, on the other hand, depend on the interplay between soft and hard modes. We explore the existence and validity of equal-time consistency conditions within and beyond perturbation theory. For this purpose, we investigate the predictions for the soft limit of the

On soft limits of large-scale structure correlation functions

Energy Technology Data Exchange (ETDEWEB)

Sagunski, Laura

2016-08-15

Large-scale structure surveys have the potential to become the leading probe for precision cosmology in the next decade. To extract valuable information on the cosmological evolution of the Universe from the observational data, it is of major importance to derive accurate theoretical predictions for the statistical large-scale structure observables, such as the power spectrum and the bispectrum of (dark) matter density perturbations. Hence, one of the greatest challenges of modern cosmology is to theoretically understand the non-linear dynamics of large-scale structure formation in the Universe from first principles. While analytic approaches to describe the large-scale structure formation are usually based on the framework of non-relativistic cosmological perturbation theory, we pursue another road in this thesis and develop methods to derive generic, non-perturbative statements about large-scale structure correlation functions. We study unequal- and equal-time correlation functions of density and velocity perturbations in the limit where one of their wavenumbers becomes small, that is, in the soft limit. In the soft limit, it is possible to link (N+1)-point and N-point correlation functions to non-perturbative 'consistency conditions'. These provide in turn a powerful tool to test fundamental aspects of the underlying theory at hand. In this work, we first rederive the (resummed) consistency conditions at unequal times by using the so-called eikonal approximation. The main appeal of the unequal-time consistency conditions is that they are solely based on symmetry arguments and thus are universal. Proceeding from this, we direct our attention to consistency conditions at equal times, which, on the other hand, depend on the interplay between soft and hard modes. We explore the existence and validity of equal-time consistency conditions within and beyond perturbation theory. For this purpose, we investigate the predictions for the soft limit of the

Equation satisfied by electron-electron mutual Coulomb repulsion energy density functional

OpenAIRE

Joubert, Daniel P.

2011-01-01

The electron-electron mutual Coulomb repulsion energy density functional satisfies an equation that links functionals and functional derivatives at N-electron and (N-1)-electron densities for densities determined from the same adiabatic scaled external potential for the N-electron system.

Analytical energy gradients for explicitly correlated wave functions. I. Explicitly correlated second-order Møller-Plesset perturbation theory

Science.gov (United States)

Győrffy, Werner; Knizia, Gerald; Werner, Hans-Joachim

2017-12-01

We present the theory and algorithms for computing analytical energy gradients for explicitly correlated second-order Møller-Plesset perturbation theory (MP2-F12). The main difficulty in F12 gradient theory arises from the large number of two-electron integrals for which effective two-body density matrices and integral derivatives need to be calculated. For efficiency, the density fitting approximation is used for evaluating all two-electron integrals and their derivatives. The accuracies of various previously proposed MP2-F12 approximations [3C, 3C(HY1), 3*C(HY1), and 3*A] are demonstrated by computing equilibrium geometries for a set of molecules containing first- and second-row elements, using double-ζ to quintuple-ζ basis sets. Generally, the convergence of the bond lengths and angles with respect to the basis set size is strongly improved by the F12 treatment, and augmented triple-ζ basis sets are sufficient to closely approach the basis set limit. The results obtained with the different approximations differ only very slightly. This paper is the first step towards analytical gradients for coupled-cluster singles and doubles with perturbative treatment of triple excitations, which will be presented in the second part of this series.

Application of the graphical unitary group approach to the energy second derivative for CI wave functions via the coupled perturbed CI equations

International Nuclear Information System (INIS)

Fox, D.J.

1983-10-01

Analytic derivatives of the potential energy for Self-Consistent-Field (SCF) wave functions have been developed in recent years and found to be useful tools. The first derivative for configuration interaction (CI) wave functions is also available. This work details the extension of analytic methods to energy second derivatives for CI wave functions. The principal extension required for second derivatives is evaluation of the first order change in the CI wave function with respect to a nuclear perturbation. The shape driven graphical unitary group approach (SDGUGA) direct CI program was adapted to evaluate this term via the coupled-perturbed CI equations. Several iterative schemes are compared for use in solving these equations. The pilot program makes no use of molecular symmetry but the timing results show that utilization of molecular symmetry is desirable. The principles for defining and solving a set of symmetry adapted equations are discussed. Evaluation of the second derivative also requires the solution of the second order coupled-perturbed Hartree-Fock equations to obtain the correction to the molecular orbitals due to the nuclear perturbation. This process takes a consistently higher percentage of the computation time than for the first order equations alone and a strategy for its reduction is discussed

Self-contained filtered density function

Science.gov (United States)

Nouri, A. G.; Nik, M. B.; Givi, P.; Livescu, D.; Pope, S. B.

2017-09-01

The filtered density function (FDF) closure is extended to a "self-contained" format to include the subgrid-scale (SGS) statistics of all of the hydro-thermo-chemical variables in turbulent flows. These are the thermodynamic pressure, the specific internal energy, the velocity vector, and the composition field. In this format, the model is comprehensive and facilitates large-eddy simulation (LES) of flows at both low and high compressibility levels. A transport equation is developed for the joint pressure-energy-velocity-composition filtered mass density function (PEVC-FMDF). In this equation, the effect of convection appears in closed form. The coupling of the hydrodynamics and thermochemistry is modeled via a set of stochastic differential equation for each of the transport variables. This yields a self-contained SGS closure. For demonstration, LES is conducted of a turbulent shear flow with transport of a passive scalar. The consistency of the PEVC-FMDF formulation is established, and its overall predictive capability is appraised via comparison with direct numerical simulation (DNS) data.

The Effect of Different Perturbations on the Stability Analysis of Light Water Reactors

International Nuclear Information System (INIS)

Dykin, Victor

2010-09-01

Neutron noise analysis techniques are studied and developed, with primary use of determining the stability of Boiling Water Reactors (BWRs). In particular, the role of a specific perturbation prevailing in Light Water Reactors, the propagating density perturbation, in the stability of BWRs and on the noise field of LWRs in general, is investigated by considering three topics. In the first topics, we investigate how the neutronic response of the reactor, usually described as a second order system driven by a white noise driving force, is affected by a non-white driving force. This latter arises from the reactivity effect of the propagating density perturbations. The investigation is performed by using spectral and correlation analysis. Propagating perturbations with different velocities are analyzed. We investigate how the accuracy of the determination of the so-called decay ratio (DR) of the system, based on the assumption of white noise driving force, deteriorates with deviations from the white noise character of the driving force. In the second topics, the space dependence of the neutron noise, induced by propagating density perturbations, represented through the perturbation of the absorption, is determined and discussed. A full analytical solution was obtained by the use of the Green's function technique. The solution was analyzed for different frequencies and different system sizes. An interesting new interference effect between the point-kinetic and space-dependent components of the induced noise was discovered and interpreted in physical terms. In the last topics, a non-linear stability analysis of a BWR is performed, using so called Reduced Order Model (ROM) techniques. A ROM is usually constructed by reducing the full set of 3D space-time dependent neutron-kinetics, thermal-hydraulics and heat transfer equations to time-dependent ones, by considering space dependence in a lumped parameter model (one or two discrete channels). The main novelty of our work

Inference of core barrel motion from neutron noise spectral density. [PWR

Energy Technology Data Exchange (ETDEWEB)

Robinson, J.C.; Shahrokhi, F.; Kryter, R.C.

