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Sample records for adaptive perturbation theory

  1. Next-Generation Force Fields from Symmetry-Adapted Perturbation Theory

    NASA Astrophysics Data System (ADS)

    McDaniel, Jesse G.; Schmidt, J. R.

    2016-05-01

    Symmetry-adapted perturbation theory (SAPT) provides a unique set of advantages for parameterizing next-generation force fields from first principles. SAPT provides a direct, basis-set superposition error free estimate of molecular interaction energies, a physically intuitive energy decomposition, and a seamless transition to an asymptotic picture of intermolecular interactions. These properties have been exploited throughout the literature to develop next-generation force fields for a variety of applications, including classical molecular dynamics simulations, crystal structure prediction, and quantum dynamics/spectroscopy. This review provides a brief overview of the formalism and theory of SAPT, along with a practical discussion of the various methodologies utilized to parameterize force fields from SAPT calculations. It also highlights a number of applications of SAPT-based force fields for chemical systems of particular interest. Finally, the review ends with a brief outlook on the future opportunities and challenges that remain for next-generation force fields based on SAPT.

  2. Intermolecular symmetry-adapted perturbation theory study of large organic complexes

    SciTech Connect

    Heßelmann, Andreas; Korona, Tatiana

    2014-09-07

    Binding energies for the complexes of the S12L database by Grimme [Chem. Eur. J. 18, 9955 (2012)] were calculated using intermolecular symmetry-adapted perturbation theory combined with a density-functional theory description of the interacting molecules. The individual interaction energy decompositions revealed no particular change in the stabilisation pattern as compared to smaller dimer systems at equilibrium structures. This demonstrates that, to some extent, the qualitative description of the interaction of small dimer systems may be extrapolated to larger systems, a method that is widely used in force-fields in which the total interaction energy is decomposed into atom-atom contributions. A comparison of the binding energies with accurate experimental reference values from Grimme, the latter including thermodynamic corrections from semiempirical calculations, has shown a fairly good agreement to within the error range of the reference binding energies.

  3. Next-Generation Force Fields from Symmetry-Adapted Perturbation Theory.

    PubMed

    McDaniel, Jesse G; Schmidt, J R

    2016-05-27

    Symmetry-adapted perturbation theory (SAPT) provides a unique set of advantages for parameterizing next-generation force fields from first principles. SAPT provides a direct, basis-set superposition error free estimate of molecular interaction energies, a physically intuitive energy decomposition, and a seamless transition to an asymptotic picture of intermolecular interactions. These properties have been exploited throughout the literature to develop next-generation force fields for a variety of applications, including classical molecular dynamics simulations, crystal structure prediction, and quantum dynamics/spectroscopy. This review provides a brief overview of the formalism and theory of SAPT, along with a practical discussion of the various methodologies utilized to parameterize force fields from SAPT calculations. It also highlights a number of applications of SAPT-based force fields for chemical systems of particular interest. Finally, the review ends with a brief outlook on the future opportunities and challenges that remain for next-generation force fields based on SAPT.

  4. Linear-scaling symmetry-adapted perturbation theory with scaled dispersion

    SciTech Connect

    Maurer, Simon A.; Beer, Matthias; Lambrecht, Daniel S.; Ochsenfeld, Christian

    2013-11-14

    We present a linear-scaling symmetry-adapted perturbation theory (SAPT) method that is based on an atomic orbital (AO) formulation of zeroth-order SAPT (SAPT0). The non-dispersive terms are realized with linear-scaling cost using both the continuous fast multipole method (CFMM) and the linear exchange (LinK) approach for integral contractions as well as our efficient Laplace-based coupled-perturbed self-consistent field method (DL-CPSCF) for evaluating response densities. The reformulation of the dispersion term is based on our linear-scaling AO Møller-Plesset second-order perturbation theory (AO-MP2) method, that uses our recently introduced QQR-type screening [S. A. Maurer, D. S. Lambrecht, J. Kussmann, and C. Ochsenfeld, J. Chem. Phys. 138, 014101 (2013)] for preselecting numerically significant energy contributions. Similar to scaled opposite-spin MP2, we neglect the exchange-dispersion term in SAPT and introduce a scaling factor for the dispersion term, which compensates for the error and at the same time accounts for basis set incompleteness effects and intramonomer correlation. We show in extensive benchmark calculations that the new scaled-dispersion (sd-)SAPT0 approach provides reliable results for small and large interacting systems where the results with a small 6-31G** basis are roughly comparable to supermolecular MP2 calculations in a triple-zeta basis. The performance of our method is demonstrated with timings on cellulose fragments, DNA systems, and cutouts of a protein-ligand complex with up to 1100 atoms on a single computer core.

  5. Cation-π interactions: accurate intermolecular potential from symmetry-adapted perturbation theory.

    PubMed

    Ansorg, Kay; Tafipolsky, Maxim; Engels, Bernd

    2013-09-01

    Symmetry-adapted perturbation theory (SAPT) is used to decompose the total intermolecular interaction energy between the ammonium cation and a benzene molecule into four physically motivated individual contributions: electrostatics, exchange, dispersion, and induction. Based on this rigorous decomposition, it is shown unambiguously that both the electrostatic and the induction energy components contribute almost equally to the attractive forces stabilizing the dimer with a nonnegligible contribution coming from the dispersion term. A polarizable potential model for the interaction of ammonium cation with benzene is parametrized by fitting these four energy components separately using the functional forms of the AMOEBA force field augmented with the missing charge penetration energy term calculated as a sum over pairwise electrostatic energies between spherical atoms. It is shown that the proposed model is able to produce accurate intermolecular interaction energies as compared to ab initio results, thus avoiding error compensation to a large extent.

  6. Intramolecular symmetry-adapted perturbation theory with a single-determinant wavefunction

    SciTech Connect

    Pastorczak, Ewa; Prlj, Antonio; Corminboeuf, Clémence; Gonthier, Jérôme F.

    2015-12-14

    We introduce an intramolecular energy decomposition scheme for analyzing non-covalent interactions within molecules in the spirit of symmetry-adapted perturbation theory (SAPT). The proposed intra-SAPT approach is based upon the Chemical Hamiltonian of Mayer [Int. J. Quantum Chem. 23(2), 341–363 (1983)] and the recently introduced zeroth-order wavefunction [J. F. Gonthier and C. Corminboeuf, J. Chem. Phys. 140(15), 154107 (2014)]. The scheme decomposes the interaction energy between weakly bound fragments located within the same molecule into physically meaningful components, i.e., electrostatic-exchange, induction, and dispersion. Here, we discuss the key steps of the approach and demonstrate that a single-determinant wavefunction can already deliver a detailed and insightful description of a wide range of intramolecular non-covalent phenomena such as hydrogen bonds, dihydrogen contacts, and π − π stacking interactions. Intra-SAPT is also used to shed the light on competing intra- and intermolecular interactions.

  7. Unitary group adapted state specific multireference perturbation theory: Formulation and pilot applications.

    PubMed

    Sen, Avijit; Sen, Sangita; Samanta, Pradipta Kumar; Mukherjee, Debashis

    2015-04-01

    We present here a comprehensive account of the formulation and pilot applications of the second-order perturbative analogue of the recently proposed unitary group adapted state-specific multireference coupled cluster theory (UGA-SSMRCC), which we call as the UGA-SSMRPT2. We also discuss the essential similarities and differences between the UGA-SSMRPT2 and the allied SA-SSMRPT2. Our theory, like its parent UGA-SSMRCC formalism, is size-extensive. However, because of the noninvariance of the theory with respect to the transformation among the active orbitals, it requires the use of localized orbitals to ensure size-consistency. We have demonstrated the performance of the formalism with a set of pilot applications, exploring (a) the accuracy of the potential energy surface (PES) of a set of small prototypical difficult molecules in their various low-lying states, using natural, pseudocanonical and localized orbitals and compared the respective nonparallelity errors (NPE) and the mean average deviations (MAD) vis-a-vis the full CI results with the same basis; (b) the efficacy of localized active orbitals to ensure and demonstrate manifest size-consistency with respect to fragmentation. We found that natural orbitals lead to the best overall PES, as evidenced by the NPE and MAD values. The MRMP2 results for individual states and of the MCQDPT2 for multiple states displaying avoided curve crossings are uniformly poorer as compared with the UGA-SSMRPT2 results. The striking aspect of the size-consistency check is the complete insensitivity of the sum of fragment energies with given fragment spin-multiplicities, which are obtained as the asymptotic limit of super-molecules with different coupled spins.

  8. Intramolecular symmetry-adapted perturbation theory with a single-determinant wavefunction.

    PubMed

    Pastorczak, Ewa; Prlj, Antonio; Gonthier, Jérôme F; Corminboeuf, Clémence

    2015-12-14

    We introduce an intramolecular energy decomposition scheme for analyzing non-covalent interactions within molecules in the spirit of symmetry-adapted perturbation theory (SAPT). The proposed intra-SAPT approach is based upon the Chemical Hamiltonian of Mayer [Int. J. Quantum Chem. 23(2), 341-363 (1983)] and the recently introduced zeroth-order wavefunction [J. F. Gonthier and C. Corminboeuf, J. Chem. Phys. 140(15), 154107 (2014)]. The scheme decomposes the interaction energy between weakly bound fragments located within the same molecule into physically meaningful components, i.e., electrostatic-exchange, induction, and dispersion. Here, we discuss the key steps of the approach and demonstrate that a single-determinant wavefunction can already deliver a detailed and insightful description of a wide range of intramolecular non-covalent phenomena such as hydrogen bonds, dihydrogen contacts, and π - π stacking interactions. Intra-SAPT is also used to shed the light on competing intra- and intermolecular interactions. PMID:26671358

  9. Levels of symmetry adapted perturbation theory (SAPT). I. Efficiency and performance for interaction energies.

    PubMed

    Parker, Trent M; Burns, Lori A; Parrish, Robert M; Ryno, Alden G; Sherrill, C David

    2014-03-01

    A systematic examination of the computational expense and accuracy of Symmetry-Adapted Perturbation Theory (SAPT) for the prediction of non-covalent interaction energies is provided with respect to both method [SAPT0, DFT-SAPT, SAPT2, SAPT2+, SAPT2+(3), and SAPT2+3; with and without CCD dispersion for the last three] and basis set [Dunning cc-pVDZ through aug-cc-pV5Z wherever computationally tractable, including truncations of diffuse basis functions]. To improve accuracy for hydrogen-bonded systems, we also include two corrections based on exchange-scaling (sSAPT0) and the supermolecular MP2 interaction energy (δMP2). When considering the best error performance relative to computational effort, we recommend as the gold, silver, and bronze standard of SAPT: SAPT2+(3)δMP2/aug-cc-pVTZ, SAPT2+/aug-cc-pVDZ, and sSAPT0/jun-cc-pVDZ. Their respective mean absolute errors in interaction energy across the S22, HBC6, NBC10, and HSG databases are 0.15 (62.9), 0.30 (4.4), and 0.49 kcal mol(-1) (0.03 h for adenine·thymine complex).

  10. Automated Lattice Perturbation Theory

    SciTech Connect

    Monahan, Christopher

    2014-11-01

    I review recent developments in automated lattice perturbation theory. Starting with an overview of lattice perturbation theory, I focus on the three automation packages currently "on the market": HiPPy/HPsrc, Pastor and PhySyCAl. I highlight some recent applications of these methods, particularly in B physics. In the final section I briefly discuss the related, but distinct, approach of numerical stochastic perturbation theory.

  11. Density perturbation theory

    SciTech Connect

    Palenik, Mark C.; Dunlap, Brett I.

    2015-07-28

    Despite the fundamental importance of electron density in density functional theory, perturbations are still usually dealt with using Hartree-Fock-like orbital equations known as coupled-perturbed Kohn-Sham (CPKS). As an alternative, we develop a perturbation theory that solves for the perturbed density directly, removing the need for CPKS. This replaces CPKS with a true Hohenberg-Kohn density perturbation theory. In CPKS, the perturbed density is found in the basis of products of occupied and virtual orbitals, which becomes ever more over-complete as the size of the orbital basis set increases. In our method, the perturbation to the density is expanded in terms of a series of density basis functions and found directly. It is possible to solve for the density in such a way that it makes the total energy stationary even if the density basis is incomplete.

  12. Spatial assignment of symmetry adapted perturbation theory interaction energy components: The atomic SAPT partition

    SciTech Connect

    Parrish, Robert M.; Sherrill, C. David

    2014-07-28

    We develop a physically-motivated assignment of symmetry adapted perturbation theory for intermolecular interactions (SAPT) into atom-pairwise contributions (the A-SAPT partition). The basic precept of A-SAPT is that the many-body interaction energy components are computed normally under the formalism of SAPT, following which a spatially-localized two-body quasiparticle interaction is extracted from the many-body interaction terms. For electrostatics and induction source terms, the relevant quasiparticles are atoms, which are obtained in this work through the iterative stockholder analysis (ISA) procedure. For the exchange, induction response, and dispersion terms, the relevant quasiparticles are local occupied orbitals, which are obtained in this work through the Pipek-Mezey procedure. The local orbital atomic charges obtained from ISA additionally allow the terms involving local orbitals to be assigned in an atom-pairwise manner. Further summation over the atoms of one or the other monomer allows for a chemically intuitive visualization of the contribution of each atom and interaction component to the overall noncovalent interaction strength. Herein, we present the intuitive development and mathematical form for A-SAPT applied in the SAPT0 approximation (the A-SAPT0 partition). We also provide an efficient series of algorithms for the computation of the A-SAPT0 partition with essentially the same computational cost as the corresponding SAPT0 decomposition. We probe the sensitivity of the A-SAPT0 partition to the ISA grid and convergence parameter, orbital localization metric, and induction coupling treatment, and recommend a set of practical choices which closes the definition of the A-SAPT0 partition. We demonstrate the utility and computational tractability of the A-SAPT0 partition in the context of side-on cation-π interactions and the intercalation of DNA by proflavine. A-SAPT0 clearly shows the key processes in these complicated noncovalent interactions, in

  13. Spatial assignment of symmetry adapted perturbation theory interaction energy components: The atomic SAPT partition.

    PubMed

    Parrish, Robert M; Sherrill, C David

    2014-07-28

    We develop a physically-motivated assignment of symmetry adapted perturbation theory for intermolecular interactions (SAPT) into atom-pairwise contributions (the A-SAPT partition). The basic precept of A-SAPT is that the many-body interaction energy components are computed normally under the formalism of SAPT, following which a spatially-localized two-body quasiparticle interaction is extracted from the many-body interaction terms. For electrostatics and induction source terms, the relevant quasiparticles are atoms, which are obtained in this work through the iterative stockholder analysis (ISA) procedure. For the exchange, induction response, and dispersion terms, the relevant quasiparticles are local occupied orbitals, which are obtained in this work through the Pipek-Mezey procedure. The local orbital atomic charges obtained from ISA additionally allow the terms involving local orbitals to be assigned in an atom-pairwise manner. Further summation over the atoms of one or the other monomer allows for a chemically intuitive visualization of the contribution of each atom and interaction component to the overall noncovalent interaction strength. Herein, we present the intuitive development and mathematical form for A-SAPT applied in the SAPT0 approximation (the A-SAPT0 partition). We also provide an efficient series of algorithms for the computation of the A-SAPT0 partition with essentially the same computational cost as the corresponding SAPT0 decomposition. We probe the sensitivity of the A-SAPT0 partition to the ISA grid and convergence parameter, orbital localization metric, and induction coupling treatment, and recommend a set of practical choices which closes the definition of the A-SAPT0 partition. We demonstrate the utility and computational tractability of the A-SAPT0 partition in the context of side-on cation-π interactions and the intercalation of DNA by proflavine. A-SAPT0 clearly shows the key processes in these complicated noncovalent interactions, in

  14. Symmetry-adapted perturbation-theory calculations of intermolecular forces employing density-functional description of monomers.

    PubMed

    Misquitta, Alston J; Szalewicz, Krzysztof

    2005-06-01

    A symmetry-adapted perturbation theory based on Kohn-Sham determinants [SAPT(KS)] and utilizing asymptotically corrected exchange-correlation potentials has been applied to the He2, Ne2, (H2O)2, and (CO2)2 dimers. It is shown that SAPT(KS) is able to recover the electrostatic, first-order exchange, second-order induction, and exchange-induction energies with an accuracy approaching and occasionally surpassing that of regular SAPT at the currently programmed theory level. The use of the asymptotic corrections is critical to achieve this accuracy. The SAPT(KS) results can be obtained at a small fraction of the time needed for regular SAPT calculations. The robustness of the SAPT(KS) method with respect to the basis set size is also demonstrated. A theoretical justification for high accuracy of SAPT(KS) predictions for the electrostatic, first-order exchange, and second-order induction energies has been provided.

  15. Degenerate density perturbation theory

    NASA Astrophysics Data System (ADS)

    Palenik, Mark C.; Dunlap, Brett I.

    2016-09-01

    Fractional occupation numbers can be used in density functional theory to create a symmetric Kohn-Sham potential, resulting in orbitals with degenerate eigenvalues. We develop the corresponding perturbation theory and apply it to a system of Nd degenerate electrons in a harmonic oscillator potential. The order-by-order expansions of both the fractional occupation numbers and unitary transformations within the degenerate subspace are determined by the requirement that a differentiable map exists connecting the initial and perturbed states. Using the X α exchange-correlation (XC) functional, we find an analytic solution for the first-order density and first- through third-order energies as a function of α , with and without a self-interaction correction. The fact that the XC Hessian is not positive definite plays an important role in the behavior of the occupation numbers.

  16. Canonical density matrix perturbation theory.

    PubMed

    Niklasson, Anders M N; Cawkwell, M J; Rubensson, Emanuel H; Rudberg, Elias

    2015-12-01

    Density matrix perturbation theory [Niklasson and Challacombe, Phys. Rev. Lett. 92, 193001 (2004)] is generalized to canonical (NVT) free-energy ensembles in tight-binding, Hartree-Fock, or Kohn-Sham density-functional theory. The canonical density matrix perturbation theory can be used to calculate temperature-dependent response properties from the coupled perturbed self-consistent field equations as in density-functional perturbation theory. The method is well suited to take advantage of sparse matrix algebra to achieve linear scaling complexity in the computational cost as a function of system size for sufficiently large nonmetallic materials and metals at high temperatures. PMID:26764847

  17. Canonical density matrix perturbation theory.

    PubMed

    Niklasson, Anders M N; Cawkwell, M J; Rubensson, Emanuel H; Rudberg, Elias

    2015-12-01

    Density matrix perturbation theory [Niklasson and Challacombe, Phys. Rev. Lett. 92, 193001 (2004)] is generalized to canonical (NVT) free-energy ensembles in tight-binding, Hartree-Fock, or Kohn-Sham density-functional theory. The canonical density matrix perturbation theory can be used to calculate temperature-dependent response properties from the coupled perturbed self-consistent field equations as in density-functional perturbation theory. The method is well suited to take advantage of sparse matrix algebra to achieve linear scaling complexity in the computational cost as a function of system size for sufficiently large nonmetallic materials and metals at high temperatures.

  18. Chemical Assignment of Symmetry-Adapted Perturbation Theory Interaction Energy Components: The Functional-Group SAPT Partition.

    PubMed

    Parrish, Robert M; Parker, Trent M; Sherrill, C David

    2014-10-14

    Recently, we introduced an effective atom-pairwise partition of the many-body symmetry-adapted perturbation theory (SAPT) interaction energy decomposition, producing a method known as atomic SAPT (A-SAPT) [Parrish, R. M.; Sherrill, C. D. J. Chem. Phys. 2014, 141, 044115]. A-SAPT provides ab initio atom-pair potentials for force field development and also automatic visualizations of the spatial contributions of noncovalent interactions, but often has difficulty producing chemically useful partitions of the electrostatic energy, due to the buildup of oscillating partial charges on adjacent functional groups. In this work, we substitute chemical functional groups in place of atoms as the relevant local quasiparticles in the partition, resulting in a functional-group-pairwise partition denoted as functional-group SAPT (F-SAPT). F-SAPT assigns integral sets of local occupied electronic orbitals and protons to chemical functional groups and linking σ bonds. Link-bond contributions can be further assigned to chemical functional groups to simplify the analysis. This approach yields a SAPT partition between pairs of functional groups with integral charge (usually neutral), preventing oscillations in the electrostatic partition. F-SAPT qualitatively matches chemical intuition and the cut-and-cap fragmentation technique but additionally yields the quantitative many-body SAPT interaction energy. The conceptual simplicity, chemical utility, and computational efficiency of F-SAPT is demonstrated in the context of phenol dimer, proflavine(+)-DNA intercalation, and a cucurbituril host-guest inclusion complex. PMID:26588139

  19. Chemical Assignment of Symmetry-Adapted Perturbation Theory Interaction Energy Components: The Functional-Group SAPT Partition.

    PubMed

    Parrish, Robert M; Parker, Trent M; Sherrill, C David

    2014-10-14

    Recently, we introduced an effective atom-pairwise partition of the many-body symmetry-adapted perturbation theory (SAPT) interaction energy decomposition, producing a method known as atomic SAPT (A-SAPT) [Parrish, R. M.; Sherrill, C. D. J. Chem. Phys. 2014, 141, 044115]. A-SAPT provides ab initio atom-pair potentials for force field development and also automatic visualizations of the spatial contributions of noncovalent interactions, but often has difficulty producing chemically useful partitions of the electrostatic energy, due to the buildup of oscillating partial charges on adjacent functional groups. In this work, we substitute chemical functional groups in place of atoms as the relevant local quasiparticles in the partition, resulting in a functional-group-pairwise partition denoted as functional-group SAPT (F-SAPT). F-SAPT assigns integral sets of local occupied electronic orbitals and protons to chemical functional groups and linking σ bonds. Link-bond contributions can be further assigned to chemical functional groups to simplify the analysis. This approach yields a SAPT partition between pairs of functional groups with integral charge (usually neutral), preventing oscillations in the electrostatic partition. F-SAPT qualitatively matches chemical intuition and the cut-and-cap fragmentation technique but additionally yields the quantitative many-body SAPT interaction energy. The conceptual simplicity, chemical utility, and computational efficiency of F-SAPT is demonstrated in the context of phenol dimer, proflavine(+)-DNA intercalation, and a cucurbituril host-guest inclusion complex.

  20. Renormalized Lie perturbation theory

    SciTech Connect

    Rosengaus, E.; Dewar, R.L.

    1981-07-01

    A Lie operator method for constructing action-angle transformations continuously connected to the identity is developed for area preserving mappings. By a simple change of variable from action to angular frequency a perturbation expansion is obtained in which the small denominators have been renormalized. The method is shown to lead to the same series as the Lagrangian perturbation method of Greene and Percival, which converges on KAM surfaces. The method is not superconvergent, but yields simple recursion relations which allow automatic algebraic manipulation techniques to be used to develop the series to high order. It is argued that the operator method can be justified by analytically continuing from the complex angular frequency plane onto the real line. The resulting picture is one where preserved primary KAM surfaces are continuously connected to one another.

  1. Perturbation theory in electron diffraction

    NASA Astrophysics Data System (ADS)

    Bakken, L. N.; Marthinsen, K.; Hoeier, R.