1977-03-15

A method was developed for inference of core barrel motion from the following statistical descriptors: cross-power spectral density, autopower spectral density, and amplitude probability density. To quantify the core barrel motion in a typical pressurized water reactor (PWR), a scale factor was calculated in both one- and two-dimensional geometries using forward, variational, and perturbation methods of discrete ordinates neutron transport. A procedure for selection of the proper frequency band limits for the statistical descriptors was developed. It was found that although perturbation theory is adequate for the calculation of the scale factor, two-dimensional geometric effects are important enough to rule out the use of a one-dimensional approximation for all but the crudest calculations. It was also found that contributions of gamma rays can be ignored and that the results are relatively insensitive to the cross-section set employed. The proper frequency band for the statistical descriptors is conveniently determined from the coherence and phase information from two ex-core power range neutron monitors positioned diametrically across the reactor vessel. Core barrel motion can then be quantified from the integral of the band-limited cross-power spectral density of two diametrically opposed ex-core monitors or, if the coherence between the pair is greater than or equal to 0.7, from a properly band-limited amplitude probability density function. Wide-band amplitude probability density functions were demonstrated to yield erroneous estimates for the magnitude of core barrel motion.

Response to perturbations of the force-free aligned pulsar atmosphere

International Nuclear Information System (INIS)

Jackson, E.A.

1978-01-01

To clarify the likely structure of the pulsar atmosphere, the response of various plasma configurations near a rotating neutron star with aligned rotational and dipole magnetic axes is investigated. These configurations represent both general infinitesimal perturbations along B of the force-free (E.B = O) atmosphere, as well as a heuristic class of finite perturbations (shell atmospheres). It is shown that the general infinitesimal perturbations along B which preserve spatial ordering involve regions of both negative and positive work, whose boundaries are at the surfaces E.B = O(E is not equal to O) and those of zero charge density (cos 2 theta = 1/3). At the latter surfaces, and on one side of the system will produce mixing of charges of opposite sign. The intersecting E.B=O surface, the response of the recombination of these charges, and their removal by gravity, shows that the force-free atmosphere is physically unstable, favouring a lower density at mid-latitude. The response of various plasma shell atmospheres is also examined and confirms the likelihood of the plasma atmosphere previously predicted from a near-vacuum analysis, provided the density is not too large. Larger density shells are found to break up into 'striated' configurations, containing two electron and one or two ion groups, which however may not develop into stable configurations. Criteria on the plasma density related to this and other responses of the plasma shells are discussed. (author)

Coupling-parameter expansion in thermodynamic perturbation theory.

Science.gov (United States)

Ramana, A Sai Venkata; Menon, S V G

2013-02-01

An approach to the coupling-parameter expansion in the liquid state theory of simple fluids is presented by combining the ideas of thermodynamic perturbation theory and integral equation theories. This hybrid scheme avoids the problems of the latter in the two phase region. A method to compute the perturbation series to any arbitrary order is developed and applied to square well fluids. Apart from the Helmholtz free energy, the method also gives the radial distribution function and the direct correlation function of the perturbed system. The theory is applied for square well fluids of variable ranges and compared with simulation data. While the convergence of perturbation series and the overall performance of the theory is good, improvements are needed for potentials with shorter ranges. Possible directions for further developments in the coupling-parameter expansion are indicated.

Stability under persistent perturbation by white noise

International Nuclear Information System (INIS)

Kalyakin, L

2014-01-01

Deterministic dynamical system which has an asymptotical stable equilibrium is considered under persistent perturbation by white noise. It is well known that if the perturbation does not vanish in the equilibrium position then there is not Lyapunov's stability. The trajectories of the perturbed system diverge from the equilibrium to arbitrarily large distances with probability 1 in finite time. New concept of stability on a large time interval is discussed. The length of interval agrees the reciprocal quantity of the perturbation parameter. The measure of stability is the expectation of the square distance from the trajectory till the equilibrium position. The method of parabolic equation is applied to both estimate the expectation and prove such stability. The main breakthrough is the barrier function derived for the parabolic equation. The barrier is constructed by using the Lyapunov function of the unperturbed system

The Wegner Estimate and the Integrated Density of States for some ...

Indian Academy of Sciences (India)

The integrated density of states (IDS) for random operators is an important function describing many physical characteristics of a random system. Properties of the IDS are derived from the Wegner estimate that describes the influence of finite-volume perturbations on a background system. In this paper, we present a simple ...

Graphene on metals: A van der Waals density functional study

DEFF Research Database (Denmark)

Vanin, Marco; Mortensen, Jens Jørgen; Kelkkanen, Kari André

2010-01-01

We use density functional theory (DFT) with a recently developed van der Waals density functional (vdW-DF) to study the adsorption of graphene on Co, Ni, Pd, Ag, Au, Cu, Pt, and Al(111) surfaces. In contrast to the local-density approximation (LDA) which predicts relatively strong binding for Ni...

A density spike on astrophysical scales from an N-field waterfall transition

Science.gov (United States)

Halpern, Illan F.; Hertzberg, Mark P.; Joss, Matthew A.; Sfakianakis, Evangelos I.

2015-09-01

Hybrid inflation models are especially interesting as they lead to a spike in the density power spectrum on small scales, compared to the CMB, while also satisfying current bounds on tensor modes. Here we study hybrid inflation with N waterfall fields sharing a global SO (N) symmetry. The inclusion of many waterfall fields has the obvious advantage of avoiding topologically stable defects for N > 3. We find that it also has another advantage: it is easier to engineer models that can simultaneously (i) be compatible with constraints on the primordial spectral index, which tends to otherwise disfavor hybrid models, and (ii) produce a spike on astrophysically large length scales. The latter may have significant consequences, possibly seeding the formation of astrophysically large black holes. We calculate correlation functions of the time-delay, a measure of density perturbations, produced by the waterfall fields, as a convergent power series in both 1 / N and the field's correlation function Δ (x). We show that for large N, the two-point function is ∝Δ2 (| x |) / N and the three-point function is ∝ Δ (| x - y |) Δ (| x |) Δ (| y |) /N2. In accordance with the central limit theorem, the density perturbations on the scale of the spike are Gaussian for large N and non-Gaussian for small N.

Bayesian error estimation in density-functional theory

DEFF Research Database (Denmark)

Mortensen, Jens Jørgen; Kaasbjerg, Kristen; Frederiksen, Søren Lund

2005-01-01

We present a practical scheme for performing error estimates for density-functional theory calculations. The approach, which is based on ideas from Bayesian statistics, involves creating an ensemble of exchange-correlation functionals by comparing with an experimental database of binding energies...

Non-adiabatic perturbations in Ricci dark energy model

International Nuclear Information System (INIS)

Karwan, Khamphee; Thitapura, Thiti

2012-01-01

We show that the non-adiabatic perturbations between Ricci dark energy and matter can grow both on superhorizon and subhorizon scales, and these non-adiabatic perturbations on subhorizon scales can lead to instability in this dark energy model. The rapidly growing non-adiabatic modes on subhorizon scales always occur when the equation of state parameter of dark energy starts to drop towards -1 near the end of matter era, except that the parameter α of Ricci dark energy equals to 1/2. In the case where α = 1/2, the rapidly growing non-adiabatic modes disappear when the perturbations in dark energy and matter are adiabatic initially. However, an adiabaticity between dark energy and matter perturbations at early time implies a non-adiabaticity between matter and radiation, this can influence the ordinary Sachs-Wolfe (OSW) effect. Since the amount of Ricci dark energy is not small during matter domination, the integrated Sachs-Wolfe (ISW) effect is greatly modified by density perturbations of dark energy, leading to a wrong shape of CMB power spectrum. The instability in Ricci dark energy is difficult to be alleviated if the effects of coupling between baryon and photon on dark energy perturbations are included

Communication: Random phase approximation renormalized many-body perturbation theory

International Nuclear Information System (INIS)

Bates, Jefferson E.; Furche, Filipp

2013-01-01

We derive a renormalized many-body perturbation theory (MBPT) starting from the random phase approximation (RPA). This RPA-renormalized perturbation theory extends the scope of single-reference MBPT methods to small-gap systems without significantly increasing the computational cost. The leading correction to RPA, termed the approximate exchange kernel (AXK), substantially improves upon RPA atomization energies and ionization potentials without affecting other properties such as barrier heights where RPA is already accurate. Thus, AXK is more balanced than second-order screened exchange [A. Grüneis et al., J. Chem. Phys. 131, 154115 (2009)], which tends to overcorrect RPA for systems with stronger static correlation. Similarly, AXK avoids the divergence of second-order Møller-Plesset (MP2) theory for small gap systems and delivers a much more consistent performance than MP2 across the periodic table at comparable cost. RPA+AXK thus is an accurate, non-empirical, and robust tool to assess and improve semi-local density functional theory for a wide range of systems previously inaccessible to first-principles electronic structure calculations

Redshift-space distortions from vector perturbations

Science.gov (United States)

Bonvin, Camille; Durrer, Ruth; Khosravi, Nima; Kunz, Martin; Sawicki, Ignacy

2018-02-01

We compute a general expression for the contribution of vector perturbations to the redshift space distortion of galaxy surveys. We show that they contribute to the same multipoles of the correlation function as scalar perturbations and should thus in principle be taken into account in data analysis. We derive constraints for next-generation surveys on the amplitude of two sources of vector perturbations, namely non-linear clustering and topological defects. While topological defects leave a very small imprint on redshift space distortions, we show that the multipoles of the correlation function are sensitive to vorticity induced by non-linear clustering. Therefore future redshift surveys such as DESI or the SKA should be capable of measuring such vector modes, especially with the hexadecapole which appears to be the most sensitive to the presence of vorticity.

Finite field-dependent symmetries in perturbative quantum gravity

International Nuclear Information System (INIS)

Upadhyay, Sudhaker

2014-01-01

In this paper we discuss the absolutely anticommuting nilpotent symmetries for perturbative quantum gravity in general curved spacetime in linear and non-linear gauges. Further, we analyze the finite field-dependent BRST (FFBRST) transformation for perturbative quantum gravity in general curved spacetime. The FFBRST transformation changes the gauge-fixing and ghost parts of the perturbative quantum gravity within functional integration. However, the operation of such symmetry transformation on the generating functional of perturbative quantum gravity does not affect the theory on physical ground. The FFBRST transformation with appropriate choices of finite BRST parameter connects non-linear Curci–Ferrari and Landau gauges of perturbative quantum gravity. The validity of the results is also established at quantum level using Batalin–Vilkovisky (BV) formulation. -- Highlights: •The perturbative quantum gravity is treated as gauge theory. •BRST and anti-BRST transformations are developed in linear and non-linear gauges. •BRST transformation is generalized by making it finite and field dependent. •Connection between linear and non-linear gauges is established. •Using BV formulation the results are established at quantum level also

The heat current density correlation function: sum rules and thermal conductivity

International Nuclear Information System (INIS)

Singh, Shaminder; Tankeshwar, K; Pathak, K N; Ranganathan, S

2006-01-01

Expressions for the second and fourth sum rules of the heat current density correlation function have been derived in an appropriate ensemble. The thermal conductivity of Lennard-Jones fluids has been calculated using these sum rules for the heat current density correlation function and the Gaussian form of the memory function. It is found that the results obtained for the thermal conductivity are in good agreement with the molecular dynamics simulation results over a wide range of densities and temperatures. Earlier results obtained using the energy current density correlation function are also discussed

The heat current density correlation function: sum rules and thermal conductivity

Energy Technology Data Exchange (ETDEWEB)

Singh, Shaminder [Department of Physics, Panjab University, Chandigarh-160 014 (India); Tankeshwar, K [Department of Physics, Panjab University, Chandigarh-160 014 (India); Pathak, K N [Department of Physics, Panjab University, Chandigarh-160 014 (India); Ranganathan, S [Department of Physics, Royal Military College, Kingston, ON, K7K 7B4 (Canada)

2006-02-01

Expressions for the second and fourth sum rules of the heat current density correlation function have been derived in an appropriate ensemble. The thermal conductivity of Lennard-Jones fluids has been calculated using these sum rules for the heat current density correlation function and the Gaussian form of the memory function. It is found that the results obtained for the thermal conductivity are in good agreement with the molecular dynamics simulation results over a wide range of densities and temperatures. Earlier results obtained using the energy current density correlation function are also discussed.

A classical density functional theory of ionic liquids.

Science.gov (United States)

Forsman, Jan; Woodward, Clifford E; Trulsson, Martin

2011-04-28

We present a simple, classical density functional approach to the study of simple models of room temperature ionic liquids. Dispersion attractions as well as ion correlation effects and excluded volume packing are taken into account. The oligomeric structure, common to many ionic liquid molecules, is handled by a polymer density functional treatment. The theory is evaluated by comparisons with simulations, with an emphasis on the differential capacitance, an experimentally measurable quantity of significant practical interest.

QCD non-perturbative study in radiative and pure-leptonic decays of Bc by wave function

International Nuclear Information System (INIS)

Guo Peng; Hou Zhaoyu; Zhi Haisu

2012-01-01

The radiative and pure-leptonic decays of B c mesons are of hadrons uncertainty in theoretical calculations. Using three types of the B c meson wave functions which describe the characteristics of the QCD non-perturbative and by controlling the parameters in them, the uncertainties of B c meson decay caused by the hadron decay model are studied in detail. The theoretical results show the branching ratios are (1.81981∼3.18961) × 10 -5 , which are sensitive to the type of wave functions. (authors)

Scattered surface charge density: A tool for surface characterization

KAUST Repository

Naydenov, Borislav

2011-11-28

We demonstrate the use of nonlocal scanning tunneling spectroscopic measurements to characterize the local structure of adspecies in their states where they are significantly less perturbed by the probe, which is accomplished by mapping the amplitude and phase of the scattered surface charge density. As an example, we study single-H-atom adsorption on the n-type Si(100)-(4 × 2) surface, and demonstrate the existence of two different configurations that are distinguishable using the nonlocal approach and successfully corroborated by density functional theory. © 2011 American Physical Society.