    1992-12-01

    The Bloch-wave approach is used for discussing multiple inelastic electron scattering and higher-order perturbation theory in inelastic high-energy electron diffraction. In contrast to previous work, the present work describes three-dimensional diffraction so that higher-order Laue zone (HOLZ) effects are incorporated. Absorption is included and eigenvalues and eigenvectors are calculated from a structure matrix with the inclusion of an absorptive potential. Centrosymmetric as well as non-centrosymmetric crystal structures are allowed. An iteration method with a defined generalized propagation function for solving the inelastic coupling equations is described. It is shown that a similar iteration method with the same propagation function can be used for obtaining higher-order perturbation terms for the wave-function when a perturbation is added to the crystal potential. Finally, perturbation theory by matrix calculations when a general perturbation is added to the structure matrix is considered.

  2. Basics of QCD perturbation theory

    SciTech Connect

    Soper, D.E.

    1997-06-01

    This is an introduction to the use of QCD perturbation theory, emphasizing generic features of the theory that enable one to separate short-time and long-time effects. The author also covers some important classes of applications: electron-positron annihilation to hadrons, deeply inelastic scattering, and hard processes in hadron-hadron collisions. 31 refs., 38 figs.

  3. Perturbation theory in thermosphere dynamics

    NASA Technical Reports Server (NTRS)

    Mayr, H. G.; Volland, H.

    1976-01-01

    It is shown that density and pressure throughout the thermosphere can be adequately described in a logarithmic expansion that provides a sound basis for the application of perturbation theory. This expansion eliminates most of the important nonlinearities associated with density variations. On the basis of this expansion, the validity of perturbation theory can be extended to cover a large variety of atmospheric conditions in which the relative temperature amplitude is less than 0.5 and wind velocities are significantly less than the speed of sound.

  4. Intermolecular forces and molecular dynamics simulation of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) using symmetry adapted perturbation theory.

    PubMed

    Taylor, DeCarlos E

    2013-04-25

    The dimer potential energy surface (PES) of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) has been explored using symmetry adapted perturbation theory based on a Kohn-Sham density functional theory description of the monomers [SAPT(DFT)]. An intermolecular potential energy function was parametrized using a grid of 880 ab initio SAPT(DFT) dimer interaction energies, and the function was used to identify stationary points on the SAPT(DFT) dimer PES. It is shown that there exists a variety of minima with a range of bonding configurations and ab initio analyses of the interaction energy components, along with radial cross sections of the PES near each minimum, are presented. Results of isothermal-isostress molecular dynamics simulations are reported, and the simulated structure, thermal expansion, sublimation enthalpy, and bulk modulus of the TATB crystal, based on the SAPT(DFT) interaction potential, are in good agreement with experiment.

  5. Adaptive Modeling Procedure Selection by Data Perturbation*

    PubMed Central

    Zhang, Yongli; Shen, Xiaotong

    2015-01-01

    Summary Many procedures have been developed to deal with the high-dimensional problem that is emerging in various business and economics areas. To evaluate and compare these procedures, modeling uncertainty caused by model selection and parameter estimation has to be assessed and integrated into a modeling process. To do this, a data perturbation method estimates the modeling uncertainty inherited in a selection process by perturbing the data. Critical to data perturbation is the size of perturbation, as the perturbed data should resemble the original dataset. To account for the modeling uncertainty, we derive the optimal size of perturbation, which adapts to the data, the model space, and other relevant factors in the context of linear regression. On this basis, we develop an adaptive data-perturbation method that, unlike its nonadaptive counterpart, performs well in different situations. This leads to a data-adaptive model selection method. Both theoretical and numerical analysis suggest that the data-adaptive model selection method adapts to distinct situations in that it yields consistent model selection and optimal prediction, without knowing which situation exists a priori. The proposed method is applied to real data from the commodity market and outperforms its competitors in terms of price forecasting accuracy. PMID:26640319

  6. Adaptation Strategies in Perturbed /s/

    ERIC Educational Resources Information Center

    Brunner, Jana; Hoole, Phil; Perrier, Pascal

    2011-01-01

    The purpose of this work is to investigate the role of three articulatory parameters (tongue position, jaw position and tongue grooving) in the production of /s/. Six normal speakers' speech was perturbed by a palatal prosthesis. The fricative was recorded acoustically and through electromagnetic articulography in four conditions: (1) unperturbed,…

  7. Geometric Hamiltonian structures and perturbation theory

    SciTech Connect

    Omohundro, S.

    1984-08-01

    We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging.

  8. Symmetry-adapted perturbation theory with Kohn-Sham orbitals using non-empirically tuned, long-range-corrected density functionals

    SciTech Connect

    Lao, Ka Un; Herbert, John M.

    2014-01-28

    The performance of second-order symmetry-adapted perturbation theory (SAPT) calculations using Kohn-Sham (KS) orbitals is evaluated against benchmark results for intermolecular interactions. Unlike previous studies of this “SAPT(KS)” methodology, the present study uses non-empirically tuned long-range corrected (LRC) functionals for the monomers. The proper v{sub xc} (r)→0 asymptotic limit is achieved by tuning the range separation parameter in order to satisfy the condition that the highest occupied KS energy level equals minus the molecule's ionization energy, for each monomer unit. Tests for He{sub 2}, Ne{sub 2}, and the S22 and S66 data sets reveal that this condition is important for accurate prediction of the non-dispersion components of the energy, although errors in SAPT(KS) dispersion energies remain unacceptably large. In conjunction with an empirical dispersion potential, however, the SAPT(KS) method affords good results for S22 and S66, and also accurately predicts the whole potential energy curve for the sandwich isomer of the benzene dimer. Tuned LRC functionals represent an attractive alternative to other asymptotic corrections that have been employed in density-functional-based SAPT calculations, and we recommend the use of tuned LRC functionals in both coupled-perturbed SAPT(DFT) calculations and dispersion-corrected SAPT(KS) calculations.

  9. Adapting SAFT-γ perturbation theory to site-based molecular dynamics simulation. III. Molecules with partial charges at bulk phases, confined geometries and interfaces

    SciTech Connect

    Ghobadi, Ahmadreza F.; Elliott, J. Richard

    2014-09-07

    In Paper I [A. F. Ghobadi and J. R. Elliott, J. Chem. Phys. 139(23), 234104 (2013)], we showed that how a third-order Weeks–Chandler–Anderson (WCA) Thermodynamic Perturbation Theory and molecular simulation can be integrated to characterize the repulsive and dispersive contributions to the Helmholtz free energy for realistic molecular conformations. To this end, we focused on n-alkanes to develop a theory for fused and soft chains. In Paper II [A. F. Ghobadi and J. R. Elliott, J. Chem. Phys. 141(2), 024708 (2014)], we adapted the classical Density Functional Theory and studied the microstructure of the realistic molecular fluids in confined geometries and vapor-liquid interfaces. We demonstrated that a detailed consistency between molecular simulation and theory can be achieved for both bulk and inhomogeneous phases. In this paper, we extend the methodology to molecules with partial charges such as carbon dioxide, water, 1-alkanols, nitriles, and ethers. We show that the electrostatic interactions can be captured via an effective association potential in the framework of Statistical Associating Fluid Theory (SAFT). Implementation of the resulting association contribution in assessing the properties of these molecules at confined geometries and interfaces presents satisfactory agreement with molecular simulation and experimental data. For example, the predicted surface tension deviates less than 4% comparing to full potential simulations. Also, the theory, referred to as SAFT-γ WCA, is able to reproduce the specific orientation of hydrophilic head and hydrophobic tail of 1-alkanols at the vapor-liquid interface of water.

  10. "Phonon" scattering beyond perturbation theory

    NASA Astrophysics Data System (ADS)

    Qiu, WuJie; Ke, XueZhi; Xi, LiLi; Wu, LiHua; Yang, Jiong; Zhang, WenQing

    2016-02-01

    Searching and designing materials with intrinsically low lattice thermal conductivity (LTC) have attracted extensive consideration in thermoelectrics and thermal management community. The concept of part-crystalline part-liquid state, or even part-crystalline part-amorphous state, has recently been proposed to describe the exotic structure of materials with chemical- bond hierarchy, in which a set of atoms is weakly bonded to the rest species while the other sublattices retain relatively strong rigidity. The whole system inherently manifests the coexistence of rigid crystalline sublattices and fluctuating noncrystalline substructures. Representative materials in the unusual state can be classified into two categories, i.e., caged and non-caged ones. LTCs in both systems deviate from the traditional T -1 relationship ( T, the absolute temperature), which can hardly be described by small-parameter-based perturbation approaches. Beyond the classical perturbation theory, an extra rattling-like scattering should be considered to interpret the liquid-like and sublattice-amorphization-induced heat transport. Such a kind of compounds could be promising high-performance thermoelectric materials, due to the extremely low LTCs. Other physical properties for these part-crystalline substances should also exhibit certain novelty and deserve further exploration.

  11. Sinusoidal error perturbation reveals multiple coordinate systems for sensorymotor adaptation.

    PubMed

    Hudson, Todd E; Landy, Michael S

    2016-02-01

    A coordinate system is composed of an encoding, defining the dimensions of the space, and an origin. We examine the coordinate encoding used to update motor plans during sensory-motor adaptation to center-out reaches. Adaptation is induced using a novel paradigm in which feedback of reach endpoints is perturbed following a sinewave pattern over trials; the perturbed dimensions of the feedback were the axes of a Cartesian coordinate system in one session and a polar coordinate system in another session. For center-out reaches to randomly chosen target locations, reach errors observed at one target will require different corrections at other targets within Cartesian- and polar-coded systems. The sinewave adaptation technique allowed us to simultaneously adapt both dimensions of each coordinate system (x-y, or reach gain and angle), and identify the contributions of each perturbed dimension by adapting each at a distinct temporal frequency. The efficiency of this technique further allowed us to employ perturbations that were a fraction the size normally used, which avoids confounding automatic adaptive processes with deliberate adjustments made in response to obvious experimental manipulations. Subjects independently corrected errors in each coordinate in both sessions, suggesting that the nervous system encodes both a Cartesian- and polar-coordinate-based internal representation for motor adaptation. The gains and phase lags of the adaptive responses are not readily explained by current theories of sensory-motor adaptation.

  12. Adaptation to transient postural perturbations

    NASA Technical Reports Server (NTRS)

    Andres, Robert O.

    1992-01-01

    This research was first proposed in May, 1986, to focus on some of the problems encountered in the analysis of postural responses gathered from crewmembers. The ultimate driving force behind this line of research was the desire to treat, predict, or explain 'Space Adaptation Syndrome' (SAS) and hence circumvent any adverse effects of space motion sickness on crewmember performance. The aim of this project was to develop an easily implemented analysis of the transient responses to platform translation that can be elicited with a protocol designed to force sensorimotor reorganization, utilizing statistically reliable criterion measures. This report will present: (1) a summary of the activity that took place in each of the three funded years of the project; (2) discussion of experimental results and their implications for future research; and (3) a list of presentations and publications resulting from this project.

  13. Perturbative theory for Brownian vortexes.

    PubMed

    Moyses, Henrique W; Bauer, Ross O; Grosberg, Alexander Y; Grier, David G

    2015-06-01

    Brownian vortexes are stochastic machines that use static nonconservative force fields to bias random thermal fluctuations into steadily circulating currents. The archetype for this class of systems is a colloidal sphere in an optical tweezer. Trapped near the focus of a strongly converging beam of light, the particle is displaced by random thermal kicks into the nonconservative part of the optical force field arising from radiation pressure, which then biases its diffusion. Assuming the particle remains localized within the trap, its time-averaged trajectory traces out a toroidal vortex. Unlike trivial Brownian vortexes, such as the biased Brownian pendulum, which circulate preferentially in the direction of the bias, the general Brownian vortex can change direction and even topology in response to temperature changes. Here we introduce a theory based on a perturbative expansion of the Fokker-Planck equation for weak nonconservative driving. The first-order solution takes the form of a modified Boltzmann relation and accounts for the rich phenomenology observed in experiments on micrometer-scale colloidal spheres in optical tweezers. PMID:26172698

  14. Perturbative theory for Brownian vortexes

    NASA Astrophysics Data System (ADS)

    Moyses, Henrique W.; Bauer, Ross O.; Grosberg, Alexander Y.; Grier, David G.

    2015-06-01

    Brownian vortexes are stochastic machines that use static nonconservative force fields to bias random thermal fluctuations into steadily circulating currents. The archetype for this class of systems is a colloidal sphere in an optical tweezer. Trapped near the focus of a strongly converging beam of light, the particle is displaced by random thermal kicks into the nonconservative part of the optical force field arising from radiation pressure, which then biases its diffusion. Assuming the particle remains localized within the trap, its time-averaged trajectory traces out a toroidal vortex. Unlike trivial Brownian vortexes, such as the biased Brownian pendulum, which circulate preferentially in the direction of the bias, the general Brownian vortex can change direction and even topology in response to temperature changes. Here we introduce a theory based on a perturbative expansion of the Fokker-Planck equation for weak nonconservative driving. The first-order solution takes the form of a modified Boltzmann relation and accounts for the rich phenomenology observed in experiments on micrometer-scale colloidal spheres in optical tweezers.

  15. Chiral perturbation theory with nucleons

    SciTech Connect

    Meissner, U.G.

    1991-09-01

    I review the constraints posed on the interactions of pions, nucleons and photons by the spontaneously broken chiral symmetry of QCD. The framework to perform these calculations, chiral perturbation theory, is briefly discussed in the meson sector. The method is a simultaneous expansion of the Greens functions in powers of external moments and quark masses around the massless case, the chiral limit. To perform this expansion, use is made of a phenomenological Lagrangian which encodes the Ward-identities and pertinent symmetries of QCD. The concept of chiral power counting is introduced. The main part of the lectures of consists in describing how to include baryons (nucleons) and how the chiral structure is modified by the fact that the nucleon mass in the chiral limit does not vanish. Particular emphasis is put on working out applications to show the strengths and limitations of the methods. Some processes which are discussed are threshold photopion production, low-energy compton scattering off nucleons, {pi}N scattering and the {sigma}-term. The implications of the broken chiral symmetry on the nuclear forces are briefly described. An alternative approach, in which the baryons are treated as very heavy fields, is touched upon.

  16. Density-fitted open-shell symmetry-adapted perturbation theory and application to π-stacking in benzene dimer cation and ionized DNA base pair steps

    NASA Astrophysics Data System (ADS)

    Gonthier, Jérôme F.; Sherrill, C. David

    2016-10-01

    Symmetry-Adapted Perturbation Theory (SAPT) is one of the most popular approaches to energy component analysis of non-covalent interactions between closed-shell systems, yielding both accurate interaction energies and meaningful interaction energy components. In recent years, the full open-shell equations for SAPT up to second-order in the intermolecular interaction and zeroth-order in the intramolecular correlation (SAPT0) were published [P. S. Zuchowski et al., J. Chem. Phys. 129, 084101 (2008); M. Hapka et al., ibid. 137, 164104 (2012)]. Here, we utilize density-fitted electron repulsion integrals to produce an efficient computational implementation. This approach is used to examine the effect of ionization on π-π interactions. For the benzene dimer radical cation, comparison against reference values indicates a good performance for open-shell SAPT0, except in cases with substantial charge transfer. For π stacking between hydrogen-bonded pairs of nucleobases, dispersion interactions still dominate binding, in spite of the creation of a positive charge.

  17. Comparison of the Effective Fragment Potential Method with Symmetry-Adapted Perturbation Theory in the Calculation of Intermolecular Energies for Ionic Liquids.

    PubMed

    Tan, Samuel Y S; Izgorodina, Ekaterina I

    2016-06-14

    The effective fragment potential (EFP) method that decomposes the interaction energy as a sum of the five fundamental forces-electrostatic, exchange-repulsion, polarization, dispersion, and charge transfer-was applied to a large test set of ionic liquid ion pairs and compared against the state-of-the-art method, Symmetry-Adapted Perturbation Theory (SAPT). The ion pairs include imidazolium and pyrrolidinium cations combined with anions that are routinely used in the field of ionic liquids. The aug-cc-pVDZ, aug-cc-pVTZ, and 6-311++G(d,p) basis sets were used for EFP, while SAPT2+3/aug-cc-pVDZ provided the benchmark energies. Differences between the two methods were found to be large, and strongly dependent on the anion type. For the aug-cc-pVTZ basis set, which produced the least errors, average relative errors were between 2.3% and 18.4% for pyrrolidinium ion pairs and between 2.1% and 27.7% for imidazolium ion pairs for each individual energetic component (excluding charge transfer), as well as the total interaction energy. Charge transfer gave the largest relative errors: 56% and 63% on average for pyrrolidinium- and imidazolium-based ion pairs, respectively. Scaling of the EFP components against SAPT2+3 showed improvement for polarization (induction) and dispersion terms, thus indicating potential for the development of cost-effective alternatives for intermolecular induction and dispersion potentials for ionic liquids.

  18. Perturbation theory in light-cone quantization

    SciTech Connect

    Langnau, A.

    1992-01-01

    A thorough investigation of light-cone properties which are characteristic for higher dimensions is very important. The easiest way of addressing these issues is by analyzing the perturbative structure of light-cone field theories first. Perturbative studies cannot be substituted for an analysis of problems related to a nonperturbative approach. However, in order to lay down groundwork for upcoming nonperturbative studies, it is indispensable to validate the renormalization methods at the perturbative level, i.e., to gain control over the perturbative treatment first. A clear understanding of divergences in perturbation theory, as well as their numerical treatment, is a necessary first step towards formulating such a program. The first objective of this dissertation is to clarify this issue, at least in second and fourth-order in perturbation theory. The work in this dissertation can provide guidance for the choice of counterterms in Discrete Light-Cone Quantization or the Tamm-Dancoff approach. A second objective of this work is the study of light-cone perturbation theory as a competitive tool for conducting perturbative Feynman diagram calculations. Feynman perturbation theory has become the most practical tool for computing cross sections in high energy physics and other physical properties of field theory. Although this standard covariant method has been applied to a great range of problems, computations beyond one-loop corrections are very difficult. Because of the algebraic complexity of the Feynman calculations in higher-order perturbation theory, it is desirable to automatize Feynman diagram calculations so that algebraic manipulation programs can carry out almost the entire calculation. This thesis presents a step in this direction. The technique we are elaborating on here is known as light-cone perturbation theory.

  19. Large-scale symmetry-adapted perturbation theory computations via density fitting and Laplace transformation techniques: investigating the fundamental forces of DNA-intercalator interactions.

    PubMed

    Hohenstein, Edward G; Parrish, Robert M; Sherrill, C David; Turney, Justin M; Schaefer, Henry F

    2011-11-01

    Symmetry-adapted perturbation theory (SAPT) provides a means of probing the fundamental nature of intermolecular interactions. Low-orders of SAPT (here, SAPT0) are especially attractive since they provide qualitative (sometimes quantitative) results while remaining tractable for large systems. The application of density fitting and Laplace transformation techniques to SAPT0 can significantly reduce the expense associated with these computations and make even larger systems accessible. We present new factorizations of the SAPT0 equations with density-fitted two-electron integrals and the first application of Laplace transformations of energy denominators to SAPT. The improved scalability of the DF-SAPT0 implementation allows it to be applied to systems with more than 200 atoms and 2800 basis functions. The Laplace-transformed energy denominators are compared to analogous partial Cholesky decompositions of the energy denominator tensor. Application of our new DF-SAPT0 program to the intercalation of DNA by proflavine has allowed us to determine the nature of the proflavine-DNA interaction. Overall, the proflavine-DNA interaction contains important contributions from both electrostatics and dispersion. The energetics of the intercalator interaction are are dominated by the stacking interactions (two-thirds of the total), but contain important contributions from the intercalator-backbone interactions. It is hypothesized that the geometry of the complex will be determined by the interactions of the intercalator with the backbone, because by shifting toward one side of the backbone, the intercalator can form two long hydrogen-bonding type interactions. The long-range interactions between the intercalator and the next-nearest base pairs appear to be negligible, justifying the use of truncated DNA models in computational studies of intercalation interaction energies.

  20. Degenerate Open Shell Density Perturbation Theory

    NASA Astrophysics Data System (ADS)

    Palenik, Mark; Dunlap, Brett

    The density perturbation theory (DPT) methodology we have developed applies the Hohenberg-Kohn theorem to perturbations in density functional theory. At each order, the energy is directly minimized with respect to the density at all lower orders. The difference between the perturbed and unperturbed densities is expanded in terms of a finite number of basis functions, and a single matrix inversion in this space reduces the complexity of the problem to that of non-interacting perturbation theory. For open-shell systems with symmetry, however, the situation becomes more complex. Typically, the perturbation will break the symmetry leading to a zeroth-order shift in the Kohn-Sham potential. Because the symmetry breaking is independent of the strength of the perturbation, the mapping from the initial to the perturbed KS potential is discontinuous and techniques from perturbation theory for noninteracting particles fail. We describe a rigorous formulation of DPT for use in systems that display an initial degeneracy, such as atoms and Fe55Cp*12 clusters and present initial calculations on these systems.

  1. The recursion relation in Lagrangian perturbation theory

    SciTech Connect

    Rampf, Cornelius

    2012-12-01

    We derive a recursion relation in the framework of Lagrangian perturbation theory, appropriate for studying the inhomogeneities of the large scale structure of the universe. We use the fact that the perturbative expansion of the matter density contrast is in one-to-one correspondence with standard perturbation theory (SPT) at any order. This correspondence has been recently shown to be valid up to fourth order for a non-relativistic, irrotational and dust-like component. Assuming it to be valid at arbitrary (higher) order, we express the Lagrangian displacement field in terms of the perturbative kernels of SPT, which are itself given by their own and well-known recursion relation. We argue that the Lagrangian solution always contains more non-linear information in comparison with the SPT solution, (mainly) if the non-perturbative density contrast is restored after the displacement field is obtained.

  2. Adapting SAFT-γ perturbation theory to site-based molecular dynamics simulation. II. Confined fluids and vapor-liquid interfaces.