Scattered surface charge density: A tool for surface characterization

KAUST Repository

Naydenov, Borislav; Mantega, Mauro; Rungger, Ivan; Sanvito, Stefano; Boland, John J.

2011-01-01

We demonstrate the use of nonlocal scanning tunneling spectroscopic measurements to characterize the local structure of adspecies in their states where they are significantly less perturbed by the probe, which is accomplished by mapping the amplitude and phase of the scattered surface charge density. As an example, we study single-H-atom adsorption on the n-type Si(100)-(4 × 2) surface, and demonstrate the existence of two different configurations that are distinguishable using the nonlocal approach and successfully corroborated by density functional theory. © 2011 American Physical Society.

Euclidean null controllability of perturbed infinite delay systems with ...

African Journals Online (AJOL)

Euclidean null controllability of perturbed infinite delay systems with limited control. ... Open Access DOWNLOAD FULL TEXT ... The results are established by placing conditions on the perturbation function which guarantee that, if the linear control base system is completely Euclidean controllable, then the perturbed system ...

New Approaches and Applications for Monte Carlo Perturbation Theory

Energy Technology Data Exchange (ETDEWEB)

Aufiero, Manuele; Bidaud, Adrien; Kotlyar, Dan; Leppänen, Jaakko; Palmiotti, Giuseppe; Salvatores, Massimo; Sen, Sonat; Shwageraus, Eugene; Fratoni, Massimiliano

2017-02-01

This paper presents some of the recent and new advancements in the extension of Monte Carlo Perturbation Theory methodologies and application. In particular, the discussed problems involve Brunup calculation, perturbation calculation based on continuous energy functions, and Monte Carlo Perturbation Theory in loosely coupled systems.

Self-contained filtered density function

International Nuclear Information System (INIS)

Nouri, Arash G.; Pope, Stephen B.

2017-01-01

The filtered density function (FDF) closure is extended to a “self-contained” format to include the subgrid-scale (SGS) statistics of all of the hydro-thermo-chemical variables in turbulent flows. These are the thermodynamic pressure, the specific internal energy, the velocity vector, and the composition field. In this format, the model is comprehensive and facilitates large-eddy simulation (LES) of flows at both low and high compressibility levels. A transport equation is developed for the joint pressure-energy-velocity-composition filtered mass density function (PEVC-FMDF). In this equation, the effect of convection appears in closed form. The coupling of the hydrodynamics and thermochemistry is modeled via a set of stochastic differential equation for each of the transport variables. This yields a self-contained SGS closure. We demonstrated how LES is conducted of a turbulent shear flow with transport of a passive scalar. Finally, the consistency of the PEVC-FMDF formulation is established, and its overall predictive capability is appraised via comparison with direct numerical simulation (DNS) data.

A Robust Mass Estimator for Dark Matter Subhalo Perturbations in Strong Gravitational Lenses

Energy Technology Data Exchange (ETDEWEB)

Minor, Quinn E. [Department of Science, Borough of Manhattan Community College, City University of New York, New York, NY 10007 (United States); Kaplinghat, Manoj [Department of Physics and Astronomy, University of California, Irvine CA 92697 (United States); Li, Nan [Department of Astronomy and Astrophysics, The University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637 (United States)

2017-08-20

A few dark matter substructures have recently been detected in strong gravitational lenses through their perturbations of highly magnified images. We derive a characteristic scale for lensing perturbations and show that they are significantly larger than the perturber’s Einstein radius. We show that the perturber’s projected mass enclosed within this radius, scaled by the log-slope of the host galaxy’s density profile, can be robustly inferred even if the inferred density profile and tidal radius of the perturber are biased. We demonstrate the validity of our analytic derivation using several gravitational lens simulations where the tidal radii and the inner log-slopes of the density profile of the perturbing subhalo are allowed to vary. By modeling these simulated data, we find that our mass estimator, which we call the effective subhalo lensing mass, is accurate to within about 10% or smaller in each case, whereas the inferred total subhalo mass can potentially be biased by nearly an order of magnitude. We therefore recommend that the effective subhalo lensing mass be reported in future lensing reconstructions, as this will allow for a more accurate comparison with the results of dark matter simulations.

Normal co-ordinate analysis, molecular structural, non-linear optical, second order perturbation studies of Tizanidine by density functional theory.

Science.gov (United States)

Sheela, N R; Muthu, S; Sampathkrishnan, S; Al-Saadi, Abdulaziz A

2015-03-15

The spectroscopic techniques and semi-empirical molecular calculations have been utilized to analyze the drug Tizanidine (5CDIBTA). The solid phase Fourier Transform Infrared (FTIR) and Fourier Transform Raman (FTR) spectral analysis of 5CDIBTA is carried out along with density functional theory (DFT) calculations (B3LYP) with the 6-311++G(d,p) basis set. Detailed interpretation of the vibrational spectra of the compound has been made on the basis of the calculated potential energy distribution (PED). The individual atomic charges by NPA using B3LYP method is studied. A study on the Mulliken atomic charges, frontier molecular orbitals (HOMO-LUMO), molecular electrostatic potential (MEP) and thermodynamic properties were performed. The electric dipole moment (μ) and the first hyperpolarizability (α) values of the investigated molecule were also computed. Copyright © 2014 Elsevier B.V. All rights reserved.

Multiconfiguration Pair-Density Functional Theory Is Free From Delocalization Error.

Science.gov (United States)

Bao, Junwei Lucas; Wang, Ying; He, Xiao; Gagliardi, Laura; Truhlar, Donald G

2017-11-16

Delocalization error has been singled out by Yang and co-workers as the dominant error in Kohn-Sham density functional theory (KS-DFT) with conventional approximate functionals. In this Letter, by computing the vertical first ionization energy for well separated He clusters, we show that multiconfiguration pair-density functional theory (MC-PDFT) is free from delocalization error. To put MC-PDFT in perspective, we also compare it with some Kohn-Sham density functionals, including both traditional and modern functionals. Whereas large delocalization errors are almost universal in KS-DFT (the only exception being the very recent corrected functionals of Yang and co-workers), delocalization error is removed by MC-PDFT, which bodes well for its future as a step forward from KS-DFT.

Site-occupation embedding theory using Bethe ansatz local density approximations

Science.gov (United States)

Senjean, Bruno; Nakatani, Naoki; Tsuchiizu, Masahisa; Fromager, Emmanuel

2018-06-01

Site-occupation embedding theory (SOET) is an alternative formulation of density functional theory (DFT) for model Hamiltonians where the fully interacting Hubbard problem is mapped, in principle exactly, onto an impurity-interacting (rather than a noninteracting) one. It provides a rigorous framework for combining wave-function (or Green function)-based methods with DFT. In this work, exact expressions for the per-site energy and double occupation of the uniform Hubbard model are derived in the context of SOET. As readily seen from these derivations, the so-called bath contribution to the per-site correlation energy is, in addition to the latter, the key density functional quantity to model in SOET. Various approximations based on Bethe ansatz and perturbative solutions to the Hubbard and single-impurity Anderson models are constructed and tested on a one-dimensional ring. The self-consistent calculation of the embedded impurity wave function has been performed with the density-matrix renormalization group method. It has been shown that promising results are obtained in specific regimes of correlation and density. Possible further developments have been proposed in order to provide reliable embedding functionals and potentials.

Benchmark density functional theory calculations for nanoscale conductance

DEFF Research Database (Denmark)

Strange, Mikkel; Bækgaard, Iben Sig Buur; Thygesen, Kristian Sommer

2008-01-01

We present a set of benchmark calculations for the Kohn-Sham elastic transmission function of five representative single-molecule junctions. The transmission functions are calculated using two different density functional theory methods, namely an ultrasoft pseudopotential plane-wave code...

SURFACE SYMMETRY ENERGY OF NUCLEAR ENERGY DENSITY FUNCTIONALS

Energy Technology Data Exchange (ETDEWEB)

Nikolov, N; Schunck, N; Nazarewicz, W; Bender, M; Pei, J

2010-12-20

We study the bulk deformation properties of the Skyrme nuclear energy density functionals. Following simple arguments based on the leptodermous expansion and liquid drop model, we apply the nuclear density functional theory to assess the role of the surface symmetry energy in nuclei. To this end, we validate the commonly used functional parametrizations against the data on excitation energies of superdeformed band-heads in Hg and Pb isotopes, and fission isomers in actinide nuclei. After subtracting shell effects, the results of our self-consistent calculations are consistent with macroscopic arguments and indicate that experimental data on strongly deformed configurations in neutron-rich nuclei are essential for optimizing future nuclear energy density functionals. The resulting survey provides a useful benchmark for further theoretical improvements. Unlike in nuclei close to the stability valley, whose macroscopic deformability hangs on the balance of surface and Coulomb terms, the deformability of neutron-rich nuclei strongly depends on the surface-symmetry energy; hence, its proper determination is crucial for the stability of deformed phases of the neutron-rich matter and description of fission rates for r-process nucleosynthesis.

Kinetic-energy density functional: Atoms and shell structure

International Nuclear Information System (INIS)

Garcia-Gonzalez, P.; Alvarellos, J.E.; Chacon, E.

1996-01-01

We present a nonlocal kinetic-energy functional which includes an anisotropic average of the density through a symmetrization procedure. This functional allows a better description of the nonlocal effects of the electron system. The main consequence of the symmetrization is the appearance of a clear shell structure in the atomic density profiles, obtained after the minimization of the total energy. Although previous results with some of the nonlocal kinetic functionals have given incipient structures for heavy atoms, only our functional shows a clear shell structure for most of the atoms. The atomic total energies have a good agreement with the exact calculations. Discussion of the chemical potential and the first ionization potential in atoms is included. The functional is also extended to spin-polarized systems. copyright 1996 The American Physical Society

Orientation of rod molecules in selective slits: a density functional theory

International Nuclear Information System (INIS)

Xu Xiaofei; Cao Dapeng; Wang Wenchuan

2008-01-01

A density functional theory (DFT) is used to investigate molecular orientation of rod fluids in selective slits. The DFT approach combines a modified fundamental measure theory (MFMT) for excluded-volume effect, the first-order thermodynamics perturbation theory for chain connectivity and the mean-field approximation for van der Waals (vdW) attraction. To study the molecular orientation, the intramolecular bonding orientation function is introduced into the DFT. First, we investigate the orientation of the surfactant-like rod molecule of AB 6 (i.e. ABBBBBB) in a nanoslit of H 20σ, where the walls selectively adsorb segment 'A'. It is observed that, with the increase of the surface energy of the wall to head segment (i.e. 'A' segment) of the rod molecule, the rod molecules adsorbed on the wall present the perpendicular orientation gradually, and assemble into a smectic-A-like monolayer finally. In addition, we also explore the molecular orientation of the rods with both end segments preferring to the wall, i.e. AB 8 A and AB 7 A, in a nanoslit of H = 10σ. Interestingly, the AB 8 A rod monolayer is compatible with either a smectic-A-like or a smectic-C-like organization, but AB 7 A rod molecules exhibit the smectic-A-like organization. The orientation factor of the AB 7 A rod molecule reaches 1, suggesting that AB 7 A rod molecules self-assemble into an ordered structure with perfectly perpendicular orientation to the wall.

Correction for dispersion and Coulombic interactions in molecular clusters with density functional derived methods: Application to polycyclic aromatic hydrocarbon clusters

Science.gov (United States)

Rapacioli, Mathias; Spiegelman, Fernand; Talbi, Dahbia; Mineva, Tzonka; Goursot, Annick; Heine, Thomas; Seifert, Gotthard

2009-06-01

The density functional based tight binding (DFTB) is a semiempirical method derived from the density functional theory (DFT). It inherits therefore its problems in treating van der Waals clusters. A major error comes from dispersion forces, which are poorly described by commonly used DFT functionals, but which can be accounted for by an a posteriori treatment DFT-D. This correction is used for DFTB. The self-consistent charge (SCC) DFTB is built on Mulliken charges which are known to give a poor representation of Coulombic intermolecular potential. We propose to calculate this potential using the class IV/charge model 3 definition of atomic charges. The self-consistent calculation of these charges is introduced in the SCC procedure and corresponding nuclear forces are derived. Benzene dimer is then studied as a benchmark system with this corrected DFTB (c-DFTB-D) method, but also, for comparison, with the DFT-D. Both methods give similar results and are in agreement with references calculations (CCSD(T) and symmetry adapted perturbation theory) calculations. As a first application, pyrene dimer is studied with the c-DFTB-D and DFT-D methods. For coronene clusters, only the c-DFTB-D approach is used, which finds the sandwich configurations to be more stable than the T-shaped ones.

Quasi-Maxwellian gravitation equations: aplication to the perturbations of the Friedmann cosmological models

International Nuclear Information System (INIS)

Salim, J.M.

1982-01-01

The perturbation theory of cosmological models, in particular Friedmann models, following the quasi-Maxwellian equations are systematically developed. Perturbations to imperfect sources are directly generalized. It is shown that Friedmann models are unstable by fluid vorticity perturbations. It is also shown that the study of gravitational waves can not be done independently of the coupling with the matter. Lifshitz results concerning matter density perturbation are found again and it is shown that some soluctions, considered in literature as physically acceptable, are naive coordinate transformations. (L.C.) [pt

Influence of Lumbar Muscle Fatigue on Trunk Adaptations during Sudden External Perturbations

Science.gov (United States)

Abboud, Jacques; Nougarou, François; Lardon, Arnaud; Dugas, Claude; Descarreaux, Martin