    PubMed

    Ghobadi, Ahmadreza F; Elliott, J Richard

    2014-07-14

    In this work, a new classical density functional theory is developed for group-contribution equations of state (EOS). Details of implementation are demonstrated for the recently-developed SAFT-γ WCA EOS and selective applications are studied for confined fluids and vapor-liquid interfaces. The acronym WCA (Weeks-Chandler-Andersen) refers to the characterization of the reference part of the third-order thermodynamic perturbation theory applied in formulating the EOS. SAFT-γ refers to the particular form of "statistical associating fluid theory" that is applied to the fused-sphere, heteronuclear, united-atom molecular models of interest. For the monomer term, the modified fundamental measure theory is extended to WCA-spheres. A new chain functional is also introduced for fused and soft heteronuclear chains. The attractive interactions are taken into account by considering the structure of the fluid, thus elevating the theory beyond the mean field approximation. The fluctuations of energy are also included via a non-local third-order perturbation theory. The theory includes resolution of the density profiles of individual groups such as CH2 and CH3 and satisfies stoichiometric constraints for the density profiles. New molecular simulations are conducted to demonstrate the accuracy of each Helmholtz free energy contribution in reproducing the microstructure of inhomogeneous systems at the united-atom level of coarse graining. At each stage, comparisons are made to assess where the present theory stands relative to the current state of the art for studying inhomogeneous fluids. Overall, it is shown that the characteristic features of real molecular fluids are captured both qualitatively and quantitatively. For example, the average pore density deviates ∼2% from simulation data for attractive pentadecane in a 2-nm slit pore. Another example is the surface tension of ethane/heptane mixture, which deviates ∼1% from simulation data while the theory reproduces the

  3. Adapting SAFT-γ perturbation theory to site-based molecular dynamics simulation. II. Confined fluids and vapor-liquid interfaces

    NASA Astrophysics Data System (ADS)

    Ghobadi, Ahmadreza F.; Elliott, J. Richard

    2014-07-01

    In this work, a new classical density functional theory is developed for group-contribution equations of state (EOS). Details of implementation are demonstrated for the recently-developed SAFT-γ WCA EOS and selective applications are studied for confined fluids and vapor-liquid interfaces. The acronym WCA (Weeks-Chandler-Andersen) refers to the characterization of the reference part of the third-order thermodynamic perturbation theory applied in formulating the EOS. SAFT-γ refers to the particular form of "statistical associating fluid theory" that is applied to the fused-sphere, heteronuclear, united-atom molecular models of interest. For the monomer term, the modified fundamental measure theory is extended to WCA-spheres. A new chain functional is also introduced for fused and soft heteronuclear chains. The attractive interactions are taken into account by considering the structure of the fluid, thus elevating the theory beyond the mean field approximation. The fluctuations of energy are also included via a non-local third-order perturbation theory. The theory includes resolution of the density profiles of individual groups such as CH2 and CH3 and satisfies stoichiometric constraints for the density profiles. New molecular simulations are conducted to demonstrate the accuracy of each Helmholtz free energy contribution in reproducing the microstructure of inhomogeneous systems at the united-atom level of coarse graining. At each stage, comparisons are made to assess where the present theory stands relative to the current state of the art for studying inhomogeneous fluids. Overall, it is shown that the characteristic features of real molecular fluids are captured both qualitatively and quantitatively. For example, the average pore density deviates ˜2% from simulation data for attractive pentadecane in a 2-nm slit pore. Another example is the surface tension of ethane/heptane mixture, which deviates ˜1% from simulation data while the theory reproduces the excess

  4. Adapting SAFT-γ perturbation theory to site-based molecular dynamics simulation. II. Confined fluids and vapor-liquid interfaces

    SciTech Connect

    Ghobadi, Ahmadreza F.; Elliott, J. Richard

    2014-07-14

    In this work, a new classical density functional theory is developed for group-contribution equations of state (EOS). Details of implementation are demonstrated for the recently-developed SAFT-γ WCA EOS and selective applications are studied for confined fluids and vapor-liquid interfaces. The acronym WCA (Weeks-Chandler-Andersen) refers to the characterization of the reference part of the third-order thermodynamic perturbation theory applied in formulating the EOS. SAFT-γ refers to the particular form of “statistical associating fluid theory” that is applied to the fused-sphere, heteronuclear, united-atom molecular models of interest. For the monomer term, the modified fundamental measure theory is extended to WCA-spheres. A new chain functional is also introduced for fused and soft heteronuclear chains. The attractive interactions are taken into account by considering the structure of the fluid, thus elevating the theory beyond the mean field approximation. The fluctuations of energy are also included via a non-local third-order perturbation theory. The theory includes resolution of the density profiles of individual groups such as CH{sub 2} and CH{sub 3} and satisfies stoichiometric constraints for the density profiles. New molecular simulations are conducted to demonstrate the accuracy of each Helmholtz free energy contribution in reproducing the microstructure of inhomogeneous systems at the united-atom level of coarse graining. At each stage, comparisons are made to assess where the present theory stands relative to the current state of the art for studying inhomogeneous fluids. Overall, it is shown that the characteristic features of real molecular fluids are captured both qualitatively and quantitatively. For example, the average pore density deviates ∼2% from simulation data for attractive pentadecane in a 2-nm slit pore. Another example is the surface tension of ethane/heptane mixture, which deviates ∼1% from simulation data while the theory

  5. Interplay between tetrel and triel bonds in RC6H4CN⋯MF3CN⋯BX3 complexes: A combined symmetry-adapted perturbation theory, Møller-Plesset, and quantum theory of atoms-in-molecules study.

    PubMed

    Yourdkhani, Sirous; Korona, Tatiana; Hadipour, Nasser L

    2015-12-15

    Intermolecular ternary complexes composed of: (1) the centrally placed trifluoroacetonitrile or its higher analogs with central carbon exchanged by silicon or germanium (M = C, Si, Ge), (2) the benzonitrile molecule or its para derivatives on one side, and (3) the boron trifluoride of trichloride molecule (X = F, Cl) on the opposite side as well as the corresponding intermolecular tetrel- and triel-bonded binary complexes, were investigated by symmetry-adapted perturbation theory (SAPT) and the supermolecular Møller-Plesset method (MP2) at the complete basis set limit for optimized geometries. A character of interactions was studied by quantum theory of atoms-in-molecules (QTAIM). A comparison of interaction energies and QTAIM bond descriptors for dimers and trimers reveals that tetrel and triel bonds increase in their strength if present together in the trimer. For the triel-bonded complex, this growth leads to a change of the bond character from closed-shell to partly covalent for Si or Ge tetrel atoms, so the resulting bonding scheme corresponds to a preliminary stage of the SN2 reaction. Limitations of the Lewis theory of acids and bases were shown by its failure in predicting the stability order of the triel complexes. The necessity of including interaction energy terms beyond the electrostatic component for an elucidation of the nature of σ- and π-holes was presented by a SAPT energy decomposition and by a study of differences in monomer electrostatic potentials obtained either from isolated monomer densities, or from densities resulting from a perturbation with the effective field of another monomer.

  6. Covariant generalization of cosmological perturbation theory

    SciTech Connect

    Enqvist, Kari; Hoegdahl, Janne; Nurmi, Sami; Vernizzi, Filippo

    2007-01-15

    We present an approach to cosmological perturbations based on a covariant perturbative expansion between two worldlines in the real inhomogeneous universe. As an application, at an arbitrary order we define an exact scalar quantity which describes the inhomogeneities in the number of e-folds on uniform density hypersurfaces and which is conserved on all scales for a barotropic ideal fluid. We derive a compact form for its conservation equation at all orders and assign it a simple physical interpretation. To make a comparison with the standard perturbation theory, we develop a method to construct gauge-invariant quantities in a coordinate system at arbitrary order, which we apply to derive the form of the nth order perturbation in the number of e-folds on uniform density hypersurfaces and its exact evolution equation. On large scales, this provides the gauge-invariant expression for the curvature perturbation on uniform density hypersurfaces and its evolution equation at any order.

  7. Renormalization group optimized perturbation theory at finite temperatures

    NASA Astrophysics Data System (ADS)

    Kneur, Jean-Loïc; Pinto, Marcus B.

    2015-12-01

    A recently developed variant of the so-called optimized perturbation theory (OPT), making it perturbatively consistent with renormalization group (RG) properties, RGOPT, was shown to drastically improve its convergence for zero temperature theories. Here the RGOPT adapted to finite temperature is illustrated with a detailed evaluation of the two-loop pressure for the thermal scalar λ ϕ4 field theory. We show that already at the simple one-loop level this quantity is exactly scale-invariant by construction and turns out to qualitatively reproduce, with a rather simple procedure, results from more sophisticated resummation methods at two-loop order, such as the two-particle irreducible approach typically. This lowest order also reproduces the exact large-N results of the O (N ) model. Although very close in spirit, our RGOPT method and corresponding results differ drastically from similar variational approaches, such as the screened perturbation theory or its QCD-version, the (resummed) hard thermal loop perturbation theory. The latter approaches exhibit a sensibly degrading scale dependence at higher orders, which we identify as a consequence of missing RG invariance. In contrast RGOPT gives a considerably reduced scale dependence at two-loop level, even for relatively large coupling values √{λ /24 }˜O (1 ), making results much more stable as compared with standard perturbation theory, with expected similar properties for thermal QCD.

  8. Geometric perturbation theory and plasma physics

    SciTech Connect

    Omohundro, S.M.

    1985-01-01

    Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory, and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure in five different ways. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle-group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a long-standing question posed by Kruskal about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no adhoc elements, which is then applied to gyromotion. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A theory motivated by free electron lasers gives new restrictions on the change of area of projected parallelepipeds under canonical transformations.

  9. Conservative perturbation theory for nonconservative systems

    NASA Astrophysics Data System (ADS)

    Shah, Tirth; Chattopadhyay, Rohitashwa; Vaidya, Kedar; Chakraborty, Sagar

    2015-12-01

    In this paper, we show how to use canonical perturbation theory for dissipative dynamical systems capable of showing limit-cycle oscillations. Thus, our work surmounts the hitherto perceived barrier for canonical perturbation theory that it can be applied only to a class of conservative systems, viz., Hamiltonian systems. In the process, we also find Hamiltonian structure for an important subset of Liénard system—a paradigmatic system for modeling isolated and asymptotic oscillatory state. We discuss the possibility of extending our method to encompass an even wider range of nonconservative systems.

  10. Conservative perturbation theory for nonconservative systems.

    PubMed

    Shah, Tirth; Chattopadhyay, Rohitashwa; Vaidya, Kedar; Chakraborty, Sagar

    2015-12-01

    In this paper, we show how to use canonical perturbation theory for dissipative dynamical systems capable of showing limit-cycle oscillations. Thus, our work surmounts the hitherto perceived barrier for canonical perturbation theory that it can be applied only to a class of conservative systems, viz., Hamiltonian systems. In the process, we also find Hamiltonian structure for an important subset of Liénard system-a paradigmatic system for modeling isolated and asymptotic oscillatory state. We discuss the possibility of extending our method to encompass an even wider range of nonconservative systems. PMID:26764794

  11. Staggered heavy baryon chiral perturbation theory

    SciTech Connect

    Bailey, Jon A.

    2008-03-01

    Although taste violations significantly affect the results of staggered calculations of pseudoscalar and heavy-light mesonic quantities, those entering staggered calculations of baryonic quantities have not been quantified. Here I develop staggered chiral perturbation theory in the light-quark baryon sector by mapping the Symanzik action into heavy baryon chiral perturbation theory. For 2+1 dynamical quark flavors, the masses of flavor-symmetric nucleons are calculated to third order in partially quenched and fully dynamical staggered chiral perturbation theory. To this order the expansion includes the leading chiral logarithms, which come from loops with virtual decuplet-like states, as well as terms of O(m{sub {pi}}{sup 3}), which come from loops with virtual octet-like states. Taste violations enter through the meson propagators in loops and tree-level terms of O(a{sup 2}). The pattern of taste symmetry breaking and the resulting degeneracies and mixings are discussed in detail. The resulting chiral forms are appropriate to lattice results obtained with operators already in use and could be used to study the restoration of taste symmetry in the continuum limit. I assume that the fourth root of the fermion determinant can be incorporated in staggered chiral perturbation theory using the replica method.

  12. Staggered heavy baryon chiral perturbation theory

    NASA Astrophysics Data System (ADS)

    Bailey, Jon A.

    2008-03-01

    Although taste violations significantly affect the results of staggered calculations of pseudoscalar and heavy-light mesonic quantities, those entering staggered calculations of baryonic quantities have not been quantified. Here I develop staggered chiral perturbation theory in the light-quark baryon sector by mapping the Symanzik action into heavy baryon chiral perturbation theory. For 2+1 dynamical quark flavors, the masses of flavor-symmetric nucleons are calculated to third order in partially quenched and fully dynamical staggered chiral perturbation theory. To this order the expansion includes the leading chiral logarithms, which come from loops with virtual decuplet-like states, as well as terms of O(mπ3), which come from loops with virtual octet-like states. Taste violations enter through the meson propagators in loops and tree-level terms of O(a2). The pattern of taste symmetry breaking and the resulting degeneracies and mixings are discussed in detail. The resulting chiral forms are appropriate to lattice results obtained with operators already in use and could be used to study the restoration of taste symmetry in the continuum limit. I assume that the fourth root of the fermion determinant can be incorporated in staggered chiral perturbation theory using the replica method.

  13. Geometric perturbation theory and plasma physics

    SciTech Connect

    Omohundro, S.M.

    1985-04-04

    Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a question about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism.

  14. An analytical theory of the motion of PHOBOS and perturbation analysis

    NASA Astrophysics Data System (ADS)

    Emelyanov, N. V.; Nasonova, L. P.

    1989-08-01

    An analytical theory of the motion of Phobos is briefly described. The theory is realized by adapting the theory of artificial-satellite motion. A theoretical estimate of the coordinate computation method accuracy is about 0.5 m at an interval of 1 to 2 yrs. The perturbations of Phobos intermediate-orbit elements are analyzed and recommendations are made to account for perturbation factors. The possibility of determining the perturbing factors parameters from Phobos observations is discussed.

  15. Continuum methods in lattice perturbation theory

    SciTech Connect

    Becher, Thomas G

    2002-11-15

    We show how methods of continuum perturbation theory can be used to simplify perturbative lattice calculations. We use the technique of asymptotic expansions to expand lattice loop integrals around the continuum limit. After the expansion, all nontrivial dependence on momenta and masses is encoded in continuum loop integrals and the only genuine lattice integrals left are tadpole integrals. Using integration-by-parts relations all of these can be expressed in terms of a small number of master integrals. Four master integrals are needed for bosonic one loop integrals, sixteen in QCD with Wilson or staggered fermions.

  16. Screened perturbation theory to three loops

    SciTech Connect

    Andersen, Jens O.; Braaten, Eric; Strickland, Michael

    2001-05-15

    The thermal physics of a massless scalar field with a {phi}{sup 4} interaction is studied within screened perturbation theory (SPT). In this method the perturbative expansion is reorganized by adding and subtracting a mass term in the Lagrangian. We consider several different mass prescriptions that generalize the one-loop gap equation to two-loop order. We calculate the pressure and entropy to three-loop order and the screening mass to two-loop order. In contrast with the weak-coupling expansion, the SPT-improved approximations appear to converge even for rather large values of the coupling constant.

  17. Effective field theory of cosmological perturbations

    NASA Astrophysics Data System (ADS)

    Piazza, Federico; Vernizzi, Filippo

    2013-11-01

    The effective field theory of cosmological perturbations stems from considering a cosmological background solution as a state displaying spontaneous breaking of time translations and (adiabatic) perturbations as the related Nambu-Goldstone modes. With this insight, one can systematically develop a theory for the cosmological perturbations during inflation and, with minor modifications, also describe in full generality the gravitational interactions of dark energy, which are relevant for late-time cosmology. The formalism displays a unique set of Lagrangian operators containing an increasing number of cosmological perturbations and derivatives. We give an introductory description of the unitary gauge formalism for theories with broken gauge symmetry—that allows us to write down the most general Lagrangian—and of the Stückelberg ‘trick’—that allows to recover gauge invariance and to make the scalar field explicit. We show how to apply this formalism to gravity and cosmology and we reproduce the detailed analysis of the action in the ADM variables. We also review some basic applications to inflation and dark energy.

  18. Degenerate adiabatic perturbation theory: Foundations and applications

    NASA Astrophysics Data System (ADS)

    Rigolin, Gustavo; Ortiz, Gerardo

    2014-08-01

    We present details and expand on the framework leading to the recently introduced degenerate adiabatic perturbation theory [Phys. Rev. Lett. 104, 170406 (2010), 10.1103/PhysRevLett.104.170406], and on the formulation of the degenerate adiabatic theorem, along with its necessary and sufficient conditions [given in Phys. Rev. A 85, 062111 (2012), 10.1103/PhysRevA.85.062111]. We start with the adiabatic approximation for degenerate Hamiltonians that paves the way to a clear and rigorous statement of the associated degenerate adiabatic theorem, where the non-Abelian geometric phase (Wilczek-Zee phase) plays a central role to its quantitative formulation. We then describe the degenerate adiabatic perturbation theory, whose zeroth-order term is the degenerate adiabatic approximation, in its full generality. The parameter in the perturbative power-series expansion of the time-dependent wave function is directly associated to the inverse of the time it takes to drive the system from its initial to its final state. With the aid of the degenerate adiabatic perturbation theory we obtain rigorous necessary and sufficient conditions for the validity of the adiabatic theorem of quantum mechanics. Finally, to illustrate the power and wide scope of the methodology, we apply the framework to a degenerate Hamiltonian, whose closed-form time-dependent wave function is derived exactly, and also to other nonexactly solvable Hamiltonians whose solutions are numerically computed.

  19. A new size extensive multireference perturbation theory.

    PubMed

    Chen, Feiwu; Fan, Zhihui

    2014-01-15

    A new multireference perturbation series is derived based on the Rayleigh-Schrödinger perturbation theory. It is orbitally invariant. Its computational cost is comparable to the single reference Møller-Plesset perturbation theory. It is demonstrated numerically that the present multireference second- and third-order energies are size extensive by two types of supermolecules composed of H2 and BH monomers. Spectroscopic constants of F2(X1Σg+),Cl2(X1Σg+),C2-(X2Σg+),B2(X3Σg-),and C2+(X4Σg-) as well as the ground state energies of H2O, NH2, and CH2 at three bond lengths have been calculated with the second multireference perturbation theory. The dissociation behaviors of CH4 and HF have also been investigated. Comparisons with other approximate theoretical models as well as the experimental data have been carried out to show their relative performances.

  20. g-FUNCTION in Perturbation Theory

    NASA Astrophysics Data System (ADS)

    Konechny, Anatoly

    We present some explicit computations checking a particular form of gradient formula for a boundary beta function in two-dimensional quantum field theory on a disk. The form of the potential function and metric that we consider were introduced in Refs. 16 and 18 in the context of background independent open string field theory. We check the gradient formula to the third order in perturbation theory around a fixed point. Special consideration is given to situations when resonant terms are present exhibiting logarithmic divergences and universal nonlinearities in beta functions. The gradient formula is found to work to the given order.

  1. The Beauty of Lattice Perturbation Theory: the Role of Lattice Perturbation Theory in B Physics

    NASA Astrophysics Data System (ADS)

    Monahan, C. J.

    2012-12-01

    As new experimental data arrive from the LHC the prospect of indirectly detecting new physics through precision tests of the Standard Model grows more exciting. Precise experimental and theoretical inputs are required to test the unitarity of the CKM matrix and to search for new physics effects in rare decays. Lattice QCD calculations of non-perturbative inputs have reached a precision at the level of a few percent; in many cases aided by the use of lattice perturbation theory. This review examines the role of lattice perturbation theory in B physics calculations on the lattice in the context of two questions: how is lattice perturbation theory used in the different heavy quark formalisms implemented by the major lattice collaborations? And what role does lattice perturbation theory play in determinations of non-perturbative contributions to the physical processes at the heart of the search for new physics? Framing and addressing these questions reveals that lattice perturbation theory is a tool with a spectrum of applications in lattice B physics.

  2. Using Lagrangian Perturbation Theory for Precision Cosmology

    NASA Astrophysics Data System (ADS)

    Sugiyama, Naonori S.

    2014-06-01

    We explore the Lagrangian perturbation theory (LPT) at one-loop order with Gaussian initial conditions. We present an expansion method to approximately compute the power spectrum LPT. Our approximate solution has good convergence in the series expansion and enables us to compute the power spectrum in LPT accurately and quickly. Non-linear corrections in this theory naturally satisfy the law of conservation of mass because the relation between matter density and the displacement vector of dark matter corresponds to the conservation of mass. By matching the one-loop solution in LPT to the two-loop solution in standard perturbation theory, we present an approximate solution of the power spectrum which has higher order corrections than the two-loop order in standard perturbation theory with the conservation of mass satisfied. With this approximation, we can use LPT to compute a non-linear power spectrum without any free parameters, and this solution agrees with numerical simulations at k = 0.2 h Mpc-1 and z = 0.35 to better than 2%.

  3. Using Lagrangian perturbation theory for precision cosmology

    SciTech Connect

    Sugiyama, Naonori S.

    2014-06-10

    We explore the Lagrangian perturbation theory (LPT) at one-loop order with Gaussian initial conditions. We present an expansion method to approximately compute the power spectrum LPT. Our approximate solution has good convergence in the series expansion and enables us to compute the power spectrum in LPT accurately and quickly. Non-linear corrections in this theory naturally satisfy the law of conservation of mass because the relation between matter density and the displacement vector of dark matter corresponds to the conservation of mass. By matching the one-loop solution in LPT to the two-loop solution in standard perturbation theory, we present an approximate solution of the power spectrum which has higher order corrections than the two-loop order in standard perturbation theory with the conservation of mass satisfied. With this approximation, we can use LPT to compute a non-linear power spectrum without any free parameters, and this solution agrees with numerical simulations at k = 0.2 h Mpc{sup –1} and z = 0.35 to better than 2%.

  4. Approaching the basis set limit for DFT calculations using an environment-adapted minimal basis with perturbation theory: Formulation, proof of concept, and a pilot implementation

    NASA Astrophysics Data System (ADS)

    Mao, Yuezhi; Horn, Paul R.; Mardirossian, Narbe; Head-Gordon, Teresa; Skylaris, Chris-Kriton; Head-Gordon, Martin

    2016-07-01

    Recently developed density functionals have good accuracy for both thermochemistry (TC) and non-covalent interactions (NC) if very large atomic orbital basis sets are used. To approach the basis set limit with potentially lower computational cost, a new self-consistent field (SCF) scheme is presented that employs minimal adaptive basis (MAB) functions. The MAB functions are optimized on each atomic site by minimizing a surrogate function. High accuracy is obtained by applying a perturbative correction (PC) to the MAB calculation, similar to dual basis approaches. Compared to exact SCF results, using this MAB-SCF (PC) approach with the same large target basis set produces <0.15 kcal/mol root-mean-square deviations for most of the tested TC datasets, and <0.1 kcal/mol for most of the NC datasets. The performance of density functionals near the basis set limit can be even better reproduced. With further improvement to its implementation, MAB-SCF (PC) is a promising lower-cost substitute for conventional large-basis calculations as a method to approach the basis set limit of modern density functionals.

  5. Approaching the basis set limit for DFT calculations using an environment-adapted minimal basis with perturbation theory: Formulation, proof of concept, and a pilot implementation.

    PubMed

    Mao, Yuezhi; Horn, Paul R; Mardirossian, Narbe; Head-Gordon, Teresa; Skylaris, Chris-Kriton; Head-Gordon, Martin

    2016-07-28

    Recently developed density functionals have good accuracy for both thermochemistry (TC) and non-covalent interactions (NC) if very large atomic orbital basis sets are used. To approach the basis set limit with potentially lower computational cost, a new self-consistent field (SCF) scheme is presented that employs minimal adaptive basis (MAB) functions. The MAB functions are optimized on each atomic site by minimizing a surrogate function. High accuracy is obtained by applying a perturbative correction (PC) to the MAB calculation, similar to dual basis approaches. Compared to exact SCF results, using this MAB-SCF (PC) approach with the same large target basis set produces <0.15 kcal/mol root-mean-square deviations for most of the tested TC datasets, and <0.1 kcal/mol for most of the NC datasets. The performance of density functionals near the basis set limit can be even better reproduced. With further improvement to its implementation, MAB-SCF (PC) is a promising lower-cost substitute for conventional large-basis calculations as a method to approach the basis set limit of modern density functionals. PMID:27475350

  6. Approaching the basis set limit for DFT calculations using an environment-adapted minimal basis with perturbation theory: Formulation, proof of concept, and a pilot implementation.