2016-01-01

Introduction: When the spine is subjected to perturbations, neuromuscular responses such as reflex muscle contractions contribute to the overall balance control and spinal stabilization mechanisms. These responses are influenced by muscle fatigue, which has been shown to trigger changes in muscle recruitment patterns. Neuromuscular adaptations, e.g., attenuation of reflex activation and/or postural oscillations following repeated unexpected external perturbations, have also been described. However, the characterization of these adaptations still remains unclear. Using high-density electromyography (EMG) may help understand how the nervous system chooses to deal with an unknown perturbation in different physiological and/or mechanical perturbation environments. Aim: To characterize trunk neuromuscular adaptations following repeated sudden external perturbations after a back muscle fatigue task using high-density EMG. Methods: Twenty-five healthy participants experienced a series of 15 sudden external perturbations before and after back muscle fatigue. Erector spinae muscle activity was recorded using high-density EMG. Trunk kinematics during perturbation trials were collected using a 3-D motion analysis system. A two-way repeated measure ANOVA was conducted to assess: (1) the adaptation effect across trials; (2) the fatigue effect; and (3) the interaction effect (fatigue × adaptation) for the baseline activity, the reflex latency, the reflex peak and trunk kinematic variables (flexion angle, velocity and time to peak velocity). Muscle activity spatial distribution before and following the fatigue task was also compared using t-tests for dependent samples. Results: An attenuation of muscle reflex peak was observed across perturbation trials before the fatigue task, but not after. The spatial distribution of muscle activity was significantly higher before the fatigue task compared to post-fatigue trials. Baseline activity showed a trend to higher values after muscle

Influence of lumbar muscle fatigue on trunk adaptations during sudden external perturbations

Directory of Open Access Journals (Sweden)

Jacques Abboud

2016-11-01

Full Text Available IntroductionWhen the spine is subjected to perturbations, neuromuscular responses such as reflex muscle contractions contribute to the overall balance control and spinal stabilization mechanisms. These responses are influenced by muscle fatigue, which has been shown to trigger changes in muscle recruitment patterns. Neuromuscular adaptations, e.g. attenuation of reflex activation and/or postural oscillations following repeated unexpected external perturbations, have also been described. However, the characterization of these adaptations still remains unclear. Using high-density electromyography (EMG may help understand how the nervous system chooses to deal with an unknown perturbation in different physiological and/or mechanical perturbation environments. AimTo characterize trunk neuromuscular adaptations following repeated sudden external perturbations after a back muscle fatigue task using high-density EMG.MethodsTwenty-five healthy participants experienced a series of 15 sudden external perturbations before and after back muscle fatigue. Erector spinae muscle activity was recorded using high-density EMG. Trunk kinematics during perturbation trials were collected using a 3-D motion analysis system. A two-way repeated measure ANOVA was conducted to assess 1 the adaptation effect across trials, 2 the fatigue effect, and 3 the interaction effect (fatigue x adaptation for the baseline activity, the reflex latency, the reflex peak and trunk kinematic variables (flexion angle, velocity and time to peak velocity. Muscle activity spatial distribution before and following the fatigue task was also compared using t-tests for dependent samples. ResultsAn attenuation of muscle reflex peak was observed across perturbation trials before the fatigue task, but not after. The spatial distribution of muscle activity was significantly higher before the fatigue task compared to post-fatigue trials. Baseline activity showed a trend to higher values after muscle

A classical density functional investigation of nucleation

International Nuclear Information System (INIS)

Ghosh, Satinath; Ghosh, Swapan K.

2009-01-01

Study of nucleation and growth phenomena in condensation is of prime importance in various applications such as crystal growth, nanoparticle synthesis, pattern formation etc. The knowledge of nucleation barrier in condensation is necessary to control the nucleation kinetics, size of the nanoparticles etc. Classical nucleation theory (CNT) assumes the density of the drop as bulk density irrespective of the size of the drop and overestimates the nucleation barrier. Here we are interested in solving the problem analytically using density functional theory (DFT) with square gradient approximation along the lines of Cahn and Hilliard. Nucleation barrier and density profile obtained in this work are consistent with other works based on nonclassical theory. (author)

Nonlocal exchange and kinetic-energy density functionals for electronic systems

International Nuclear Information System (INIS)

Glossman, M.D.; Rubio, A.; Balbas, L.C.; Alonso, J.A.

1992-01-01

The nonlocal weighted density approximation (WDA) to the exchange and kinetic-energy functionals of many electron systems proposed several years ago by Alonso and Girifalco is used to compute, within the framework of density functional theory, the ground-state electronic density and total energy of noble gas atoms and of neutral jellium-like sodium clusters containing up to 500 atoms. These results are compared with analogous calculations using the well known Thomas-Fermi-Weizsacker-Dirac (TFWD) approximations for the kinetic (TFW) and exchange (D) energy density functionals. An outstanding improvement of the total and exchange energies, of the density at the nucleus and of the expectation values is obtained for atoms within the WDA scheme. For sodium clusters the authors notice a sizeable contribution of the nonlocal effects to the total energy and to the density profiles. In the limit of very large clusters these effects should affect the surface energy of the bulk metal

Constraints on parton density functions from D0

Energy Technology Data Exchange (ETDEWEB)

Hays, Jonathan M.; /Imperial Coll., London

2008-04-01

Five recent results from D0 which either impact or have the potential to impact on uncertainties in parton density functions are presented. Many analyses at D0 are sensitive to the modeling of the partonic structure of the proton. When theoretical and experimental uncertainties are well controlled there exists the possibility for additional constraints on parton density functions (PDF). Five measurements are presented which either have already been included in global parton fits or have the potential to contribute in the future.

Higher-accuracy van der Waals density functional

DEFF Research Database (Denmark)

Lee, Kyuho; Murray, Éamonn D.; Kong, Lingzhu

2010-01-01

We propose a second version of the van der Waals density functional of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)], employing a more accurate semilocal exchange functional and the use of a large-N asymptote gradient correction in determining the vdW kernel. The predicted binding energy...

Perturbative quantum chromodynamics

International Nuclear Information System (INIS)

Radyushkin, A.V.

1987-01-01

The latest achievements in perturbative quantum chromodynamics (QCD) relating to the progress in factorization of small and large distances are presented. The following problems are concerned: Development of the theory of Sudakov effects on the basis of mean contour formalism. Development of nonlocal condensate formalism. Calculation of hadron wave functions and hadron distribution functions using QCD method of sum rules. Development of the theory of Regge behaviour in QCD, behaviour of structure functions at small x. Study of polarization effects in hadron processes with high momentum transfer

A comparative study of density functional and density functional tight binding calculations of defects in graphene

Energy Technology Data Exchange (ETDEWEB)

Zobelli, Alberto [Laboratoire de Physique des Solides, Univ. Paris Sud, CNRS UMR, Orsay (France); Ivanovskaya, Viktoria; Wagner, Philipp; Yaya, Abu; Ewels, Chris P. [Institut des Materiaux Jean Rouxel (IMN), CNRS UMR, University of Nantes (France); Suarez-Martinez, Irene [Nanochemistry Research Institute, Curtin University of Technology, Perth, Western Australia (Australia)

2012-02-15

The density functional tight binding approach (DFTB) is well adapted for the study of point and line defects in graphene based systems. After briefly reviewing the use of DFTB in this area, we present a comparative study of defect structures, energies, and dynamics between DFTB results obtained using the dftb+ code, and density functional results using the localized Gaussian orbital code, AIMPRO. DFTB accurately reproduces structures and energies for a range of point defect structures such as vacancies and Stone-Wales defects in graphene, as well as various unfunctionalized and hydroxylated graphene sheet edges. Migration barriers for the vacancy and Stone-Wales defect formation barriers are accurately reproduced using a nudged elastic band approach. Finally we explore the potential for dynamic defect simulations using DFTB, taking as an example electron irradiation damage in graphene. DFTB-MD derived sputtering energy threshold map for a carbon atom in a graphene plane. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Existence of time-dependent density-functional theory for open electronic systems: time-dependent holographic electron density theorem.

Science.gov (United States)

Zheng, Xiao; Yam, ChiYung; Wang, Fan; Chen, GuanHua

2011-08-28

We present the time-dependent holographic electron density theorem (TD-HEDT), which lays the foundation of time-dependent density-functional theory (TDDFT) for open electronic systems. For any finite electronic system, the TD-HEDT formally establishes a one-to-one correspondence between the electron density inside any finite subsystem and the time-dependent external potential. As a result, any electronic property of an open system in principle can be determined uniquely by the electron density function inside the open region. Implications of the TD-HEDT on the practicality of TDDFT are also discussed.

Postfragmentation density function for bacterial aggregates in laminar flow.

Science.gov (United States)

Byrne, Erin; Dzul, Steve; Solomon, Michael; Younger, John; Bortz, David M

2011-04-01

The postfragmentation probability density of daughter flocs is one of the least well-understood aspects of modeling flocculation. We use three-dimensional positional data of Klebsiella pneumoniae bacterial flocs in suspension and the knowledge of hydrodynamic properties of a laminar flow field to construct a probability density function of floc volumes after a fragmentation event. We provide computational results which predict that the primary fragmentation mechanism for large flocs is erosion. The postfragmentation probability density function has a strong dependence on the size of the original floc and indicates that most fragmentation events result in clumps of one to three bacteria eroding from the original floc. We also provide numerical evidence that exhaustive fragmentation yields a limiting density inconsistent with the log-normal density predicted in the literature, most likely due to the heterogeneous nature of K. pneumoniae flocs. To support our conclusions, artificial flocs were generated and display similar postfragmentation density and exhaustive fragmentation. ©2011 American Physical Society

Optical properties of body-centered tetragonal C4: Insights from many-body perturbation and time-dependent density functional theories

Science.gov (United States)

Tarighi Ahmadpour, Mahdi; Rostamnejadi, Ali; Hashemifar, S. Javad

2018-04-01

We study the electronic structure and optical properties of a body-centered tetragonal phase of carbon (bct-C4) within the framework of time-dependent density functional theory and Bethe-Salpeter equation. The results indicate that the optical properties of bct-C4 are strongly affected by the electron-hole interaction. It is demonstrated that the long-range corrected exchange-correlation kernels could fairly reproduce the Bethe-Salpeter equation results. The effective carrier number reveals that at energies above 30 eV, the excitonic effects are not dominant any more and that the optical transitions originate mainly from electronic excitations. The emerged peaks in the calculated electron energy loss spectra are discussed in terms of plasmon excitations and interband transitions. The results of the research indicate that bct-C4 is an indirect wide-band-gap semiconductor, which is transparent in the visible region and opaque in the ultraviolet spectral range.

Invariant exchange perturbation theory for multicenter systems: Time-dependent perturbations

International Nuclear Information System (INIS)

Orlenko, E. V.; Evstafev, A. V.; Orlenko, F. E.

2015-01-01

A formalism of exchange perturbation theory (EPT) is developed for the case of interactions that explicitly depend on time. Corrections to the wave function obtained in any order of perturbation theory and represented in an invariant form include exchange contributions due to intercenter electron permutations in complex multicenter systems. For collisions of atomic systems with an arbitrary type of interaction, general expressions are obtained for the transfer (T) and scattering (S) matrices in which intercenter electron permutations between overlapping nonorthogonal states belonging to different centers (atoms) are consistently taken into account. The problem of collision of alpha particles with lithium atoms accompanied by the redistribution of electrons between centers is considered. The differential and total charge-exchange cross sections of lithium are calculated

Linking density functional and mode coupling models for supercooled liquids.

Science.gov (United States)

Premkumar, Leishangthem; Bidhoodi, Neeta; Das, Shankar P

2016-03-28

We compare predictions from two familiar models of the metastable supercooled liquid, respectively, constructed with thermodynamic and dynamic approaches. In the so called density functional theory the free energy F[ρ] of the liquid is a functional of the inhomogeneous density ρ(r). The metastable state is identified as a local minimum of F[ρ]. The sharp density profile characterizing ρ(r) is identified as a single particle oscillator, whose frequency is obtained from the parameters of the optimum density function. On the other hand, a dynamic approach to supercooled liquids is taken in the mode coupling theory (MCT) which predict a sharp ergodicity-non-ergodicity transition at a critical density. The single particle dynamics in the non-ergodic state, treated approximately, represents a propagating mode whose characteristic frequency is computed from the corresponding memory function of the MCT. The mass localization parameters in the above two models (treated in their simplest forms) are obtained, respectively, in terms of the corresponding natural frequencies depicted and are shown to have comparable magnitudes.

Linking density functional and mode coupling models for supercooled liquids

Energy Technology Data Exchange (ETDEWEB)

Premkumar, Leishangthem; Bidhoodi, Neeta; Das, Shankar P. [School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067 (India)

2016-03-28

We compare predictions from two familiar models of the metastable supercooled liquid, respectively, constructed with thermodynamic and dynamic approaches. In the so called density functional theory the free energy F[ρ] of the liquid is a functional of the inhomogeneous density ρ(r). The metastable state is identified as a local minimum of F[ρ]. The sharp density profile characterizing ρ(r) is identified as a single particle oscillator, whose frequency is obtained from the parameters of the optimum density function. On the other hand, a dynamic approach to supercooled liquids is taken in the mode coupling theory (MCT) which predict a sharp ergodicity-non-ergodicity transition at a critical density. The single particle dynamics in the non-ergodic state, treated approximately, represents a propagating mode whose characteristic frequency is computed from the corresponding memory function of the MCT. The mass localization parameters in the above two models (treated in their simplest forms) are obtained, respectively, in terms of the corresponding natural frequencies depicted and are shown to have comparable magnitudes.

Functional differential equation approach to the large N expansion and mean field perturbation theory

International Nuclear Information System (INIS)

Bender, C.M.; Cooper, F.