    PubMed

    Mao, Yuezhi; Horn, Paul R; Mardirossian, Narbe; Head-Gordon, Teresa; Skylaris, Chris-Kriton; Head-Gordon, Martin

    2016-07-28

    Recently developed density functionals have good accuracy for both thermochemistry (TC) and non-covalent interactions (NC) if very large atomic orbital basis sets are used. To approach the basis set limit with potentially lower computational cost, a new self-consistent field (SCF) scheme is presented that employs minimal adaptive basis (MAB) functions. The MAB functions are optimized on each atomic site by minimizing a surrogate function. High accuracy is obtained by applying a perturbative correction (PC) to the MAB calculation, similar to dual basis approaches. Compared to exact SCF results, using this MAB-SCF (PC) approach with the same large target basis set produces <0.15 kcal/mol root-mean-square deviations for most of the tested TC datasets, and <0.1 kcal/mol for most of the NC datasets. The performance of density functionals near the basis set limit can be even better reproduced. With further improvement to its implementation, MAB-SCF (PC) is a promising lower-cost substitute for conventional large-basis calculations as a method to approach the basis set limit of modern density functionals.

  7. Perturbation theory for solitons in optical fibers

    NASA Astrophysics Data System (ADS)

    Kaup, D. J.

    1990-11-01

    Using a singular perturbation expansion, we study the evolution of a Raman loss compensated soliton in an optical fiber. Our analytical results agree quite well with the numerical results of Mollenauer, Gordon, and Islam [IEEE J. Quantum Electron. QE-22, 157 (1986)]. However, there are some differences in that our theory predicts an additional structure that was only partially seen in the numerical calculations. Our analytical results do give a quite good qualitative and quantitative check of the numerical results.

  8. Tests of Chiral Perturbation Theory with COMPASS

    SciTech Connect

    Friedrich, Jan

    2010-12-28

    The COMPASS experiment at CERN studies with high precision pion-photon induced reactions on nuclear targets via the Primakoff effect. This offers the possibility to test chiral perturbation theory (ChPT) in various channels: Pion Compton scattering allows to clarify the longstanding question of the pion polarisabilities, single neutral pion production is related to the chiral anomaly, and for the two-pion production cross sections exist as yet untested ChPT predictions.

  9. Perturbation Theory for Superfluid in Nonuniform Potential

    NASA Astrophysics Data System (ADS)

    Koshida, Shinji; Kato, Yusuke

    2016-05-01

    Perturbation theory of superfluid fraction in terms of nonuniform potential is constructed. We find that the coefficient of the leading term is determined by the dynamical structure factor or density fluctuation of the system. The results for the ideal Bose gas and the interacting Bose system with linear dispersion are consistent to implications from Landau's criterion. We also find that the superfluidity of Tomonaga-Luttinger liquid with K>2 is shown to be stable against nonuniform potential.

  10. Dark matter dispersion tensor in perturbation theory

    NASA Astrophysics Data System (ADS)

    Aviles, Alejandro

    2016-03-01

    We compute the dark matter velocity dispersion tensor up to third order in perturbation theory using the Lagrangian formalism, revealing growing solutions at the third and higher orders. Our results are general and can be used for any other perturbative formalism. As an application, corrections to the matter power spectrum are calculated, and we find that some of them have the same structure as those in the effective field theory of large-scale structure, with "EFT-like" coefficients that grow quadratically with the linear growth function and are further suppressed by powers of the logarithmic linear growth factor f ; other corrections present additional k dependence. Due to the velocity dispersions, there exists a free-streaming scale that suppresses the whole 1-loop power spectrum. Furthermore, we find that as a consequence of the nonlinear evolution, the free-streaming length is shifted towards larger scales, wiping out more structure than that expected in linear theory. Therefore, we argue that the formalism developed here is better suited for a perturbation treatment of warm dark matter or neutrino clustering, where the velocity dispersion effects are well known to be important. We discuss implications related to the nature of dark matter.

  11. Perturbative quantum gravity in double field theory

    NASA Astrophysics Data System (ADS)

    Boels, Rutger H.; Horst, Christoph

    2016-04-01

    We study perturbative general relativity with a two-form and a dilaton using the double field theory formulation which features explicit index factorisation at the Lagrangian level. Explicit checks to known tree level results are performed. In a natural covariant gauge a ghost-like scalar which contributes even at tree level is shown to decouple consistently as required by perturbative unitarity. In addition, a lightcone gauge is explored which bypasses the problem altogether. Using this gauge to study BCFW on-shell recursion, we can show that most of the D-dimensional tree level S-matrix of the theory, including all pure graviton scattering amplitudes, is reproduced by the double field theory. More generally, we argue that the integrand may be reconstructed from its single cuts and provide limited evidence for off-shell cancellations in the Feynman graphs. As a straightforward application of the developed technology double field theory-like expressions for four field string corrections are derived.

  12. Inflationary perturbation theory is geometrical optics in phase space

    SciTech Connect

    Seery, David; Frazer, Jonathan; Mulryne, David J.; Ribeiro, Raquel H. E-mail: D.Mulryne@qmul.ac.uk E-mail: R.Ribeiro@damtp.cam.ac.uk

    2012-09-01

    A pressing problem in comparing inflationary models with observation is the accurate calculation of correlation functions. One approach is to evolve them using ordinary differential equations ({sup t}ransport equations{sup )}, analogous to the Schwinger-Dyson hierarchy of in-out quantum field theory. We extend this approach to the complete set of momentum space correlation functions. A formal solution can be obtained using raytracing techniques adapted from geometrical optics. We reformulate inflationary perturbation theory in this language, and show that raytracing reproduces the familiar 'δN' Taylor expansion. Our method produces ordinary differential equations which allow the Taylor coefficients to be computed efficiently. We use raytracing methods to express the gauge transformation between field fluctuations and the curvature perturbation, ζ, in geometrical terms. Using these results we give a compact expression for the nonlinear gauge-transform part of f{sub NL} in terms of the principal curvatures of uniform energy-density hypersurfaces in field space.

  13. Applications of partially quenched chiral perturbation theory

    SciTech Connect

    Golterman, M.F.; Leung, K.C.

    1998-05-01

    Partially quenched theories are theories in which the valence- and sea-quark masses are different. In this paper we calculate the nonanalytic one-loop corrections of some physical quantities: the chiral condensate, weak decay constants, Goldstone boson masses, B{sub K}, and the K{sup +}{r_arrow}{pi}{sup +}{pi}{sup 0} decay amplitude, using partially quenched chiral perturbation theory. Our results for weak decay constants and masses agree with, and generalize, results of previous work by Sharpe. We compare B{sub K} and the K{sup +} decay amplitude with their real-world values in some examples. For the latter quantity, two other systematic effects that plague lattice computations, namely, finite-volume effects and unphysical values of the quark masses and pion external momenta, are also considered. We find that typical one-loop corrections can be substantial. {copyright} {ital 1998} {ital The American Physical Society}

  14. Efficient perturbation theory for quantum lattice models.

    PubMed

    Hafermann, H; Li, G; Rubtsov, A N; Katsnelson, M I; Lichtenstein, A I; Monien, H

    2009-05-22

    We present a novel approach to long-range correlations beyond dynamical mean-field theory, through a ladder approximation to dual fermions. The new technique is applied to the two-dimensional Hubbard model. We demonstrate that the transformed perturbation series for the nonlocal dual fermions has superior convergence properties over standard diagrammatic techniques. The critical Néel temperature of the mean-field solution is suppressed in the ladder approximation, in accordance with quantum Monte Carlo results. An illustration of how the approach captures and allows us to distinguish short- and long-range correlations is given.

  15. A new perturbation theory for electrolyte solutions

    NASA Astrophysics Data System (ADS)

    Drunsel, F.; Zmpitas, W.; Gross, J.

    2014-08-01

    Developing physically based equations of state for electrolyte solutions is demanding due to the long range behaviour of the Coulombic interaction potentials. In this work, we present a new perturbation approach for nonprimitive model electrolyte solutions consisting of hard spheres with a positive or negative point charge or with point dipoles. We overcome the problem of diverging correlation integrals by separating the interaction potentials into short ranged parts and a long ranged contribution. For the point charges, the division is done like in most implementations of the Ewald sum. The perturbation expansion to 3rd order is formulated using the short ranged part of the potentials only, which results in converging correlation integrals for which we provide simple analytical expressions. The long range contribution to the Helmholtz energy is taken into account by a analytical term that has recently been presented by Rodgers and Weeks [J. M. Rodgers and J. D. Weeks, J. Chem. Phys. 131, 244108 (2009)]. In order to assess the proposed theory, we present molecular simulation data for Helmholtz energies of the same model electrolyte solutions. Predictions for the Helmholtz energy from the new theory are found to be in very good agreement with results from the molecular simulations for all state points we regarded.

  16. Molecular cluster perturbation theory. I. Formalism

    NASA Astrophysics Data System (ADS)

    Byrd, Jason N.; Jindal, Nakul; Molt, Robert W., Jr.; Bartlett, Rodney J.; Sanders, Beverly A.; Lotrich, Victor F.

    2015-11-01

    We present second-order molecular cluster perturbation theory (MCPT(2)), a linear scaling methodology to calculate arbitrarily large systems with explicit calculation of individual wave functions in a coupled-cluster framework. This new MCPT(2) framework uses coupled-cluster perturbation theory and an expansion in terms of molecular dimer interactions to obtain molecular wave functions that are infinite order in both the electronic fluctuation operator and all possible dimer (and products of dimers) interactions. The MCPT(2) framework has been implemented in the new SIA/Aces4 parallel architecture, making use of the advanced dynamic memory control and fine-grained parallelism to perform very large explicit molecular cluster calculations. To illustrate the power of this method, we have computed energy shifts, lattice site dipole moments, and harmonic vibrational frequencies via explicit calculation of the bulk system for the polar and non-polar polymorphs of solid hydrogen fluoride. The explicit lattice size (without using any periodic boundary conditions) was expanded up to 1000 HF molecules, with 32,000 basis functions and 10,000 electrons. Our obtained HF lattice site dipole moments and harmonic vibrational frequencies agree well with the existing literature.

  17. Remarks on simple modified perturbation theory

    NASA Astrophysics Data System (ADS)

    Shirkov, D. V.

    2015-03-01

    The goal is to devise a pQCD modification that should be regular in the low energy region and could serve practically for the data analysis below 1 GeV up to the infra-red limit. The recently observed "blow-up" of the 4-loop pQCD series for the Bjorken sum rule form-factor around Q ≲ 1 GeV and partial resolving of the issue with the help of the Analytic Perturbation Theory (APT) until Q ˜ 0.6 GeV provided the impetus for this attempt. The " massive pQCD" under construction has two grounds. The first is pQCD with only one parameter added, an effective " glueball mass" m ρ ≲ M glb ≲ 1 GeV, serving as an infrared regulator. Roughly, we introduce it by changing the ultra-violet ln Q 2 for a massive log, ln( Q 2 + M {/glb 2}) regular in the low energy region and finite in the infra-red limit. The second stems from the ghost-free APT comprising non-power perturbative expansion that makes it compatible with linear integral transformations.

  18. Modified contour-improved perturbation theory

    SciTech Connect

    Cvetic, Gorazd; Loewe, Marcelo; Martinez, Cristian; Valenzuela, Cristian

    2010-11-01

    The semihadronic tau decay width allows a clean extraction of the strong coupling constant at low energies. We present a modification of the standard ''contour-improved'' method based on a derivative expansion of the Adler function. The new approach has some advantages compared to contour-improved perturbation theory. The renormalization scale dependence is weaker by more than a factor of 2 and the last term of the expansion is reduced by about 10%, while the renormalization scheme dependence remains approximately equal. The extracted QCD coupling at the tau mass scale is by 2% lower than the contour-improved value. We find {alpha}{sub s}(M{sub Z}{sup 2})=0.1211{+-}0.0010.

  19. Perturbative analysis in higher-spin theories

    NASA Astrophysics Data System (ADS)

    Didenko, V. E.; Misuna, N. G.; Vasiliev, M. A.

    2016-07-01

    A new scheme of the perturbative analysis of the nonlinear HS equations is developed giving directly the final result for the successive application of the homotopy integrations which appear in the standard approach. It drastically simplifies the analysis and results from the application of the standard spectral sequence approach to the higherspin covariant derivatives, allowing us in particular to reduce multiple homotopy integrals resulting from the successive application of the homotopy trick to a single integral. Efficiency of the proposed method is illustrated by various examples. In particular, it is shown how the Central on-shell theorem of the free theory immediately results from the nonlinear HS field equations with no intermediate computations.

  20. Non-perturbative String Theory from Water Waves

    SciTech Connect

    Iyer, Ramakrishnan; Johnson, Clifford V.; Pennington, Jeffrey S.; /SLAC

    2012-06-14

    We use a combination of a 't Hooft limit and numerical methods to find non-perturbative solutions of exactly solvable string theories, showing that perturbative solutions in different asymptotic regimes are connected by smooth interpolating functions. Our earlier perturbative work showed that a large class of minimal string theories arise as special limits of a Painleve IV hierarchy of string equations that can be derived by a similarity reduction of the dispersive water wave hierarchy of differential equations. The hierarchy of string equations contains new perturbative solutions, some of which were conjectured to be the type IIA and IIB string theories coupled to (4, 4k ? 2) superconformal minimal models of type (A, D). Our present paper shows that these new theories have smooth non-perturbative extensions. We also find evidence for putative new string theories that were not apparent in the perturbative analysis.

  1. Flexoelectricity from density-functional perturbation theory

    NASA Astrophysics Data System (ADS)

    Stengel, Massimiliano

    2013-11-01

    We derive the complete flexoelectric tensor, including electronic and lattice-mediated effects, of an arbitrary insulator in terms of the microscopic linear response of the crystal to atomic displacements. The basic ingredient, which can be readily calculated from first principles in the framework of density-functional perturbation theory, is the quantum-mechanical probability current response to a long-wavelength acoustic phonon. Its second-order Taylor expansion in the wave vector q around the Γ (q=0) point in the Brillouin zone naturally yields the flexoelectric tensor. At order one in q we recover Martin's theory of piezoelectricity [Martin, Phys. Rev. B 5, 1607 (1972)], thus providing an alternative derivation thereof. To put our derivations on firm theoretical grounds, we perform a thorough analysis of the nonanalytic behavior of the dynamical matrix and other response functions in a vicinity of Γ. Based on this analysis, we find that there is an ambiguity in the specification of the “zero macroscopic field” condition in the flexoelectric case; such arbitrariness can be related to an analytic band-structure term, in close analogy to the theory of deformation potentials. As a by-product, we derive a rigorous generalization of the Cochran-Cowley formula [Cochran and Cowley, J. Phys. Chem. Solids 23, 447 (1962)] to higher orders in q. This can be of great utility in building reliable atomistic models of electromechanical phenomena, as well as for improving the accuracy of the calculation of phonon dispersion curves. Finally, we discuss the physical interpretation of the various contributions to the flexoelectric response, either in the static or dynamic regime, and we relate our findings to earlier theoretical works on the subject.

  2. Kato expansion in quantum canonical perturbation theory

    NASA Astrophysics Data System (ADS)

    Nikolaev, Andrey

    2016-06-01

    This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson's ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.

  3. Tractability gains in symmetry-adapted perturbation theory including coupled double excitations: CCD+ST(CCD) dispersion with natural orbital truncations.

    PubMed

    Parrish, Robert M; Hohenstein, Edward G; Sherrill, C David

    2013-11-01

    This work focuses on efficient and accurate treatment of the intermolecular dispersion interaction using the CCD+ST(CCD) dispersion approach formulated by Williams et al. [J. Chem. Phys. 103, 4586 (1995)]. We apply natural orbital truncation techniques to the solution of the monomer coupled-cluster double (CCD) equations, yielding substantial accelerations in this computationally demanding portion of the SAPT2+(CCD), SAPT2+(3)(CCD), and SAPT2+3(CCD) analyses. It is shown that the wholly rate-limiting dimer-basis particle-particle ladder term can be computed in a reduced natural virtual space which is essentially the same size as the monomer-basis virtual space, with an error on the order of a few thousandths of 1 kcal mol(-1). Coupled with our existing natural orbital techniques for the perturbative triple excitation contributions [E. G. Hohenstein and C. D. Sherrill, J. Chem. Phys. 133, 104107 (2010)], this technique provides speedups of greater than an order of magnitude for the evaluation of the complete SAPT2+3(CCD) decomposition, with a total error of a few hundredths of 1 kcal mol(-1). The combined approach yields tractability gains of almost 2× in the system size, allowing for SAPT2+3(CCD)/aug-cc-pVTZ analysis to be performed for systems such as adenine-thymine for the first time. Natural orbital based SAPT2+3(CCD)/aug-cc-pVTZ results are presented for stacked and hydrogen-bonded configurations of uracil dimer and the adenine-thymine dimer.

  4. Perturbation Theory for Parent Hamiltonians of Matrix Product States

    NASA Astrophysics Data System (ADS)

    Szehr, Oleg; Wolf, Michael M.

    2015-05-01

    This article investigates the stability of the ground state subspace of a canonical parent Hamiltonian of a Matrix product state against local perturbations. We prove that the spectral gap of such a Hamiltonian remains stable under weak local perturbations even in the thermodynamic limit, where the entire perturbation might not be bounded. Our discussion is based on preceding work by Yarotsky that develops a perturbation theory for relatively bounded quantum perturbations of classical Hamiltonians. We exploit a renormalization procedure, which on large scale transforms the parent Hamiltonian of a Matrix product state into a classical Hamiltonian plus some perturbation. We can thus extend Yarotsky's results to provide a perturbation theory for parent Hamiltonians of Matrix product states and recover some of the findings of the independent contributions (Cirac et al in Phys Rev B 8(11):115108, 2013) and (Michalakis and Pytel in Comm Math Phys 322(2):277-302, 2013).

  5. A synthetic theory for the perturbations of Titan on Hyperion

    NASA Astrophysics Data System (ADS)

    Taylor, D. B.

    1992-11-01

    A theory for Hyperion is developed in which the perturbations by Titan have been developed synthetically. These perturbations were derived by fitting a sum of periodic terms to the numerical integration of Sinclair and Taylor (1985) extended to +/- 25 yr from the epoch used, 1973.87. A theory for Hyperion, constructed by adding the solar perturbations to the synthetic theory and including expressions for the motion of the orbit plane, was, together with the theories for the other major satellites of Saturn fitted to observations from 1967 to 1983.

  6. Concurrent multiple-state analytic perturbation theory via supersymmetry

    NASA Astrophysics Data System (ADS)

    Dhatt, Sharmistha; Bhattacharyya, Kamal

    2011-04-01

    Conventional nondegenerate perturbation theory for some nth state starts with the corresponding unperturbed state. The present formulation yields recursively perturbation expansions for any bound state using the sole information of the unperturbed ground state. Logarithmic perturbation theory is exploited along with supersymmetric quantum mechanics to achieve this end. As the method involves ground-state perturbations of a series of supersymmetric Hamiltonians, concern about nodal shifts of targeted excited states arises only at the ultimate step, thus, minimizing considerably the labor of clumsy computations involved in dealing with excited states.

  7. Quarks in Coulomb gauge perturbation theory

    SciTech Connect

    Popovici, C.; Watson, P.; Reinhardt, H.

    2009-02-15

    Coulomb gauge quantum chromodynamics within the first order functional formalism is considered. The quark contributions to the Dyson-Schwinger equations are derived and one-loop perturbative results for the two-point functions are presented.

  8. Aspects of Perturbative Quantum Field Theory

    NASA Astrophysics Data System (ADS)

    Srednyak, Stanislav

    This thesis consists of three parts. The first is devoted to the calculation of multiplicity of two-gluon production in heavy ion collisions in the framework of Colour Glass Condensate. The second exhibits a finite basis for the perturbative correlation functions at a given loop order. The third demonstrates that the number of integrations in a perturbative amplitude can be reduced in half in even dimensions, and provides explicit formula for such a reduction in the (2,2) signature.

  9. Gauge and motion in perturbation theory

    NASA Astrophysics Data System (ADS)

    Pound, Adam

    2015-08-01

    Through second order in perturbative general relativity, a small compact object in an external vacuum spacetime obeys a generalized equivalence principle: although it is accelerated with respect to the external background geometry, it is in free fall with respect to a certain effective vacuum geometry. However, this single principle takes very different mathematical forms, with very different behaviors, depending on how one treats perturbed motion. Furthermore, any description of perturbed motion can be altered by a gauge transformation. In this paper, I clarify the relationship between two treatments of perturbed motion and the gauge freedom in each. I first show explicitly how one common treatment, called the Gralla-Wald approximation, can be derived from a second, called the self-consistent approximation. I next present a general treatment of smooth gauge transformations in both approximations, in which I emphasize that the approximations' governing equations can be formulated in an invariant manner. All of these analyses are carried through second perturbative order, but the methods are general enough to go to any order. Furthermore, the tools I develop, and many of the results, should have broad applicability to any description of perturbed motion, including osculating-geodesic and two-timescale descriptions.

  10. Second-order perturbation theory: Problems on large scales

    NASA Astrophysics Data System (ADS)

    Pound, Adam

    2015-11-01

    In general-relativistic perturbation theory, a point mass accelerates away from geodesic motion due to its gravitational self-force. Because the self-force is small, one can often approximate the motion as geodesic. However, it is well known that self-force effects accumulate over time, making the geodesic approximation fail on long time scales. It is less well known that this failure at large times translates to a failure at large distances as well. At second perturbative order, two large-distance pathologies arise: spurious secular growth and infrared-divergent retarded integrals. Both stand in the way of practical computations of second-order self-force effects. Utilizing a simple flat-space scalar toy model, I develop methods to overcome these obstacles. The secular growth is tamed with a multiscale expansion that captures the system's slow evolution. The divergent integrals are eliminated by matching to the correct retarded solution at large distances. I also show how to extract conservative self-force effects by taking local-in-time "snapshots" of the global solution. These methods are readily adaptable to the physically relevant case of a point mass orbiting a black hole.

  11. Renormalization-scheme-invariant perturbation theory: Miracle or mirage

    SciTech Connect

    Chyla, J.

    1985-05-15

    A recently proposed solution to the renormalization-scheme ambiguity in perturbation theory is critically analyzed and shown to possess another kind of ambiguity closely related to the one it is supposed to cure.

  12. Convergent perturbation theory for lattice models with fermions

    NASA Astrophysics Data System (ADS)

    Sazonov, V. K.