1985-01-01

An apparent difference between formulating mean field perturbation theory for lambdaphi 4 field theory via path integrals or via functional differential equations when there are external sources present is shown not to exist when mean field theory is considered as the N = 1 limit of the 0(N)lambdaphi 4 field theory. A simply method is given for determining the 1/N expansion for the Green's functions in the presence of external sources by directly solving the functional differential equations order by order in 1/N. The 1/N expansion for the effective action GAMMA(phi,chi) is obtained by directly integrating the functional differential equations for the fields phi and chi (equivalent1/2lambda/Nphi/sub α/phi/sup α/-μ 2 ) in the presence of two external sources j = -deltaGAMMA/deltaphi, S = -deltaGAMMA/deltachi

Influence of the potential well and the potential barrier on the density distribution of confined-model fluids

CERN Document Server

Lee, B H; Lee, C H; Seong Baek Seok

2000-01-01

A density functional perturbative approximation, which is based on the density functional expansion of the one-particle direct correlation function of model fluids with respect to the bulk density, has been employed to investigate the influence of the potential well and the potential barrier on the density behavior of confined-model fluids. The mean spherical approximation has been used to calculate the two-particle direct correlation function of the model fluids. At lower densities, the density distributions are strongly affected by the barrier height and the well depth of the model potential, the contribution from the short-range repulsive part being especially important. However, the effects of the barrier height and the well depth of the model potential decrease with increasing bulk density. The calculated results also show that in the region where the effect of the wall-fluid interaction is relatively weak, the square-barrier part of the model potential leads to a nonuniformity in the density distributio...

Density functional theory a practical introduction

CERN Document Server

Sholl, David

2009-01-01

Demonstrates how anyone in math, science, and engineering can master DFT calculations Density functional theory (DFT) is one of the most frequently used computational tools for studying and predicting the properties of isolated molecules, bulk solids, and material interfaces, including surfaces. Although the theoretical underpinnings of DFT are quite complicated, this book demonstrates that the basic concepts underlying the calculations are simple enough to be understood by anyone with a background in chemistry, physics, engineering, or mathematics. The authors show how the widespread availability of powerful DFT codes makes it possible for students and researchers to apply this important computational technique to a broad range of fundamental and applied problems. Density Functional Theory: A Practical Introduction offers a concise, easy-to-follow introduction to the key concepts and practical applications of DFT, focusing on plane-wave DFT. The authors have many years of experience introducing DFT to studen...

Teaching Density Functional Theory Through Experiential Learning

International Nuclear Information System (INIS)

Narasimhan, Shobhana

2015-01-01

Today, quantum mechanical density functional theory is often the method of choice for performing accurate calculations on atomic, molecular and condensed matter systems. Here, I share some of my experiences in teaching the necessary basics of solid state physics, as well as the theory and practice of density functional theory, in a number of workshops held in developing countries over the past two decades. I discuss the advantages of supplementing the usual mathematically formal teaching methods, characteristic of graduate courses, with the use of visual imagery and analogies. I also describe a successful experiment we carried out, which resulted in a joint publication co-authored by 67 lecturers and students participating in a summer school. (paper)

Relationship of Quantum Entanglement to Density Functional Theory

OpenAIRE

Rajagopal, A. K.; Rendell, R. W.

2005-01-01

The maximum von Neumann entropy principle subject to given constraints of mean values of some physical observables determines the density matrix. Similarly the stationary action principle in the case of time-dependent (dissipative) situations under similar constraints yields the density matrix. The free energy and measures of entanglement are expressed in terms of such a density matrix and thus define respective functionals of the mean values. In the light of several model calculations, it is...

Cumulants in perturbation expansions for non-equilibrium field theory

International Nuclear Information System (INIS)

Fauser, R.

1995-11-01

The formulation of perturbation expansions for a quantum field theory of strongly interacting systems in a general non-equilibrium state is discussed. Non-vanishing initial correlations are included in the formulation of the perturbation expansion in terms of cumulants. The cumulants are shown to be the suitable candidate for summing up the perturbation expansion. Also a linked-cluster theorem for the perturbation series with cumulants is presented. Finally a generating functional of the perturbation series with initial correlations is studied. We apply the methods to a simple model of a fermion-boson system. (orig.)

Cosmological perturbations on the phantom brane

Energy Technology Data Exchange (ETDEWEB)

Bag, Satadru; Sahni, Varun [Inter-University Centre for Astronomy and Astrophysics, Pune (India); Viznyuk, Alexander; Shtanov, Yuri, E-mail: satadru@iucaa.in, E-mail: viznyuk@bitp.kiev.ua, E-mail: shtanov@bitp.kiev.ua, E-mail: varun@iucaa.in [Bogolyubov Institute for Theoretical Physics, Kiev 03680 (Ukraine)

2016-07-01

We obtain a closed system of equations for scalar perturbations in a multi-component braneworld. Our braneworld possesses a phantom-like equation of state at late times, w {sub eff} < −1, but no big-rip future singularity. In addition to matter and radiation, the braneworld possesses a new effective degree of freedom—the 'Weyl fluid' or 'dark radiation'. Setting initial conditions on super-Hubble spatial scales at the epoch of radiation domination, we evolve perturbations of radiation, pressureless matter and the Weyl fluid until the present epoch. We observe a gradual decrease in the amplitude of the Weyl-fluid perturbations after Hubble-radius crossing, which results in a negligible effect of the Weyl fluid on the evolution of matter perturbations on spatial scales relevant for structure formation. Consequently, the quasi-static approximation of Koyama and Maartens provides a good fit to the exact results during the matter-dominated epoch. We find that the late-time growth of density perturbations on the brane proceeds at a faster rate than in ΛCDM. Additionally, the gravitational potentials Φ and Ψ evolve differently on the brane than in ΛCDM, for which Φ = Ψ. On the brane, by contrast, the ratio Φ/Ψ exceeds unity during the late matter-dominated epoch ( z ∼< 50). These features emerge as smoking gun tests of phantom brane cosmology and allow predictions of this scenario to be tested against observations of galaxy clustering and large-scale structure.

Source-Free Exchange-Correlation Magnetic Fields in Density Functional Theory.

Science.gov (United States)

Sharma, S; Gross, E K U; Sanna, A; Dewhurst, J K

2018-03-13

Spin-dependent exchange-correlation energy functionals in use today depend on the charge density and the magnetization density: E xc [ρ, m]. However, it is also correct to define the functional in terms of the curl of m for physical external fields: E xc [ρ,∇ × m]. The exchange-correlation magnetic field, B xc , then becomes source-free. We study this variation of the theory by uniquely removing the source term from local and generalized gradient approximations to the functional. By doing so, the total Kohn-Sham moments are improved for a wide range of materials for both functionals. Significantly, the moments for the pnictides are now in good agreement with experiment. This source-free method is simple to implement in all existing density functional theory codes.

Chemical hardness and density functional theory

Indian Academy of Sciences (India)

Unknown

RALPH G PEARSON. Chemistry Department, University of California, Santa Barbara, CA 93106, USA. Abstract. The concept of chemical hardness is reviewed from a personal point of view. Keywords. Hardness; softness; hard & soft acids bases (HSAB); principle of maximum hardness. (PMH) density functional theory (DFT) ...

Density functional and neural network analysis

DEFF Research Database (Denmark)

Jalkanen, K. J.; Suhai, S.; Bohr, Henrik

1997-01-01

Density functional theory (DFT) calculations have been carried out for hydrated L-alanine, L-alanyl-L-alanine and N-acetyl L-alanine N'-methylamide and examined with respect to the effect of water on the structure, the vibrational frequencies, vibrational absorption (VA) and vibrational circular...

Self-similar perturbations of a Friedmann universe

International Nuclear Information System (INIS)

Carr, B.J.; Yahil, A.

1990-01-01