    2016-05-01

    The standard perturbation theory in QFT and lattice models leads to the asymptotic expansions. However, an appropriate regularization of the path or lattice integrals allows one to construct convergent series with an infinite radius of the convergence. In the earlier studies, this approach was applied to the purely bosonic systems. Here, using bosonization, we develop the convergent perturbation theory for a toy lattice model with interacting fermionic and bosonic fields.

  13. Adjoint Function: Physical Basis of Variational & Perturbation Theory in Transport

    2009-07-27

    Version 00 Dr. J.D. Lewins has now released the following legacy book for free distribution: Importance: The Adjoint Function: The Physical Basis of Variational and Perturbation Theory in Transport and Diffusion Problems, North-Holland Publishing Company - Amsterdam, 582 pages, 1966 Introduction: Continuous Systems and the Variational Principle 1. The Fundamental Variational Principle 2. The Importance Function 3. Adjoint Equations 4. Variational Methods 5. Perturbation and Iterative Methods 6. Non-Linear Theory

  14. Higher-order Lagrangian perturbative theory for the Cosmic Web

    NASA Astrophysics Data System (ADS)

    Tatekawa, Takayuki; Mizuno, Shuntaro

    2016-10-01

    Zel'dovich proposed Lagrangian perturbation theory (LPT) for structure formation in the Universe. After this, higher-order perturbative equations have been derived. Recently fourth-order LPT (4LPT) have been derived by two group. We have shown fifth-order LPT (5LPT) In this conference, we notice fourth- and more higher-order perturbative equations. In fourth-order perturbation, because of the difference in handling of spatial derivative, there are two groups of equations. Then we consider the initial conditions for cosmological N-body simulations. Crocce, Pueblas, and Scoccimarro (2007) noticed that second-order perturbation theory (2LPT) is required for accuracy of several percents. We verify the effect of 3LPT initial condition for the simulations. Finally we discuss the way of further improving approach and future applications of LPTs.

  15. Cosmological perturbation theory in 1+1 dimensions

    NASA Astrophysics Data System (ADS)

    McQuinn, Matthew; White, Martin

    2016-01-01

    Many recent studies have highlighted certain failures of the standard Eulerian-space cosmological perturbation theory (SPT). Its problems include (1) not capturing large-scale bulk flows [leading to an Script O( 1) error in the 1-loop SPT prediction for the baryon acoustic peak in the correlation function], (2) assuming that the Universe behaves as a pressureless, inviscid fluid, and (3) treating fluctuations on scales that are non-perturbative as if they were. Recent studies have highlighted the successes of perturbation theory in Lagrangian space or theories that solve equations for the effective dynamics of smoothed fields. Both approaches mitigate some or all of the aforementioned issues with SPT. We discuss these physical developments by specializing to the simplified 1D case of gravitationally interacting sheets, which allows us to substantially reduces the analytic overhead and still (as we show) maintain many of the same behaviors as in 3D. In 1D, linear-order Lagrangian perturbation theory ("the Zeldovich approximation") is exact up to shell crossing, and we prove that nth-order Eulerian perturbation theory converges to the Zeldovich approximation as narrow ∞. In no 1D cosmology that we consider (including a CDM-like case and power-law models) do these theories describe accurately the matter power spectrum on any mildly nonlinear scale. We find that theories based on effective equations are much more successful at describing the dynamics. Finally, we discuss many topics that have recently appeared in the perturbation theory literature such as beat coupling, the shift and smearing of the baryon acoustic oscillation feature, and the advantages of Fourier versus configuration space. Our simplified 1D case serves as an intuitive review of these perturbation theory results.

  16. Multipartitioning Møller-Plesset perturbation theory: Size-extensivity at third order and symmetry conservation

    NASA Astrophysics Data System (ADS)

    Rolik, Zoltán; Szabados, Ágnes

    Multipartitioning multireference many-body perturbation theory (Zaitevskii and Malrieu, Chem. Phys. Lett. 1995, 233, 597) is investigated with regard to symmetry and size-extensivity. We show that the spin-adapted formulation suffers from spatial symmetry breaking and propose a general symmetry-conserving zero-order Hamiltonian. We analyze size-extensivity of various partitionings at the third order and find that extensivity holds if one-particle quantities in the zero-order Hamiltonian are properly chosen. In particular, third order of the spin-adapted and general symmetry-adapted theory prove to be extensive.

  17. Precise effective masses from density functional perturbation theory

    NASA Astrophysics Data System (ADS)

    Laflamme Janssen, J.; Gillet, Y.; Poncé, S.; Martin, A.; Torrent, M.; Gonze, X.

    2016-05-01

    The knowledge of effective masses is a key ingredient to analyze numerous properties of semiconductors, like carrier mobilities, (magneto)transport properties, or band extrema characteristics yielding carrier densities and density of states. Currently, these masses are usually calculated using finite-difference estimation of density functional theory (DFT) electronic band curvatures. However, finite differences require an additional convergence study and are prone to numerical noise. Moreover, the concept of effective mass breaks down at degenerate band extrema. We assess the former limitation by developing a method that allows to obtain the Hessian of DFT bands directly, using density functional perturbation theory. Then, we solve the latter issue by adapting the concept of "transport equivalent effective mass" to the k .p ̂ framework. The numerical noise inherent to finite-difference methods is thus eliminated, along with the associated convergence study. The resulting method is therefore more general, more robust, and simpler to use, which makes it especially appropriate for high-throughput computing. After validating the developed techniques, we apply them to the study of silicon, graphane, and arsenic. The formalism is implemented into the abinit software and supports the norm-conserving pseudopotential approach, the projector augmented-wave method, and the inclusion of spin-orbit coupling. The derived expressions also apply to the ultrasoft pseudopotential method.

  18. Density perturbations in general modified gravitational theories

    SciTech Connect

    De Felice, Antonio; Tsujikawa, Shinji; Mukohyama, Shinji

    2010-07-15

    We derive the equations of linear cosmological perturbations for the general Lagrangian density f(R,{phi},X)/2+L{sub c}, where R is a Ricci scalar, {phi} is a scalar field, and X=-{partial_derivative}{sup {mu}{phi}{partial_derivative}}{sub {mu}{phi}/}2 is a field kinetic energy. We take into account a nonlinear self-interaction term L{sub c}={xi}({phi}) {open_square}{phi}({partial_derivative}{sup {mu}{phi}{partial_derivative}}{sub {mu}{phi}}) recently studied in the context of ''Galileon'' cosmology, which keeps the field equations at second order. Taking into account a scalar-field mass explicitly, the equations of matter density perturbations and gravitational potentials are obtained under a quasistatic approximation on subhorizon scales. We also derive conditions for the avoidance of ghosts and Laplacian instabilities associated with propagation speeds. Our analysis includes most of modified gravity models of dark energy proposed in literature; and thus it is convenient to test the viability of such models from both theoretical and observational points of view.

  19. Perturbation Theory of Massive Yang-Mills Fields

    DOE R&D Accomplishments Database

    Veltman, M.

    1968-08-01

    Perturbation theory of massive Yang-Mills fields is investigated with the help of the Bell-Treiman transformation. Diagrams containing one closed loop are shown to be convergent if there are more than four external vector boson lines. The investigation presented does not exclude the possibility that the theory is renormalizable.

  20. Perturbation theory via Feynman diagrams in classical mechanics

    NASA Astrophysics Data System (ADS)

    Penco, R.; Mauro, D.

    2006-09-01

    In this paper we show how Feynman diagrams, which are used as a tool to implement perturbation theory in quantum field theory, can be very useful also in classical mechanics, provided we introduce also at the classical level concepts such as path integrals and generating functionals.

  1. Degenerate R-S perturbation theory

    NASA Technical Reports Server (NTRS)

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

    1973-01-01

    A concise, systematic procedure is given for determining the Rayleigh-Schrodinger 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)st 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.

  2. Adaptive Wing Camber Optimization: A Periodic Perturbation Approach

    NASA Technical Reports Server (NTRS)

    Espana, Martin; Gilyard, Glenn

    1994-01-01

    Available redundancy among aircraft control surfaces allows for effective wing camber modifications. As shown in the past, this fact can be used to improve aircraft performance. To date, however, algorithm developments for in-flight camber optimization have been limited. This paper presents a perturbational approach for cruise optimization through in-flight camber adaptation. The method uses, as a performance index, an indirect measurement of the instantaneous net thrust. As such, the actual performance improvement comes from the integrated effects of airframe and engine. The algorithm, whose design and robustness properties are discussed, is demonstrated on the NASA Dryden B-720 flight simulator.

  3. Rapid adaptation to Coriolis force perturbations of arm trajectory.

    PubMed

    Lackner, J R; Dizio, P

    1994-07-01

    line to the wrong place. Aftereffects of opposite sign were transiently present in the postrotary movements. 5. These observations fail to support current equilibrium point models, both alpha and lambda, of movement control. Such theories would not predict endpoint errors under our experimental conditions, in which the Coriolis force is absent at the beginning and end of a movement. Our results indicate that detailed aspects of movement trajectory are being continuously monitored on the basis of proprioceptive feedback in relation to motor commands. Adaptive compensations can be initiated after one perturbation despite the absence of either visual or tactile feedback about movement trajectory and endpoint error. Moreover, movement trajectory and end-point can be remapped independently.(ABSTRACT TRUNCATED AT 400 WORDS)

  4. Rapid adaptation to Coriolis force perturbations of arm trajectory

    NASA Technical Reports Server (NTRS)

    Lackner, J. R.; Dizio, P.

    1994-01-01

    line to the wrong place. Aftereffects of opposite sign were transiently present in the postrotary movements. 5. These observations fail to support current equilibrium point models, both alpha and lambda, of movement control. Such theories would not predict endpoint errors under our experimental conditions, in which the Coriolis force is absent at the beginning and end of a movement. Our results indicate that detailed aspects of movement trajectory are being continuously monitored on the basis of proprioceptive feedback in relation to motor commands. Adaptive compensations can be initiated after one perturbation despite the absence of either visual or tactile feedback about movement trajectory and endpoint error. Moreover, movement trajectory and end-point can be remapped independently.(ABSTRACT TRUNCATED AT 400 WORDS).

  5. One-loop chiral perturbation theory with two fermion representations

    NASA Astrophysics Data System (ADS)

    DeGrand, Thomas; Golterman, Maarten; Neil, Ethan T.; Shamir, Yigal

    2016-07-01

    We develop chiral perturbation theory for chirally broken theories with fermions in two different representations of the gauge group. Any such theory has a nonanomalous singlet U (1 )A symmetry, yielding an additional Nambu-Goldstone boson when spontaneously broken. We calculate the next-to-leading order corrections for the pseudoscalar masses and decay constants, which include the singlet Nambu-Goldstone boson, as well as for the two condensates. The results can be generalized to more than two representations.

  6. String perturbation theory and effective Lagrangians

    SciTech Connect

    Klebanov, I.

    1987-09-01

    We isolate logarithmic divergences from bosonic string amplitudes on a disc. These divergences are compared with 'tadpole' divergences in the effective field theory with a cosmological term, which also contains an effective potential for the dilation. Also, corrections to ..beta..-functions are compared with variations of the effective action. In both cases we find an inconsistency between the two. This is a serious problem which could undermine our ability to remove divergences from the bosonic string.

  7. Quasi-degenerate perturbation theory using matrix product states.

    PubMed

    Sharma, Sandeep; Jeanmairet, Guillaume; Alavi, Ali

    2016-01-21

    In this work, we generalize the recently proposed matrix product state perturbation theory (MPSPT) for calculating energies of excited states using quasi-degenerate (QD) perturbation theory. Our formulation uses the Kirtman-Certain-Hirschfelder canonical Van Vleck perturbation theory, which gives Hermitian effective Hamiltonians at each order, and also allows one to make use of Wigner's 2n + 1 rule. Further, our formulation satisfies Granovsky's requirement of model space invariance which is important for obtaining smooth potential energy curves. Thus, when we use MPSPT with the Dyall Hamiltonian, we obtain a model space invariant version of quasi-degenerate n-electron valence state perturbation theory (NEVPT), a property that the usual formulation of QD-NEVPT2 based on a multipartitioning technique lacked. We use our method on the benchmark problems of bond breaking of LiF which shows ionic to covalent curve crossing and the twist around the double bond of ethylene where significant valence-Rydberg mixing occurs in the excited states. In accordance with our previous work, we find that multi-reference linearized coupled cluster theory is more accurate than other multi-reference theories of similar cost.

  8. Tensor perturbations in a general class of Palatini theories

    SciTech Connect

    Jiménez, Jose Beltrán; Heisenberg, Lavinia; Olmo, Gonzalo J. E-mail: laviniah@kth.se

    2015-06-01

    We study a general class of gravitational theories formulated in the Palatini approach and derive the equations governing the evolution of tensor perturbations. In the absence of torsion, the connection can be solved as the Christoffel symbols of an auxiliary metric which is non-trivially related to the space-time metric. We then consider background solutions corresponding to a perfect fluid and show that the tensor perturbations equations (including anisotropic stresses) for the auxiliary metric around such a background take an Einstein-like form. This facilitates the study in a homogeneous and isotropic cosmological scenario where we explicitly establish the relation between the auxiliary metric and the space-time metric tensor perturbations. As a general result, we show that both tensor perturbations coincide in the absence of anisotropic stresses.

  9. Effective gravitational couplings for cosmological perturbations in generalized Proca theories

    NASA Astrophysics Data System (ADS)

    De Felice, Antonio; Heisenberg, Lavinia; Kase, Ryotaro; Mukohyama, Shinji; Tsujikawa, Shinji; Zhang, Ying-li

    2016-08-01

    We consider the finite interactions of the generalized Proca theory including the sixth-order Lagrangian and derive the full linear perturbation equations of motion on the flat Friedmann-Lemaître-Robertson-Walker background in the presence of a matter perfect fluid. By construction, the propagating degrees of freedom (besides the matter perfect fluid) are two transverse vector perturbations, one longitudinal scalar, and two tensor polarizations. The Lagrangians associated with intrinsic vector modes neither affect the background equations of motion nor the second-order action of tensor perturbations, but they do give rise to nontrivial modifications to the no-ghost condition of vector perturbations and to the propagation speeds of vector and scalar perturbations. We derive the effective gravitational coupling Geff with matter density perturbations under a quasistatic approximation on scales deep inside the sound horizon. We find that the existence of intrinsic vector modes allows a possibility for reducing Geff. In fact, within the parameter space, Geff can be even smaller than the Newton gravitational constant G at the late cosmological epoch, with a peculiar phantom dark energy equation of state (without ghosts). The modifications to the slip parameter η and the evolution of the growth rate f σ8 are discussed as well. Thus, dark energy models in the framework of generalized Proca theories can be observationally distinguished from the Λ CDM model according to both cosmic growth and expansion history. Furthermore, we study the evolution of vector perturbations and show that outside the vector sound horizon the perturbations are nearly frozen and start to decay with oscillations after the horizon entry.

  10. An improved thermodynamic perturbation theory for Mercedes-Benz water

    NASA Astrophysics Data System (ADS)

    Urbic, T.; Vlachy, V.; Kalyuzhnyi, Yu. V.; Dill, K. A.

    2007-11-01

    We previously applied Wertheim's thermodynamic perturbation theory for associative fluids to the simple Mercedes-Benz model of water. We found that the theory reproduced well the physical properties of hot water, but was less successful in capturing the more structured hydrogen bonding that occurs in cold water. Here, we propose an improved version of the thermodynamic perturbation theory in which the effective density of the reference system is calculated self-consistently. The new theory is a significant improvement, giving good agreement with Monte Carlo simulations of the model, and predicting key anomalies of cold water, such as minima in the molar volume and large heat capacity, in addition to giving good agreement with the isothermal compressibility and thermal expansion coefficient.

  11. An improved thermodynamic perturbation theory for Mercedes-Benz water.

    PubMed

    Urbic, T; Vlachy, V; Kalyuzhnyi, Yu V; Dill, K A

    2007-11-01

    We previously applied Wertheim's thermodynamic perturbation theory for associative fluids to the simple Mercedes-Benz model of water. We found that the theory reproduced well the physical properties of hot water, but was less successful in capturing the more structured hydrogen bonding that occurs in cold water. Here, we propose an improved version of the thermodynamic perturbation theory in which the effective density of the reference system is calculated self-consistently. The new theory is a significant improvement, giving good agreement with Monte Carlo simulations of the model, and predicting key anomalies of cold water, such as minima in the molar volume and large heat capacity, in addition to giving good agreement with the isothermal compressibility and thermal expansion coefficient.

  12. An improved thermodynamic perturbation theory for Mercedes-Benz water.

    PubMed

    Urbic, T; Vlachy, V; Kalyuzhnyi, Yu V; Dill, K A

    2007-11-01

    We previously applied Wertheim's thermodynamic perturbation theory for associative fluids to the simple Mercedes-Benz model of water. We found that the theory reproduced well the physical properties of hot water, but was less successful in capturing the more structured hydrogen bonding that occurs in cold water. Here, we propose an improved version of the thermodynamic perturbation theory in which the effective density of the reference system is calculated self-consistently. The new theory is a significant improvement, giving good agreement with Monte Carlo simulations of the model, and predicting key anomalies of cold water, such as minima in the molar volume and large heat capacity, in addition to giving good agreement with the isothermal compressibility and thermal expansion coefficient. PMID:17994831

  13. Incentive theory III: Adaptive clocks.

    PubMed

    Killeen, P R

    1984-01-01

    Incentive theory is extended to address the phenomenon of autoshaping. To do so, it is necessary to permit the speed of the animal's internal clock to vary with rates of reinforcement; clock speed is the basis for the animal's calculations of reinforcement densities. This notion of an "adaptive clock" is consistent with other effects, such as the partial-reinforcement extinction effect, and permits us to deal with the various experimental manipulations that are found in autoshaping experiments from a unified perspective.

  14. Invalidity of standard perturbation techniques in cosmic ray transport theory

    NASA Technical Reports Server (NTRS)

    Kaiser, T. B.; Birmingham, T. J.; Jones, F. C.

    1973-01-01

    It is contended that the existence of particles with arbitrarily long correlation times invalidates the condition necessary for the applicability of standard perturbation techniques in cosmic ray transport theory. It is also argued that Klimas and Sandri's (1971) conclusion about a non-Markovian time development of the particle distribution is unwarranted.

  15. Nonperturbative Quantum Physics from Low-Order Perturbation Theory.

    PubMed

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

    2015-10-01

    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.

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

    SciTech Connect

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

    2015-02-15

    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.

  17. Perturbation-iteration theory for analyzing microwave striplines

    NASA Technical Reports Server (NTRS)

    Kretch, B. E.

    1985-01-01

    A perturbation-iteration technique is presented for determining the propagation constant and characteristic impedance of an unshielded microstrip transmission line. The method converges to the correct solution with a few iterations at each frequency and is equivalent to a full wave analysis. The perturbation-iteration method gives a direct solution for the propagation constant without having to find the roots of a transcendental dispersion equation. The theory is presented in detail along with numerical results for the effective dielectric constant and characteristic impedance for a wide range of substrate dielectric constants, stripline dimensions, and frequencies.

  18. Perturbations of single-field inflation in modified gravity theory

    NASA Astrophysics Data System (ADS)

    Qiu, Taotao; Xia, Jun-Qing

    2015-05-01

    In this paper, we study the case of single field inflation within the framework of modified gravity theory where the gravity part has an arbitrary form f (R). Via a conformal transformation, this case can be transformed into its Einstein frame where it looks like a two-field inflation model. However, due to the existence of the isocurvature modes in such a multi-degree-of-freedom (m.d.o.f.) system, the (curvature) perturbations are not equivalent in two frames, so despite of its convenience, it is illegal to treat the perturbations in its Einstein frame as the "real" ones as we always do for pure f (R) theory or single field with nonminimal coupling. Here by pulling the results of curvature perturbations back into its original Jordan frame, we show explicitly the power spectrum and spectral index of the perturbations in the Jordan frame, as well as how it differs from the Einstein frame. We also fit our results with the newest Planck data. Since there is large parameter space in these models, we show that it is easy to fit the data very well.

  19. Effects of xenon insertion into hydrogen bromide. Comparison of the electronic structure of the HBr···CO2 and HXeBr···CO2 complexes using quantum chemical topology methods: electron localization function, atoms in molecules and symmetry adapted perturbation theory.

    PubMed

    Makarewicz, Emilia; Gordon, Agnieszka J; Mierzwicki, Krzysztof; Latajka, Zdzislaw; Berski, Slawomir

    2014-06-01

    Quantum chemistry methods have been applied to study the influence of the Xe atom inserted into the hydrogen-bromine bond (HBr → HXeBr), particularly on the nature of atomic interactions in the HBr···CO2 and HXeBr···CO2 complexes. Detailed analysis of the nature of chemical bonds has been carried out using topological analysis of the electron localization function, while topological analysis of electron density was used to gain insight into the nature of weak nonbonding interactions. Symmetry-adapted perturbation theory within the orbital approach was applied for greater understanding of the physical contributions to the total interaction energy.

  20. Perturbation theory and nonperturbative effects: A happy marriage ?

    NASA Astrophysics Data System (ADS)

    Chýla, J.

    1992-03-01

    Perturbation expansions in renormalized quantum field theories are reformulated in a way that permits a straightforward handling of situations when in the conventional approach, i.e. in fixed renormalization scheme, these expansions are factorially divergent and even of asymptotically constant sign. The result takes the form of convergent (under certain circumstances) expansions in a set of functions Z k(a, χ) of the couplant and the free parameter χ which specifies the procedure involved. The value of χ is shown to be correlated to the basic properties of nonperturbative effects as embodied in power corrections. Close connection of this procedure to Borel summation technique is demonstrated and its relation to conventional perturbation theory in fixed renormalization schemes elucidated.

  1. Calculation of exchange energies using algebraic perturbation theory

    SciTech Connect

    Burrows, B. L.; Dalgarno, A.; Cohen, M.

    2010-04-15

    An algebraic perturbation theory is presented for efficient calculations of localized states and hence of exchange energies, which are the differences between low-lying states of the valence electron of a molecule, formed by the collision of an ion Y{sup +} with an atom X. For the case of a homonuclear molecule these are the gerade and ungerade states and the exchange energy is an exponentially decreasing function of the internuclear distance. For such homonuclear systems the theory is used in conjunction with the Herring-Holstein technique to give accurate exchange energies for a range of intermolecular separations R. Since the perturbation parameter is essentially 1/R, this method is suitable for large R. In particular, exchange energies are calculated for X{sub 2}{sup +} systems, where X is H, Li, Na, K, Rb, or Cs.

  2. On the non-linear scale of cosmological perturbation theory

    SciTech Connect

    Blas, Diego; Garny, Mathias; Konstandin, Thomas E-mail: mathias.garny@desy.de

    2013-09-01

    We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections at any order in perturbation theory. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

  3. Topological susceptibility in staggered fermion chiral perturbation theory

    SciTech Connect

    Billeter, Brian; DeTar, Carleton; Osborn, James

    2004-10-01

    The topological susceptibility of the vacuum in quantum chromodynamics has been simulated numerically using the Asqtad improved staggered fermion formalism. At nonzero lattice spacing, the residual fermion doublers (fermion tastes) in the staggered fermion formalism give contributions to the susceptibility that deviate from conventional continuum chiral perturbation theory. In this brief report, we estimate the taste-breaking artifact and compare it with results of recent simulations, finding that it accounts for roughly half of the scaling violation.

  4. Solution of coupled and singular perturbation methods using duality theory.

    NASA Technical Reports Server (NTRS)

    Chan, W. L.; Leininger, G. G.

    1973-01-01

    Dual variational techniques developed by Chan and Leininger (1972) are summarized, and duality theory in the form of the Complementary Variational Principle is employed to provide a suboptimal measure for the singular and epsilon-coupled perturbation methods proposed by Kokotovic and Cruz. The suboptimal measure is independent of any a priori knowledge of the optimal solution, thereby providing an absolute estimate of the performance loss rather than an estimate relative to the unknown optimal solution.

  5. Including the {delta}(1232) resonance in baryon chiral perturbation theory

    SciTech Connect

    Hacker, C.; Wies, N.; Scherer, S.; Gegelia, J.

    2005-11-01

    Baryon chiral perturbation theory with explicit {delta}(1232) degrees of freedom is considered. The most general interactions of pions, nucleons, and {delta} consistent with all underlying symmetries as well as with the constraint structure of higher-spin fields are constructed. By use of the extended on-mass-shell renormalization scheme, a manifestly Lorentz-invariant effective-field theory with a systematic power counting is obtained. As applications, we discuss the mass of the nucleon, the pion-nucleon {sigma} term, and the pole of the {delta} propagator.

  6. Improving the ultraviolet behavior in baryon chiral perturbation theory

    SciTech Connect

    Djukanovic, D.; Schindler, M.R.; Scherer, S.; Gegelia, J.

    2005-08-15

    We introduce a new formulation of baryon chiral perturbation theory which improves the ultraviolet behavior of propagators and can be interpreted as a smooth cutoff regularization scheme. It is equivalent to the standard approach, preserves all symmetries, and therefore satisfies the Ward identities. Our formulation is equally well defined in the vacuum, one-nucleon, and few-nucleon sectors of the theory. The equations (Bethe-Salpeter, Lippmann-Schwinger, etc.) for the scattering amplitudes of the few-nucleon sector are free of divergences in the new approach. Unlike the usual cutoff regularization, our 'cutoffs' are parameters of the Lagrangian and do not have to be removed.

  7. Implementation, verification, and application of multicycle depletion perturbation theory

    SciTech Connect

    White, J.R.; Burns, T.J.; Williams, M.L.

    1980-01-01

    Several application-oriented features of generalized depletion perturbation theory (DPT) are analyzed from the viewpoint of the reactor designer. The detailed theory is first reduced to some new terminology necessary for an adequate understanding of DPT. Using this terminology, the main features and computational accuracy of this new technique are illustrated through representative DPT calculations utilizing a CDS-type heterogeneous reactor model. Several examples are presented that indicate the potential of DPT methods as an alternate computational tool for certain types of reactor physics analyses.

  8. Cosmological perturbation theory, instantaneous gauges, and local inertial frames

    NASA Astrophysics Data System (ADS)

    Bičák, Jiří; Katz, Joseph; Lynden-Bell, Donald

    2007-09-01

    Linear perturbations of Friedmann-Robertson-Walker universes with any curvature and cosmological constant are studied in a general gauge without decomposition into harmonics. Desirable gauges are selected as those which embody best Mach’s principle: in these gauges local inertial frames can be determined instantaneously via the perturbed Einstein field equations from the distributions of energy and momentum in the universe. The inertial frames are identified by their “accelerations and rotations” with respect to the cosmological frames associated with the “Machian gauges.” In closed spherical universes, integral gauge conditions are imposed to eliminate motions generated by the conformal Killing vectors. The meaning of Traschen’s integral-constraint vectors is thus elucidated. For all three types of Friedmann-Robertson-Walker universes the Machian gauges admit much less residual freedom than the synchronous or generalized harmonic gauge. Mach’s principle is best exhibited in the Machian gauges in closed spherical universes. Independent of any Machian motivation, the general perturbation equations and discussion of gauges are useful for cosmological perturbation theory.

  9. Cosmological perturbations and quasistatic assumption in f (R ) theories

    NASA Astrophysics Data System (ADS)

    Chiu, Mu-Chen; Taylor, Andy; Shu, Chenggang; Tu, Hong

    2015-11-01

    f (R ) gravity is one of the simplest theories of modified gravity to explain the accelerated cosmic expansion. Although it is usually assumed that the quasi-Newtonian approach (a combination of the quasistatic approximation and sub-Hubble limit) for cosmic perturbations is good enough to describe the evolution of large scale structure in f (R ) models, some studies have suggested that this method is not valid for all f (R ) models. Here, we show that in the matter-dominated era, the pressure and shear equations alone, which can be recast into four first-order equations to solve for cosmological perturbations exactly, are sufficient to solve for the Newtonian potential, Ψ , and the curvature potential, Φ . Based on these two equations, we are able to clarify how the exact linear perturbations fit into different limits. We find that the Compton length controls the quasistatic behaviors in f (R ) gravity. In addition, regardless the validity of quasistatic approximation, a strong version of the sub-Hubble limit alone is sufficient to reduce the exact linear perturbations in any viable f (R ) gravity to second order. Our findings disagree with some previous studies where we find little difference between our exact and quasi-Newtonian solutions even up to k =10 c-1H0.

  10. System-reservoir theory with anharmonic baths: a perturbative approach

    NASA Astrophysics Data System (ADS)

    Bhadra, Chitrak; Banerjee, Dhruba

    2016-04-01

    In this paper we develop the formalism of a general system coupled to a reservoir (the words ‘bath’ and ‘reservoir’ will be used interchangeably) consisting of nonlinear oscillators, based on perturbation theory at the classical level, by extending the standard Zwanzig approach of elimination of bath degrees of freedom order by order in perturbation. We observe that the fluctuation dissipation relation (FDR) of the second kind in its standard form for harmonic baths gets modified due to the nonlinearity and this is manifested through higher powers of {{k}\\text{B}}T in the expression for two-time noise correlation. On the flip side, this very modification allows us to define a dressed (renormalized) system-bath coupling that depends on the temperature and the nonlinear parameters of the bath in such a way that the structure of the FDR (of the second kind) is maintained. As an aside, we also observe that the first moment of the noise arising from a nonlinear bath can be non-zero, even in the absence of any external drive, if the reservoir potential is asymmetric with respect to one of its minima, about which one builds up the perturbation theory.

  11. Development of depletion perturbation theory for a reactor nodal code

    SciTech Connect

    Bowman, S.M.

    1981-09-01

    A generalized depletion perturbation (DPT) theory formulation for light water reactor (LWR) depletion problems is developed and implemented into the three-dimensional LWR nodal code SIMULATE. This development applies the principles of the original derivation by M.L. Williams to the nodal equations solved by SIMULATE. The present formulation is first described in detail, and the nodal coupling methodology in SIMULATE is used to determine partial derivatives of the coupling coefficients. The modifications to the original code and the new DPT options available to the user are discussed. Finally, the accuracy and the applicability of the new DPT capability to LWR design analysis are examined for several LWR depletion test cases. The cases range from simple static cases to a realistic PWR model for an entire fuel cycle. Responses of interest included K/sub eff/, nodal peaking, and peak nodal exposure. The nonlinear behavior of responses with respect to perturbations of the various types of cross sections was also investigated. The time-dependence of the sensitivity coefficients for different responses was examined and compared. Comparison of DPT results for these examples to direct calculations reveals the limited applicability of depletion perturbation theory to LWR design calculations at the present. The reasons for these restrictions are discussed, and several methods which might improve the computational accuracy of DPT are proposed for future research.

  12. A simple extrapolation of thermodynamic perturbation theory to infinite order

    SciTech Connect

    Ghobadi, Ahmadreza F.; Elliott, J. Richard

    2015-09-21

    Recent analyses of the third and fourth order perturbation contributions to the equations of state for square well spheres and Lennard-Jones chains show trends that persist across orders and molecular models. In particular, the ratio between orders (e.g., A{sub 3}/A{sub 2}, where A{sub i} is the ith order perturbation contribution) exhibits a peak when plotted with respect to density. The trend resembles a Gaussian curve with the peak near the critical density. This observation can form the basis for a simple recursion and extrapolation from the highest available order to infinite order. The resulting extrapolation is analytic and therefore cannot fully characterize the critical region, but it remarkably improves accuracy, especially for the binodal curve. Whereas a second order theory is typically accurate for the binodal at temperatures within 90% of the critical temperature, the extrapolated result is accurate to within 99% of the critical temperature. In addition to square well spheres and Lennard-Jones chains, we demonstrate how the method can be applied semi-empirically to the Perturbed Chain - Statistical Associating Fluid Theory (PC-SAFT)

  13. Communication: Random phase approximation renormalized many-body perturbation theory

    SciTech Connect

    Bates, Jefferson E.; Furche, Filipp

    2013-11-07

    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.

  14. Infrared propagators of Yang-Mills theory from perturbation theory

    SciTech Connect

    Tissier, Matthieu; Wschebor, Nicolas

    2010-11-15

    We show that the correlation functions of ghosts and gluons for the pure Yang-Mills theory in Landau gauge can be accurately reproduced for all momenta by a one-loop calculation. The key point is to use a massive extension of the Faddeev-Popov action. The agreement with lattice simulation is excellent in d=4. The one-loop calculation also reproduces all the characteristic features of the lattice simulations in d=3 and naturally explains the peculiarities of the propagators in d=2.

  15. Master equation based steady-state cluster perturbation theory

    NASA Astrophysics Data System (ADS)

    Nuss, Martin; Dorn, Gerhard; Dorda, Antonius; von der Linden, Wolfgang; Arrigoni, Enrico

    2015-09-01

    A simple and efficient approximation scheme to study electronic transport characteristics of strongly correlated nanodevices, molecular junctions, or heterostructures out of equilibrium is provided by steady-state cluster perturbation theory. In this work, we improve the starting point of this perturbative, nonequilibrium Green's function based method. Specifically, we employ an improved unperturbed (so-called reference) state ρ̂S, constructed as the steady state of a quantum master equation within the Born-Markov approximation. This resulting hybrid method inherits beneficial aspects of both the quantum master equation as well as the nonequilibrium Green's function technique. We benchmark this scheme on two experimentally relevant systems in the single-electron transistor regime: an electron-electron interaction based quantum diode and a triple quantum dot ring junction, which both feature negative differential conductance. The results of this method improve significantly with respect to the plain quantum master equation treatment at modest additional computational cost.

  16. B{sub K} in staggered chiral perturbation theory

    SciTech Connect

    Water, Ruth S. van de; Sharpe, Stephen R.

    2006-01-01

    We calculate the kaon B parameter, B{sub K}, to next-to-leading order in staggered chiral perturbation theory. We find expressions for partially quenched QCD with three sea quarks, quenched QCD, and full QCD with m{sub u}=m{sub d}{ne}m{sub s}. We extend the usual power counting to include the effects of using perturbative (rather than nonperturbative) matching factors. Taste breaking enters through the O(a{sup 2}) terms in the effective action, through O(a{sup 2}) terms from the discretization of operators, and through the truncation of matching factors. These effects cause mixing with several additional operators, complicating the chiral and continuum extrapolations. In addition to the staggered expressions, we present B{sub K} at next-to-leading order in continuum PQ{chi}PT for N{sub f}=3 sea quarks with m{sub u}=m{sub d}{ne}m{sub s}.

  17. Adiabaticity and gravity theory independent conservation laws for cosmological perturbations

    NASA Astrophysics Data System (ADS)

    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.

  18. Staggered chiral perturbation theory in the two-flavor case

    SciTech Connect

    Du Xining

    2010-07-01

    I study two-flavor staggered chiral perturbation theory in the light pseudoscalar sector. The pion mass and decay constant are calculated through next-to-leading order in the partially-quenched case. In the limit where the strange quark mass is large compared to the light quark masses and the taste splittings, I show that the SU(2) staggered chiral theory emerges from the SU(3) staggered chiral theory, as expected. Explicit relations between SU(2) and SU(3) low energy constants and taste-violating parameters are given. The results are useful for SU(2) chiral fits to asqtad data and allow one to incorporate effects from varying strange quark masses.

  19. Resummed thermodynamic perturbation theory for bond cooperativity in associating fluids

    SciTech Connect

    Marshall, Bennett D. Chapman, Walter G.

    2013-12-07

    We develop a resummed thermodynamic perturbation theory for bond cooperativity in associating fluids by extension of Wertheim's multi-density formalism. We specifically consider the case of an associating hard sphere with two association sites and both pairwise and triplet contributions to the energy, such that the first bond in an associated cluster receives an energy −ε{sup (1)} and each subsequent bond in the cluster receives an energy −ε{sup (2)}. To test the theory we perform new Monte Carlo simulations for potentials of this type. Theory and simulation are found to be in excellent agreement. We show that decreasing the energetic benefit of hydrogen bonding can actually result in a decrease in internal energy in the fluid. We also predict that when ε{sup (1)} = 0 and ε{sup (2)} is nonzero there is a transition temperature where the system transitions from a fluid of monomers to a mixture of monomers and very long chains.

  20. Open-shell M∅ller—Plesset perturbation theory

    NASA Astrophysics Data System (ADS)

    Amos, Roger D.; Andrews, Jamie S.; Handy, Nicholas C.; Knowles, Peter J.

    1991-10-01

    In a previous paper, the spin constrained unrestricted Hartree—Fock method (SUHF) was introduced, in which the UHF method was amended by a constraint that < Ŝ2> should have a prescribed value with λ the associated Lagrange multiplier. It was shown that the limit λ→∞ gave the high spin restricted open-shell Hartree—Fock (ROHF) wavefunction and energy, although the orbitals are rotated. Here it is shown how the λ→∞ results are achieved analytically directly from ROHF calculations. M∅ller—Plesset perturbation theory may then be set up within the amended Fock operators of SUHF theory, based upon the unrestricted formalism. Single replacement contributions enter into the first-order wavefunction. The convergence of this restricted open-shell M∅ller—Plesset perturbation theory (ROMP) is examined to high order using our full configuration interaction program. The calculations show none of the slow convergence properties associated with the UMP series. For NH 2 (C 2v, 1.5 re) and CN ( re). ROMP2 and ROMP4 are a substantial improvement over UMP2 and UMP4.

  1. Electroproduction of pions at threshold in chiral perturbation theory

    SciTech Connect

    Lee, T.S.H.; Bernard, V.; Kaiser, N.; Meissner, U.G.

    1995-08-01

    The electroproduction of pions off protons close to threshold is studied within the framework of baryon chiral perturbation theory. The approach is based on the fundamental QCD property that at low energies the strong interactions are dictated by the spontaneously broken chiral symmetry. The calculation was done up to the 1-loop level by carrying out order-by-order renormalization procedures. A thorough study of the low-energy theorems related to electroproduction of pions was carried out. Our study showed how the axial radius of the nucleon can be related to the S-wave multipoles E{sub 0+}{sup (-)} and L{sub 0+}{sup (-)}.

  2. Chiral perturbation theory and off-shell electromagnetic form factors

    SciTech Connect

    Rudy, T.E.; Fearing, H.W.; Scherer, S.

    1995-05-10

    The off-shell electromagnetic vertex of pions and kaons is calculated to {ital O}({ital p}{sup 4}) in the momentum expansion within the framework of chiral perturbation theory to one loop. The formalism of Gasser and Leutwyler is extended to accommodate the most general form for off-shell Green`s functions in the pseudoscalar meson sector. To that end we identify the structures at {ital O}({ital p}{sup 4}) which were initially removed by using the equation of motion of the lowest-order lagrangian. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.

  3. Cosmological post-Newtonian equations from nonlinear perturbation theory

    SciTech Connect

    Noh, Hyerim; Hwang, Jai-chan E-mail: jchan@knu.ac.kr

    2013-08-01

    We derive the basic equations of the cosmological first-order post-Newtonian approximation from the recently formulated fully nonlinear and exact cosmological perturbation theory in Einstein's gravity. Apparently the latter, being exact, should include the former, and here we use this fact as a new derivation of the former. The complete sets of equations in both approaches are presented without fixing the temporal gauge conditions so that we can use the gauge choice as an advantage. Comparisons between the two approaches are made. Both are potentially important in handling relativistic aspects of nonlinear processes occurring in cosmological structure formation. We consider an ideal fluid and include the cosmological constant.

  4. Resonant Perturbation Theory of Decoherence and Relaxation of Quantum Bits

    DOE PAGES

    Merkli, M.; Berman, G. P.; Sigal, I. M.

    2010-01-01

    We describe our recenmore » t results on the resonant perturbation theory of decoherence and relaxation for quantum systems with many qubits. The approach represents a rigorous analysis of the phenomenon of decoherence and relaxation for general N -level systems coupled to reservoirs of bosonic fields. We derive a representation of the reduced dynamics valid for all times t ≥ 0 and for small but fixed interaction strength. Our approach does not involve master equation approximations and applies to a wide variety of systems which are not explicitly solvable.« less

  5. Adiabatic perturbation theory of electronic stopping in insulators

    NASA Astrophysics Data System (ADS)

    Horsfield, Andrew P.; Lim, Anthony; Foulkes, W. M. C.; Correa, Alfredo A.

    2016-06-01

    A model able to explain the complicated structure of electronic stopping at low velocities in insulating materials is presented. It is shown to be in good agreement with results obtained from time-dependent density-functional theory for the stopping of a channeling Si atom in a Si crystal. If we define the repeat frequency f =v /λ , where λ is the periodic repeat length of the crystal along the direction the channeling atom is traveling, and v is the velocity of the channeling atom, we find that electrons experience a perturbing force that varies in time at integer multiples l of f . This enables electronic excitations at low atom velocity, but their contributions diminish rapidly with increasing values of l . The expressions for stopping power are derived using adiabatic perturbation theory for many-electron systems, and they are then specialized to the case of independent electrons. A simple model for the nonadiabatic matrix elements is described, along with the procedure for determining its parameters.

  6. Heavy-light semileptonic decays in staggered chiral perturbation theory

    NASA Astrophysics Data System (ADS)

    Aubin, C.; Bernard, C.

    2007-07-01

    We calculate the form factors for the semileptonic decays of heavy-light pseudoscalar mesons in partially quenched staggered chiral perturbation theory (SχPT), working to leading order in 1/mQ, where mQ is the heavy-quark mass. We take the light meson in the final state to be a pseudoscalar corresponding to the exact chiral symmetry of staggered quarks. The treatment assumes the validity of the standard prescription for representing the staggered “fourth-root trick” within SχPT by insertions of factors of 1/4 for each sea-quark loop. Our calculation is based on an existing partially quenched continuum chiral perturbation theory calculation with degenerate sea quarks by Bećirević, Prelovsek, and Zupan, which we generalize to the staggered (and nondegenerate) case. As a byproduct, we obtain the continuum partially quenched results with nondegenerate sea quarks. We analyze the effects of nonleading chiral terms, and find a relation among the coefficients governing the analytic valence mass dependence at this order. Our results are useful in analyzing lattice computations of form factors B→π and D→K, when the light quarks are simulated with the staggered action.

  7. Invariant exchange perturbation theory for multicenter systems and its application to the calculation of magnetic chains in manganites

    SciTech Connect

    Orlenko, E. V. Ershova, E. V.; Orlenko, F. E.

    2013-10-15

    The formalism of exchange perturbation theory is presented with regard to the general principles of constructing an antisymmetric vector with the use of the Young diagrams and tableaux in which the coordinate and spin parts are not separated. The form of the energy and wave function corrections coincides with earlier obtained expressions, which are reduced in the present paper to a simpler form of a symmetry-adapted perturbation operator, which preserves all intercenter exchange contributions. The exchange perturbation theory (EPT) formalism itself is presented in the standard form of invariant perturbation theory that takes into account intercenter electron permutations between overlapping nonorthogonal states. As an example of application of the formalism of invariant perturbation theory, we consider the magnetic properties of perovskite manganites La{sub 1/3}Ca{sub 2/3}MnO{sub 3} that are associated with the charge and spin ordering in magnetic chains of manganese. We try to interpret the experimental results obtained from the study of the effect of doping the above alloys by the model of superexchange interaction in manganite chains that is constructed on the basis of the exchange perturbation theory (EPT) formalism. The model proposed makes it possible to carry out a quantitative analysis of the effect of substitution of manganese atoms by doping elements with different electron configurations on the electronic structure and short-range order in a magnetic chain of manganites.

  8. A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories

    NASA Astrophysics Data System (ADS)

    Lagos, Macarena; Baker, Tessa; Ferreira, Pedro G.; Noller, Johannes

    2016-08-01

    We present a method for parametrizing linear cosmological perturbations of theories of gravity, around homogeneous and isotropic backgrounds. The method is sufficiently general and systematic that it can be applied to theories with any degrees of freedom (DoFs) and arbitrary gauge symmetries. In this paper, we focus on scalar-tensor and vector-tensor theories, invariant under linear coordinate transformations. In the case of scalar-tensor theories, we use our framework to recover the simple parametrizations of linearized Horndeski and ``Beyond Horndeski'' theories, and also find higher-derivative corrections. In the case of vector-tensor theories, we first construct the most general quadratic action for perturbations that leads to second-order equations of motion, which propagates two scalar DoFs. Then we specialize to the case in which the vector field is time-like (à la Einstein-Aether gravity), where the theory only propagates one scalar DoF. As a result, we identify the complete forms of the quadratic actions for perturbations, and the number of free parameters that need to be defined, to cosmologically characterize these two broad classes of theories.

  9. Prosodic Adaptations to Pitch Perturbation in Running Speech

    ERIC Educational Resources Information Center

    Patel, Rupal; Niziolek, Caroline; Reilly, Kevin; Guenther, Frank H.

    2011-01-01

    Purpose: A feedback perturbation paradigm was used to investigate whether prosodic cues are controlled independently or in an integrated fashion during sentence production. Method: Twenty-one healthy speakers of American English were asked to produce sentences with emphatic stress while receiving real-time auditory feedback of their productions.…

  10. Perturbative Interpretation of Adaptive Thouless-Anderson-Palmer Free Energy

    NASA Astrophysics Data System (ADS)

    Yasuda, Muneki; Takahashi, Chako; Tanaka, Kazuyuki

    2016-07-01

    In conventional well-known derivation methods for the adaptive Thouless-Anderson-Palmer (TAP) free energy, special assumptions that are difficult to mathematically justify except in some mean-field models, must be made. Here, we present a new adaptive TAP free energy derivation method. Using this derivation technique, without any special assumptions, the adaptive TAP free energy can be simply obtained as a high-temperature expansion of the Gibbs free energy.

  11. Staggered chiral perturbation theory for heavy-light mesons

    NASA Astrophysics Data System (ADS)

    Aubin, C.; Bernard, C.

    2006-01-01

    We incorporate heavy-light mesons into staggered chiral perturbation theory (SχPT), working to leading order in 1/mQ, where mQ is the heavy-quark mass. At first nontrivial order in the chiral expansion, staggered taste violations affect the chiral logarithms for heavy-light quantities only through the light-meson propagators in loops. There are also new analytic contributions coming from additional terms in the Lagrangian involving heavy-light and light mesons. Using this heavy-light SχPT, we perform the one-loop calculation of the B (or D) meson leptonic decay constant in the partially quenched and full QCD cases. In our treatment, we assume the validity both of the “fourth root trick” to reduce four staggered tastes to one, and of the SχPT prescription to represent this trick by insertions of factors of 1/4 for each sea-quark loop.

  12. Virtual Compton scattering off the nucleon in chiral perturbation theory

    SciTech Connect

    Hemmert, T.R.; Holstein, B.R.; Knoechlein, G.; Scherer, S.

    1997-03-01

    We investigate the spin-independent part of the virtual Compton scattering (VCS) amplitude off the nucleon within the framework of chiral perturbation theory. We perform a consistent calculation to third order in external momenta according to Weinberg`s power counting. With this calculation we can determine the second- and fourth-order structure-dependent coefficients of the general low-energy expansion of the spin-averaged VCS amplitude based on gauge invariance, crossing symmetry, and the discrete symmetries. We discuss the kinematical regime to which our calculation can be applied and compare our expansion with the multipole expansion by Guichon, Liu, and Thomas. We establish the connection of our calculation with the generalized polarizabilities of the nucleon where it is possible. {copyright} {ital 1997} {ital The American Physical Society}

  13. Determination of the Sediment Carrying Capacity Based on Perturbed Theory

    PubMed Central

    Ni, Zhi-hui; Zeng, Qiang; Li-chun, Wu

    2014-01-01

    According to the previous studies of sediment carrying capacity, a new method of sediment carrying capacity on perturbed theory was proposed. By taking into account the average water depth, average flow velocity, settling velocity, and other influencing factors and introducing the median grain size as one main influencing factor in deriving the new formula, we established a new sediment carrying capacity formula. The coefficients were determined by the principle of dimensional analysis, multiple linear regression method, and the least square method. After that, the new formula was verified through measuring data of natural rivers and flume tests and comparing the verified results calculated by Cao Formula, Zhang Formula, Li Formula, Engelung-Hansen Formula, Ackers-White Formula, and Yang Formula. According to the compared results, it can be seen that the new method is of high accuracy. It could be a useful reference for the determination of sediment carrying capacity. PMID:25136652

  14. The entry-exit function and geometric singular perturbation theory

    NASA Astrophysics Data System (ADS)

    De Maesschalck, Peter; Schecter, Stephen

    2016-04-01

    For small ε > 0, the system x ˙ = ε, z ˙ = h (x , z , ε) z, with h (x , 0 , 0) < 0 for x < 0 and h (x , 0 , 0) > 0 for x > 0, admits solutions that approach the x-axis while x < 0 and are repelled from it when x > 0. The limiting attraction and repulsion points are given by the well-known entry-exit function. For h (x , z , ε) z replaced by h (x , z , ε)z2, we explain this phenomenon using geometric singular perturbation theory. We also show that the linear case can be reduced to the quadratic case, and we discuss the smoothness of the return map to the line z =z0, z0 > 0, in the limit ε → 0.

  15. Stochastic many-body perturbation theory for anharmonic molecular vibrations

    NASA Astrophysics Data System (ADS)

    Hermes, Matthew R.; Hirata, So

    2014-08-01

    A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm-1 and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.

  16. Stochastic many-body perturbation theory for anharmonic molecular vibrations

    SciTech Connect

    Hermes, Matthew R.; Hirata, So

    2014-08-28

    A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm{sup −1} and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.

  17. Application and development of multiconfigurational localized perturbation theory

    NASA Astrophysics Data System (ADS)

    Dunietz, Barry D.; Friesner, Richard A.

    2001-12-01

    Generalization of localized perturbation theory, which results with a method able to span the spin space correctly, is presented. This generalization is achieved by using a multiconfigurational (MC) wave function as the reference. This is the most comprehensive expansion used within MC-LMP2 approach to date, with, however, low computational cost [computational scaling with system size (N) of the new method is O(N3)]. Recently, we have reported the successful Jaguar2 (J2) model for calculating atomization energies. Within the MC-LMP2 framework, the J2 model for calculating heats of formation is based on the generalized valence bond-perfect pairing (GVB-PP) wave function. The J2 model was applied only to closed shell cases because of the perfect pairing (PP) restriction in the reference function. In order to describe other systems, the PP restriction needs to be lifted. This work describes efforts in that direction. The PP restriction can be lifted by a restricted configuration interaction (RCI) procedure applied to the GVB-PP wave function. In this paper, the equations describing the application of LMP2 theory to self-consistent RCI wave function are derived and explained. The RCI wave function is a "true" MC expansion as opposed to the GVB-PP, which uses only a single spin eigenfunction (SEF). We also present the self-consistent (SC) optimization of the RCI wave function. The SC-RCI-LMP2 is the first MC-LMP2 method where the spin space is spanned in the reference. This is important for describing the nondynamical correlation (near degeneracy) effects associated, for example, with bond breaking processes. The SC-RCI-LMP2 is an efficient method applicable to large systems; it is shown to reproduce the potential energy surfaces calculated by the complete active space-second order perturbation (CAS-SCF-PT2) method. This is demonstrated, for the first time, on some widely used test cases.

  18. Recent Advances in Open-Shell Perturbation Theory and Coupled-Cluster Theory

    NASA Technical Reports Server (NTRS)

    Lee, Timothy J.; Langhoff, Stephen R. (Technical Monitor)

    1995-01-01

    Comparisons of various recently developed open-shell RHF perturbation theories will be presented. Among the aspects considered are spin-contamination, computational cost, and quality of numerical results. In addition, a new approach to avoid the disk storage and I/O bottlenecks in large scale coupled-cluster calculations will be discussed.

  19. Renal transport of taurine adapts to perturbed taurine homeostasis.

    PubMed Central

    Rozen, R; Scriver, C R

    1982-01-01

    Renal adaptation apparently contributes to the homeostasis of taurine, a beta-amino compound that behaves as a conserved metabolite in the mammal. We studied two strains of inbred mice: C3H/HeJ (low-taurine excreter) and C57BL/6J (high-taurine excreter due to impaired basolateral membrane permeability to taurine). Low-protein and low-sulfur amino acid diets fed for two weeks significantly decreased plasma taurine in both strains, decreased fractional taurine excretion in vivo (particularly in the C57BL strain), and increased net uptake of taurine by renal cortex slices and isolated brush-border membrane vesicles (BBMV) in vitro in both strains. Renal adaptation was less obvious in vivo in the low-taurine excreter C3H strain, but in vitro adaptation, as observed in slices and BBMV (P less than 0.01), was greater than that observed in the C57BL strain. Renal cellular taurine content fell (P less than 0.01) only in the adapted C3H strain. The in vitro adaptive response was not confined to taurine; BBMV uptake of D-glucose and L-alanine was also enhanced in the adapted state. Specificity of the stimulus for adaptation was tested with a low-phenylalanine diet; a modest adaptation was observed in vivo and in vitro but only in the C3H strain. BBMV adaptation did not correlate with blood methionine but correlated inversely with plasma taurine (r = 0.71, P less than 0.05), implying that change in extracellular taurine may be a signal for renal adaptation in taurine homeostasis in the mammal. PMID:6952257

  20. Staggered chiral perturbation theory and the fourth-root trick

    NASA Astrophysics Data System (ADS)

    Bernard, C.

    2006-06-01

    Staggered chiral perturbation theory (SχPT) takes into account the “fourth-root trick” for reducing unwanted (taste) degrees of freedom with staggered quarks by multiplying the contribution of each sea quark loop by a factor of 1/4. In the special case of four staggered fields (four flavors, nF=4), I show here that certain assumptions about analyticity and phase structure imply the validity of this procedure for representing the rooting trick in the chiral sector. I start from the observation that, when the four flavors are degenerate, the fourth root simply reduces nF=4 to nF=1. One can then treat nondegenerate quark masses by expanding around the degenerate limit. With additional assumptions on decoupling, the result can be extended to the more interesting cases of nF=3, 2, or 1. An apparent paradox associated with the one-flavor case is resolved. Coupled with some expected features of unrooted staggered quarks in the continuum limit, in particular, the restoration of taste symmetry, SχPT then implies that the fourth-root trick induces no problems (for example, a violation of unitarity that persists in the continuum limit) in the lowest energy sector of staggered lattice QCD. It also says that the theory with staggered valence quarks and rooted staggered sea quarks behaves like a simple, partially-quenched theory, not like a mixed theory in which sea and valence quarks have different lattice actions. In most cases, the assumptions made in this paper are not only sufficient but also necessary for the validity of SχPT, so that a variety of possible new routes for testing this validity are opened.

  1. Staggered chiral perturbation theory and the fourth-root trick

    SciTech Connect

    Bernard, C.

    2006-06-01

    Staggered chiral perturbation theory (S{chi}PT) takes into account the 'fourth-root trick' for reducing unwanted (taste) degrees of freedom with staggered quarks by multiplying the contribution of each sea quark loop by a factor of 1/4. In the special case of four staggered fields (four flavors, n{sub F}=4), I show here that certain assumptions about analyticity and phase structure imply the validity of this procedure for representing the rooting trick in the chiral sector. I start from the observation that, when the four flavors are degenerate, the fourth root simply reduces n{sub F}=4 to n{sub F}=1. One can then treat nondegenerate quark masses by expanding around the degenerate limit. With additional assumptions on decoupling, the result can be extended to the more interesting cases of n{sub F}=3, 2, or 1. An apparent paradox associated with the one-flavor case is resolved. Coupled with some expected features of unrooted staggered quarks in the continuum limit, in particular, the restoration of taste symmetry, S{chi}PT then implies that the fourth-root trick induces no problems (for example, a violation of unitarity that persists in the continuum limit) in the lowest energy sector of staggered lattice QCD. It also says that the theory with staggered valence quarks and rooted staggered sea quarks behaves like a simple, partially-quenched theory, not like a mixed theory in which sea and valence quarks have different lattice actions. In most cases, the assumptions made in this paper are not only sufficient but also necessary for the validity of S{chi}PT, so that a variety of possible new routes for testing this validity are opened.

  2. Kaon B-parameter in mixed action chiral perturbation theory

    SciTech Connect

    Aubin, C.; Laiho, Jack; Water, Ruth S. van de

    2007-02-01

    We calculate the kaon B-parameter, B{sub K}, in chiral perturbation theory for a partially quenched, mixed-action theory with Ginsparg-Wilson valence quarks and staggered sea quarks. We find that the resulting expression is similar to that in the continuum, and in fact has only two additional unknown parameters. At 1-loop order, taste-symmetry violations in the staggered sea sector only contribute to flavor-disconnected diagrams by generating an O(a{sup 2}) shift to the masses of taste-singlet sea-sea mesons. Lattice discretization errors also give rise to an analytic term which shifts the tree-level value of B{sub K} by an amount of O(a{sup 2}). This term, however, is not strictly due to taste breaking, and is therefore also present in the expression for B{sub K} for pure Ginsparg-Wilson lattice fermions. We also present a numerical study of the mixed B{sub K} expression in order to demonstrate that both discretization errors and finite volume effects are small and under control on the MILC improved staggered lattices.

  3. Staggered chiral perturbation theory at next-to-leading order

    SciTech Connect

    Sharpe, Stephen R.; Van de Water, Ruth S.

    2005-06-01

    We study taste and Euclidean rotational symmetry violation for staggered fermions at nonzero lattice spacing using staggered chiral perturbation theory. We extend the staggered chiral Lagrangian to O(a{sup 2}p{sup 2}), O(a{sup 4}), and O(a{sup 2}m), the orders necessary for a full next-to-leading order calculation of pseudo-Goldstone boson masses and decay constants including analytic terms. We then calculate a number of SO(4) taste-breaking quantities, which involve only a small subset of these next-to-leading order operators. We predict relationships between SO(4) taste-breaking splittings in masses, pseudoscalar decay constants, and dispersion relations. We also find predictions for a few quantities that are not SO(4) breaking. All these results hold also for theories in which the fourth root of the fermionic determinant is taken to reduce the number of quark tastes; testing them will therefore provide evidence for or against the validity of this trick.

  4. A stochastic perturbation theory for non-autonomous systems

    SciTech Connect

    Moon, W.; Wettlaufer, J. S.

    2013-12-15

    We develop a perturbation theory for a class of first order nonlinear non-autonomous stochastic ordinary differential equations that arise in climate physics. The perturbative procedure produces moments in terms of integral delay equations, whose order by order decay is characterized in a Floquet-like sense. Both additive and multiplicative sources of noise are discussed and the question of how the nature of the noise influences the results is addressed theoretically and numerically. By invoking the Martingale property, we rationalize the transformation of the underlying Stratonovich form of the model to an Ito form, independent of whether the noise is additive or multiplicative. The generality of the analysis is demonstrated by developing it both for a Brownian particle moving in a periodically forced quartic potential, which acts as a simple model of stochastic resonance, as well as for our more complex climate physics model. The validity of the approach is shown by comparison with numerical solutions. The particular climate dynamics problem upon which we focus involves a low-order model for the evolution of Arctic sea ice under the influence of increasing greenhouse gas forcing ΔF{sub 0}. The deterministic model, developed by Eisenman and Wettlaufer [“Nonlinear threshold behavior during the loss of Arctic sea ice,” Proc. Natl. Acad. Sci. U.S.A. 106(1), 28–32 (2009)] exhibits several transitions as ΔF{sub 0} increases and the stochastic analysis is used to understand the manner in which noise influences these transitions and the stability of the system.

  5. Whitham theory for perturbed Korteweg-de Vries equation

    NASA Astrophysics Data System (ADS)

    Kamchatnov, A. M.

    2016-10-01

    Original Whitham's method of derivation of modulation equations is applied to systems whose dynamics is described by a perturbed Korteweg-de Vries equation. Two situations are distinguished: (i) the perturbation leads to appearance of right-hand sides in the modulation equations so that they become non-uniform; (ii) the perturbation leads to modification of the matrix of Whitham velocities. General form of Whitham modulation equations is obtained in both cases. The essential difference between them is illustrated by an example of so-called 'generalized Korteweg-de Vries equation'. Method of finding steady-state solutions of perturbed Whitham equations in the case of dissipative perturbations is considered.

  6. Singular perturbation theory for predicting extravasation of Brownian particles

    PubMed Central

    Shah, Preyas; Fitzgibbon, Sean; Narsimhan, Vivek; Shaqfeh, Eric S. G.

    2013-01-01

    Motivated by recent studies on tumor treatments using the drug delivery of nanoparticles, we provide a singular perturbation theory and perform Brownian dynamics simulations to quantify the extravasation rate of Brownian particles in a shear flow over a circular pore with a lumped mass transfer resistance. The analytic theory we present is an expansion in the limit of a vanishing Péclet number (P), which is the ratio of convective fluxes to diffusive fluxes on the length scale of the pore. We state the concentration of particles near the pore and the extravasation rate (Sherwood number) to O(P1/2). This model improves upon previous studies because the results are valid for all values of the particle mass transfer coefficient across the pore, as modeled by the Damköhler number (κ), which is the ratio of the reaction rate to the diffusive mass transfer rate at the boundary. Previous studies focused on the adsorption-dominated regime (i.e., κ → ∞). Specifically, our work provides a theoretical basis and an interpolation-based approximate method for calculating the Sherwood number (a measure of the extravasation rate) for the case of finite resistance [κ ~ O(1)] at small Péclet numbers, which are physiologically important in the extravasation of nanoparticles. We compare the predictions of our theory and an approximate method to Brownian dynamics simulations with reflection–reaction boundary conditions as modeled by κ. They are found to agree well at small P and for the κ ≪ 1 and κ ≫ 1 asymptotic limits representing the diffusion-dominated and adsorption-dominated regimes, respectively. Although this model neglects the finite size effects of the particles, it provides an important first step toward understanding the physics of extravasation in the tumor vasculature. PMID:24563548

  7. Polarizability of the pion: No conflict between dispersion theory and chiral perturbation theory

    SciTech Connect

    Pasquini, B.; Drechsel, D.; Scherer, S.

    2008-06-15

    Recent attempts to determine the pion polarizability by dispersion relations yield values that disagree with the predictions of chiral perturbation theory. These dispersion relations are based on specific forms for the absorptive part of the Compton amplitudes. The analytic properties of these forms are examined, and the strong enhancement of intermediate-meson contributions is shown to be connected with spurious singularities. If the basic requirements of dispersion relations are taken into account, the results of dispersion theory and effective field theory are not inconsistent.

  8. Extended multi-configuration quasi-degenerate perturbation theory: The new approach to multi-state multi-reference perturbation theory

    NASA Astrophysics Data System (ADS)

    Granovsky, Alexander A.

    2011-06-01

    The distinctive desirable features, both mathematically and physically meaningful, for all partially contracted multi-state multi-reference perturbation theories (MS-MR-PT) are explicitly formulated. The original approach to MS-MR-PT theory, called extended multi-configuration quasi-degenerate perturbation theory (XMCQDPT), having most, if not all, of the desirable properties is introduced. The new method is applied at the second order of perturbation theory (XMCQDPT2) to the 11A' - 21A' conical intersection in allene molecule, the avoided crossing in LiF molecule, and the 11A1 to 21A1 electronic transition in cis-1,3-butadiene. The new theory has several advantages compared to those of well-established approaches, such as second order multi-configuration quasi-degenerate perturbation theory and multi-state-second order complete active space perturbation theory. The analysis of the prevalent approaches to the MS-MR-PT theory performed within the framework of the XMCQDPT theory unveils the origin of their common inherent problems. We describe the efficient implementation strategy that makes XMCQDPT2 an especially useful general-purpose tool in the high-level modeling of small to large molecular systems.

  9. BOLD coherence reveals segregated functional neural interactions when adapting to distinct torque perturbations

    PubMed Central

    Tunik, Eugene; Schmitt, Paul J.; Grafton, Scott T.

    2007-01-01

    In the natural world, we experience and adapt to multiple extrinsic perturbations. This poses a challenge to neural circuits in discriminating between different context-appropriate responses. Using event-related fMRI, we characterized the neural dynamics involved in this process by randomly delivering a position- or velocity-dependent torque perturbation to subjects’ arms during a target capture task. Each perturbation was color-cued during movement preparation to provide contextual information. Though trajectories differed between perturbations, subjects significantly reduced error under both conditions. This was paralleled by reduced BOLD signal in the right dentate nucleus, the left sensorimotor cortex, and the left intraparietal sulcus. Trials included ‘NoGo’ conditions to dissociate activity related to preparation from execution and adaptation. Subsequent analysis identified perturbation-specific neural processes underlying preparation (‘NoGo’) and adaptation (‘Go’) early and late into learning. Between-perturbation comparisons of BOLD magnitude revealed negligible differences for both preparation and adaptation trials. However, a network-level analysis of BOLD coherence revealed that by late learning, response preparation (‘NoGo’) was attributed to a relative focusing of coherence within cortical and basal ganglia networks in both perturbation conditions, demonstrating a common network interaction for establishing arbitrary visuomotor associations. Conversely, late-learning adaptation (‘Go’) was attributed to a focusing of BOLD coherence between a cortical-basal ganglia network in the viscous condition and between a cortical-cerebellar network in the positional condition. Our findings demonstrate that trial-to-trial acquisition of two distinct adaptive responses is attributed not to anatomically segregated regions, but to differential functional interactions within common sensorimotor circuits. PMID:17202232

  10. Optimal Control Modification for Robust Adaptation of Singularly Perturbed Systems with Slow Actuators

    NASA Technical Reports Server (NTRS)

    Nguyen, Nhan T.; Ishihara, Abraham; Stepanyan, Vahram; Boskovic, Jovan

    2009-01-01

    Recently a new optimal control modification has been introduced that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations as with the standard model-reference adaptive control. This modification is based on an optimal control formulation to minimize the L2 norm of the tracking error. The optimal control modification adaptive law results in a stable adaptation in the presence of a large adaptive gain. This study examines the optimal control modification adaptive law in the context of a system with a time scale separation resulting from a fast plant with a slow actuator. A singular perturbation analysis is performed to derive a modification to the adaptive law by transforming the original system into a reduced-order system in slow time. The model matching conditions in the transformed time coordinate results in increase in the feedback gain and modification of the adaptive law.

  11. Time-dependent perturbation theory in quantum mechanics and the renormalization group

    NASA Astrophysics Data System (ADS)

    Bhattacharjee, J. K.; Ray, D. S.

    2016-06-01

    Time-dependent perturbation theory in quantum mechanics is divergent at long times when the perturbation induces a resonance between two eigenstates of the unperturbed Hamiltonian. Divergences in perturbation theory are also common in quantum field theory and in critical phenomena. The renormalization group (RG) was designed to deal with these divergences. In the last two decades, this procedure has been extended to dynamical systems where the perturbation theory diverges in the long-time limit. In this article, we first review the connection between RG in the context of field theory and RG in the context of dynamical systems. We then show that the long-time divergence in the resonant situation in the time-dependent perturbation theory in quantum mechanics can be removed by using a RG-aided calculational scheme.

  12. Thermodynamic properties of van der Waals fluids from Monte Carlo simulations and perturbative Monte Carlo theory

    NASA Astrophysics Data System (ADS)

    Díez, A.; Largo, J.; Solana, J. R.

    2006-08-01

    Computer simulations have been performed for fluids with van der Waals potential, that is, hard spheres with attractive inverse power tails, to determine the equation of state and the excess energy. On the other hand, the first- and second-order perturbative contributions to the energy and the zero- and first-order perturbative contributions to the compressibility factor have been determined too from Monte Carlo simulations performed on the reference hard-sphere system. The aim was to test the reliability of this "exact" perturbation theory. It has been found that the results obtained from the Monte Carlo perturbation theory for these two thermodynamic properties agree well with the direct Monte Carlo simulations. Moreover, it has been found that results from the Barker-Henderson [J. Chem. Phys. 47, 2856 (1967)] perturbation theory are in good agreement with those from the exact perturbation theory.

  13. Hyperfine Coupling Constants from Internally Contracted Multireference Perturbation Theory.

    PubMed

    Shiozaki, Toru; Yanai, Takeshi

    2016-09-13

    We present an accurate method for calculating hyperfine coupling constants (HFCCs) based on the complete active space second-order perturbation theory (CASPT2) with full internal contraction. The HFCCs are computed as a first-order property using the relaxed CASPT2 spin-density matrix that takes into account orbital and configurational relaxation due to dynamical electron correlation. The first-order unrelaxed spin-density matrix is calculated from one- and two-body spin-free counterparts that are readily available in the CASPT2 nuclear gradient program [M. K. MacLeod and T. Shiozaki, J. Chem. Phys. 142, 051103 (2015)], whereas the second-order part is computed directly using the newly extended automatic code generator. The relaxation contribution is then calculated from the so-called Z-vectors that are available in the CASPT2 nuclear gradient program. Numerical results are presented for the CN and AlO radicals, for which the CASPT2 values are comparable (or, even superior in some cases) to the ones computed by the coupled-cluster and density matrix renormalization group methods. The HFCCs for the hexaaqua complexes with V(II), Cr(III), and Mn(II) are also presented to demonstrate the accuracy and efficiency of our code. PMID:27479148

  14. Staggered chiral perturbation theory for heavy-light mesons

    SciTech Connect

    Aubin, C.; Bernard, C.

    2006-01-01

    We incorporate heavy-light mesons into staggered chiral perturbation theory (S{chi}PT), working to leading order in 1/m{sub Q}, where m{sub Q} is the heavy-quark mass. At first nontrivial order in the chiral expansion, staggered taste violations affect the chiral logarithms for heavy-light quantities only through the light-meson propagators in loops. There are also new analytic contributions coming from additional terms in the Lagrangian involving heavy-light and light mesons. Using this heavy-light S{chi}PT, we perform the one-loop calculation of the B (or D) meson leptonic decay constant in the partially quenched and full QCD cases. In our treatment, we assume the validity both of the 'fourth root trick' to reduce four staggered tastes to one, and of the S{chi}PT prescription to represent this trick by insertions of factors of 1/4 for each sea-quark loop.

  15. Hyperfine Coupling Constants from Internally Contracted Multireference Perturbation Theory.

    PubMed

    Shiozaki, Toru; Yanai, Takeshi

    2016-09-13

    We present an accurate method for calculating hyperfine coupling constants (HFCCs) based on the complete active space second-order perturbation theory (CASPT2) with full internal contraction. The HFCCs are computed as a first-order property using the relaxed CASPT2 spin-density matrix that takes into account orbital and configurational relaxation due to dynamical electron correlation. The first-order unrelaxed spin-density matrix is calculated from one- and two-body spin-free counterparts that are readily available in the CASPT2 nuclear gradient program [M. K. MacLeod and T. Shiozaki, J. Chem. Phys. 142, 051103 (2015)], whereas the second-order part is computed directly using the newly extended automatic code generator. The relaxation contribution is then calculated from the so-called Z-vectors that are available in the CASPT2 nuclear gradient program. Numerical results are presented for the CN and AlO radicals, for which the CASPT2 values are comparable (or, even superior in some cases) to the ones computed by the coupled-cluster and density matrix renormalization group methods. The HFCCs for the hexaaqua complexes with V(II), Cr(III), and Mn(II) are also presented to demonstrate the accuracy and efficiency of our code.

  16. Equation-of-motion coupled cluster perturbation theory revisited

    SciTech Connect

    Eriksen, Janus J. Jørgensen, Poul; Olsen, Jeppe; Gauss, Jürgen

    2014-05-07

    The equation-of-motion coupled cluster (EOM-CC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally converges towards the full configuration interaction energy limit. The series is based on a Møller-Plesset partitioning of the Hamiltonian and thus size extensive at any order in the perturbation, thereby remedying the major deficiency inherent to previous perturbation series based on the EOM-CC ansatz.

  17. Adaptive strategies of remote systems operators exposed to perturbed camera-viewing conditions

    NASA Technical Reports Server (NTRS)

    Stuart, Mark A.; Manahan, Meera K.; Bierschwale, John M.; Sampaio, Carlos E.; Legendre, A. J.

    1991-01-01

    This report describes a preliminary investigation of the use of perturbed visual feedback during the performance of simulated space-based remote manipulation tasks. The primary objective of this NASA evaluation was to determine to what extent operators exhibit adaptive strategies which allow them to perform these specific types of remote manipulation tasks more efficiently while exposed to perturbed visual feedback. A secondary objective of this evaluation was to establish a set of preliminary guidelines for enhancing remote manipulation performance and reducing the adverse effects. These objectives were accomplished by studying the remote manipulator performance of test subjects exposed to various perturbed camera-viewing conditions while performing a simulated space-based remote manipulation task. Statistical analysis of performance and subjective data revealed that remote manipulation performance was adversely affected by the use of perturbed visual feedback and performance tended to improve with successive trials in most perturbed viewing conditions.

  18. Relation between the standard perturbation theory and regularized multi-point propagator method

    SciTech Connect

    Sugiyama, Naonori S.; Futamase, Toshifumi

    2013-06-01

    We investigate the relation between the regularized multi-propagator method, called 'Reg PT', and the standard perturbation theory. Reg PT is one of the most successful models to describe nonlinear evolution of dark matter fluctuations. However, Reg PT is a mathematically unproven interpolation formula between the large-scale solution calculated by the standard perturbation theory and the limiting solution in the small scale calculated by the multi-point propagator method. In this paper, we give an alternative explanation for Reg PT in the context of the standard perturbation theory, showing that Reg PT does not ever have more effective information on nonlinear matter evolution than the standard perturbation theory. In other words, the solutions of the standard perturbation theory reproduce the results of N-body simulations better than those of Reg PT, especially at the high-k region. This fact means that the standard perturbation theory at the two-loop level is still one of the best predictions of the nonlinear power spectrum to date. Nevertheless, the standard perturbation theory has not been preferred because of the divergent behavior of the solution at small scales. To solve this problem, we also propose a modified standard perturbation theory which avoids the divergence.

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

    NASA Technical Reports Server (NTRS)

    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.

  20. GNSS-derived Geocenter Coordinates Viewed by Perturbation Theory

    NASA Astrophysics Data System (ADS)

    Meindl, Michael; Beutler, Gerhard; Thaller, Daniela; Dach, Rolf; Jäggi, Adrian; Rothacher, Markus

    2013-04-01

    Time series of geocenter coordinates were determined with data of the two global navigation satellite systems (GNSS) GPS and GLONASS. The data was recorded in the years 2008-2011 by a global network of 92 combined GPS/GLONASS receivers. Two types of solutions were generated for each system, one including the estimation of geocenter coordinates and one without these parameters. A fair agreement for GPS and GLONASS estimates was found in the x- and y-coordinate series of the geocenter. Artifacts do, however, clearly show up in the z-coordinate. Large periodic variations in the GLONASS geocenter z-coordinates of about 40 cm peak-to-peak are related to the maximum elevation angles of the Sun above/below the orbital planes of the satellite system. A detailed analysis revealed that these artifacts are almost uniquely governed by the differences of the estimates of direct solar radiation pressure (SRP) in the two solution series (with and without geocenter estimation). This effect can be explained by first-order perturbation theory of celestial mechanics. The relation between the geocenter z-coordinate and the corresponding SRP parameters will be presented. Our theory is applicable to all satellite observing techniques. In addition to GNSS, we applied it to satellite laser ranging (SLR) solutions based on LAGEOS observations. The correlation between geocenter and SRP parameters is not a critical issue for SLR, because these parameters do not have to be estimated. This basic difference between SLR and GNSS analyses explains why SLR is an excellent tool to determine geodetic datum parameters like the geocenter coordinates. The correlation between orbit parameters and the z-component of the geocenter is not limited to a particular orbit model, e.g., that of CODE. The issue should be studied for alternative (e.g., box-wing) models: As soon as non-zero mean values (over one revolution) of the out-of-plane force component exist, one has to expect biased geocenter estimates. The

  1. Motor adaptation to Coriolis force perturbations of reaching movements: endpoint but not trajectory adaptation transfers to the nonexposed arm.

    PubMed

    Dizio, P; Lackner, J R

    1995-10-01

    1. Reaching movements made in a rotating room generate Coriolis forces that are directly proportional to the cross product of the room's angular velocity and the arm's linear velocity. Such Coriolis forces are inertial forces not involving mechanical contact with the arm. 2. We measured the trajectories of arm movements made in darkness to a visual target that was extinguished at the onset of each reach. Prerotation subjects pointed with both the right and left arms in alternating sets of eight movements. During rotation at 10 rpm, the subjects reached only with the right arm. Postrotation, the subjects pointed with the left and right arms, starting with the left, in alternating sets of eight movements. 3. The initial perrotary reaching movements of the right arm were highly deviated both in movement path and endpoint relative to the prerotation reaches of the right arm. With additional movements, subjects rapidly regained straight movement paths and accurate endpoints despite the absence of visual or tactile feedback about reaching accuracy. The initial postrotation reaches of the left arm followed straight paths to the wrong endpoint. The initial postrotation reaches of the right arm had paths with mirror image curvature to the initial perrotation reaches of the right arm but went to the correct endpoint. 4. These observations are inconsistent with current equilibrium point models of movement control. Such theories predict accurate reaches under our experimental conditions. Our observations further show independent implementation of movement and posture, as evidenced by transfer of endpoint adaptation to the nonexposed arm without transfer of path adaptation. Endpoint control may occur at a relatively central stage that represents general constraints such as gravitoinertial force background or egocentric direction relative to both arms, and control of path may occur at a more peripheral stage that represents moments of inertia and muscle dynamics unique to each

  2. Motor adaptation to Coriolis force perturbations of reaching movements: endpoint but not trajectory adaptation transfers to the nonexposed arm

    NASA Technical Reports Server (NTRS)

    Dizio, P.; Lackner, J. R.

    1995-01-01

    1. Reaching movements made in a rotating room generate Coriolis forces that are directly proportional to the cross product of the room's angular velocity and the arm's linear velocity. Such Coriolis forces are inertial forces not involving mechanical contact with the arm. 2. We measured the trajectories of arm movements made in darkness to a visual target that was extinguished at the onset of each reach. Prerotation subjects pointed with both the right and left arms in alternating sets of eight movements. During rotation at 10 rpm, the subjects reached only with the right arm. Postrotation, the subjects pointed with the left and right arms, starting with the left, in alternating sets of eight movements. 3. The initial perrotary reaching movements of the right arm were highly deviated both in movement path and endpoint relative to the prerotation reaches of the right arm. With additional movements, subjects rapidly regained straight movement paths and accurate endpoints despite the absence of visual or tactile feedback about reaching accuracy. The initial postrotation reaches of the left arm followed straight paths to the wrong endpoint. The initial postrotation reaches of the right arm had paths with mirror image curvature to the initial perrotation reaches of the right arm but went to the correct endpoint. 4. These observations are inconsistent with current equilibrium point models of movement control. Such theories predict accurate reaches under our experimental conditions. Our observations further show independent implementation of movement and posture, as evidenced by transfer of endpoint adaptation to the nonexposed arm without transfer of path adaptation. Endpoint control may occur at a relatively central stage that represents general constraints such as gravitoinertial force background or egocentric direction relative to both arms, and control of path may occur at a more peripheral stage that represents moments of inertia and muscle dynamics unique to each

  3. A Perturbation Theory for Hamilton's Principal Function: Applications to Boundary Value Problems

    NASA Astrophysics Data System (ADS)

    Munoa, Oier Penagaricano

    This thesis introduces an analytical perturbation theory for Hamilton's principal function and Hamilton's characteristic function. Based on Hamilton's principle and the research carried out by Sir William Rowan Hamilton, a perturbation theory is developed to analytically solve two-point boundary value problems. The principal function is shown to solve the two-point boundary value problem through simple differentiation and elimination. The characteristic function is related to the principal function through a Legendre transformation, and can also be used to solve two-point boundary value problems. In order to obtain the solution to the perturbed two-point boundary value problem the knowledge of the nominal solution is sufficient. The perturbation theory is applied to the two body problem to study the perturbed dynamics in the vicinity of the Hohmann transfer. It is found that the perturbation can actually offer a lower cost two-impulse transfer to the target orbit than the Hohmann transfer. The numerical error analysis of the perturbation theory is shown for different orders of calculation. Coupling Hamilton's principal and characteristic functions yields an analytical perturbation theory for the initial value problem, where the state of the perturbed system can be accurately obtained. The perturbation theory is applied to the restricted three-body problem, where the system is viewed as a two-body problem perturbed by the presence of a third body. It is shown that the first order theory can be sufficient to solve the problem, winch is expressed in terms of Delaunay elements. The solution to the initial value problem is applied to derive a Keplerian periapsis map that can be used for low-energy space mission design problems.

  4. Gauge invariant perturbation theory and non-critical string models of Yang-Mills theories

    NASA Astrophysics Data System (ADS)

    Lugo, Adrián R.; Sturla, Mauricio B.

    2010-04-01

    We carry out a gauge invariant analysis of certain perturbations of D - 2-branes solutions of low energy string theories. We get generically a system of second order coupled differential equations, and show that only in very particular cases it is possible to reduce it to just one differential equation. Later, we apply it to a multi-parameter, generically singular family of constant dilaton solutions of non-critical string theories in D dimensions, a generalization of that recently found in arXiv:0709.0471 [hep-th]. According to arguments coming from the holographic gauge theory-gravity correspondence, and at least in some region of the parameters space, we obtain glue-ball spectra of Yang-Mills theories in diverse dimensions, putting special emphasis in the scalar metric perturbations not considered previously in the literature in the non critical setup. We compare our numerical results to those studied previously and to lattice results, finding qualitative and in some cases, tuning properly the parameters, quantitative agreement. These results seem to show some kind of universality of the models, as well as an irrelevance of the singular character of the solutions. We also develop the analysis for the T-dual, non trivial dilaton family of solutions, showing perfect agreement between them.

  5. Applications of adaptive state estimation theory

    NASA Technical Reports Server (NTRS)

    Moose, R. L.; Vanlandingham, H. F.; Mccabe, D. H.

    1980-01-01

    Two main areas of application of adaptive state estimation theory are presented. Following a review of the basic estimation approach, its application to both the control of nonlinear plants and to the problem of tracking maneuvering targets is presented. Results are brought together from these two areas of investigation to provide insight into the wide range of possible applications of the general estimation method.

  6. Adaptive piezoelectric shell structures: theory and experiments

    NASA Astrophysics Data System (ADS)

    Tzou, H. S.; Zhong, J. P.

    1993-07-01

    Active "smart" space and mechanical structures with adaptive dynamic characteristics have long been interested in a variety of high-performance systems, e.g. flexible space structures, flexible robots, "smart" machines etc. In this paper, an active adaptive structure made of piezoelectric materials is proposed and evaluated. Electromechanical equations of motion and generalised boundary conditions of a generic piezoelectric shell subjected to mechanical and electrical excitations are derived using Hamilton's principle and the linear piezoelectric theory. The structural adaptivity is achieved by a voltage feedback (open or closed loops) utilising the converse piezoelectric effect. Applications of the theory is demonstrated in a bimorph beam case and a cylindrical shell case. Frequency manipulation of the bimorph beam is studied theoretically and experimentally. Damping control of the cylindrical shell via in-plane membrane forces is also investigated.

  7. Changes in cortical activity associated with adaptive behavior during repeated balance perturbation of unpredictable timing

    PubMed Central

    Mierau, Andreas; Hülsdünker, Thorben; Strüder, Heiko K.

    2015-01-01

    The compensation for a sudden balance perturbation, unpracticed and unpredictable in timing and magnitude is accompanied by pronounced postural instability that is suggested to be causal to falls. However, subsequent presentations of an identical perturbation are characterized by a marked decrease of the amplitude of postural reactions; a phenomenon called adaptation or habituation. This study aimed to identify cortical characteristics associated with adaptive behavior during repetitive balance perturbations based on single-trial analyses of the P1 and N1 perturbation-evoked potentials. Thirty-seven young men were exposed to ten transient balance perturbations while balancing on the dominant leg. Thirty two-channel electroencephalography (EEG), surface electromyography (EMG) of the ankle plantar flexor muscles and postural sway (i.e., Euclidean distance of the supporting platform) were recorded simultaneously. The P1 and N1 potentials were localized and the amplitude/latency was analyzed trial by trial. The best match sources for P1 and N1 potentials were located in the parietal (Brodmann area (BA) 5) and midline fronto-central cortex (BA 6), respectively. The amplitude and latency of the P1 potential remained unchanged over trials. In contrast, a significant adaptation of the N1 amplitude was observed. Similar adaptation effects were found with regard to postural sway and ankle plantarflexors EMG activity of the non-dominant (free) leg; i.e., an indicator for reduced muscular co-contraction and/or less temporary bipedal stance to regain stability. Significant but weak correlations were found between N1 amplitude and postural sway as well as EMG activity. These results highlight the important role of the midline fronto-central cortex for adaptive behavior associated with balance control. PMID:26528154

  8. Cosmological density perturbations in a conformal scalar field theory

    NASA Astrophysics Data System (ADS)

    Libanov, M. V.; Rubakov, V. A.

    2012-02-01

    We consider a scenario in which primordial scalar perturbations are generated when a complex conformal scalar field rolls down its negative quartic potential. Initially, these are perturbations of the phase of this field, which are then converted into adiabatic perturbations of the density. The existence of perturbations in the radial field direction, which have a red power spectrum, is a potentially dangerous feature of this scenario. But we show that in the linear order in the small parameter, the self-coupling, the infrared effects are completely nullified by an appropriate field redefinition. We evaluate the statistical anisotropy inherent in the model because of the presence of the long-wave perturbations of the radial field component. In the linear order in the self-coupling, the infrared effects do not affect the statistical anisotropy. They are manifested only at the quadratic order in the self-coupling, weakly (logarithmically) enhancing the corresponding contribution to the statistical anisotropy. The resulting statistical anisotropy is a combination of a large term, which decreases as the momentum increases, and a momentum-independent nonamplified term.

  9. Relativistic many-body perturbation theory for general open-shell multiplet states of atoms

    NASA Astrophysics Data System (ADS)

    Ishikawa, Yasuyuki; Koc, Konrad

    1996-06-01

    A relativistic many-body perturbation theory, which accounts for relativistic and electron-correlation effects for general open-shell multiplet states of atoms and molecules, is developed and implemented with analytic basis sets of Gaussian spinors. The theory retains the essential aspects of Mo/ller-Plesset perturbation theory by employing the relativistic single-Fock-operator method of Koc and Ishikawa [Phys. Rev. A 49, 794 (1994)] for general open-shell systems. Open-shell Dirac-Fock and relativistic many-body perturbation calculations are reported for the ground and low-lying excited states of Li, B2+, Ne7+, and Ca11+.

  10. Application of MACSYMA to first order perturbation theory in celestial mechanics

    NASA Technical Reports Server (NTRS)

    Anderson, J. D.; Lau, E. L.

    1977-01-01

    The application of MACSYMA to general first order perturbation theory in celestial mechanics is explored. Methods of derivation of small variations in the Keplerian orbital elements are developed. As an example of the methods, the small general relativistic perturbations on the two-body Newtonian motion, resulting from the rotation of the central body, are developed in detail.

  11. Theory of perturbative pulse train based coherent control

    NASA Astrophysics Data System (ADS)

    Grinev, Timur; Brumer, Paul

    2014-03-01

    A theoretical description of coherent control of excited state dynamics using pulse trains in the perturbative regime, as carried out in recent experiments, is presented. Analytical expressions relating the excited state populations to the pulse train control parameters are derived. Numerical examples are provided for models of pyrazine and β-carotene, and the significant role of overlapping resonances is exposed.

  12. Adaptation to large-magnitude treadmill-based perturbations: improvements in reactive balance response

    PubMed Central

    Patel, Prakruti; Bhatt, Tanvi

    2015-01-01

    We aimed to examine the trial-to-trial changes in the reactive balance response to large magnitude slip-like treadmill perturbations in stance and whether the acquired adaptive changes could be appropriately scaled to a higher intensity perturbation. Seventeen young adults experienced 15 slips for training on level I intensity. Pre- and post-training slips were delivered at a higher intensity (20% > level I). Pre- and post-slip onset stability (at liftoff and touchdown of stepping limb) was measured as the shortest distance of the center of mass (COM) position (XCOM/BOS) and velocity (ẊCOM/BOS) relative to base of support (BOS) from a predicted threshold for backward loss of balance. The number of steps to recover balance, compensatory step length and peak trunk angle were recorded. The post-slip onset stability (at liftoff and touchdown) significantly increased across the trials with no change in preslip stability. Improvement in stability at touchdown positively correlated with an anterior shift in XCOM/BOS but not with ẊCOM/BOS. Consequently, the number of steps required to recover balance declined. The adaptive change in XCOM/BOS resulted from an increase in compensatory step length and reduced trunk extension. Individuals also improved post-slip onset stability on a higher intensity perturbation post-training compared with the pre-training trial. The results support that the CNS adapts to fixed intensity slip-like perturbations primarily by improving the reactive stability via modulation in compensatory step length and trunk extension. Furthermore, based on prior experience from the training phase, the acquired adaptive response can be successfully calibrated to a higher intensity perturbation. PMID:25649245

  13. Reply to 'Comment on 'Polarizability of the pion: No conflict between dispersion theory and chiral perturbation theory''

    SciTech Connect

    Pasquini, B.; Drechsel, D.; Scherer, S.

    2010-02-15

    We show that the alleged discrepancies between chiral perturbation theory (ChPT) and dispersion theory, reported for the polarizability of the pion by Fil'kov and Kashevarov [Phys. Rev. C 72, 035211 (2005)], result from applying dispersion theory to nonanalytic functions.

  14. Automatic Generation of Analytic Equations for Vibrational and Rovibrational Constants from Fourth-Order Vibrational Perturbation Theory

    NASA Astrophysics Data System (ADS)

    Matthews, Devin A.; Gong, Justin Z.; Stanton, John F.

    2014-06-01

    The derivation of analytic expressions for vibrational and rovibrational constants, for example the anharmonicity constants χij and the vibration-rotation interaction constants α^B_r, from second-order vibrational perturbation theory (VPT2) can be accomplished with pen and paper and some practice. However, the corresponding quantities from fourth-order perturbation theory (VPT4) are considerably more complex, with the only known derivations by hand extensively using many layers of complicated intermediates and for rotational quantities requiring specialization to orthorhombic cases or the form of Watson's reduced Hamiltonian. We present an automatic computer program for generating these expressions with full generality based on the adaptation of an existing numerical program based on the sum-over-states representation of the energy to a computer algebra context. The measures taken to produce well-simplified and factored expressions in an efficient manner are discussed, as well as the framework for automatically checking the correctness of the generated equations.

  15. Perturbation theory, effective field theory, and oscillations in the power spectrum

    NASA Astrophysics Data System (ADS)

    Vlah, Zvonimir; Seljak, Uroš; Yat Chu, Man; Feng, Yu

    2016-03-01

    We explore the relationship between the nonlinear matter power spectrum and the various Lagrangian and Standard Perturbation Theories (LPT and SPT). We first look at it in the context of one dimensional (1-d) dynamics, where 1LPT is exact at the perturbative level and one can exactly resum the SPT series into the 1LPT power spectrum. Shell crossings lead to non-perturbative effects, and the PT ignorance can be quantified in terms of their ratio, which is also the transfer function squared in the absence of stochasticity. At the order of PT we work, this parametrization is equivalent to the results of effective field theory (EFT), and can thus be expanded in terms of the same parameters. We find that its radius of convergence is larger than the SPT loop expansion. The same EFT parametrization applies to all SPT loop terms and if stochasticity can be ignored, to all N-point correlators. In 3-d, the LPT structure is considerably more complicated, and we find that LPT models with parametrization motivated by the EFT exhibit running with k and that SPT is generally a better choice. Since these transfer function expansions contain free parameters that change with cosmological model their usefulness for broadband power is unclear. For this reason we test the predictions of these models on baryonic acoustic oscillations (BAO) and other primordial oscillations, including string monodromy models, for which we ran a series of simulations with and without oscillations. Most models are successful in predicting oscillations beyond their corresponding PT versions, confirming the basic validity of the model. We show that if primordial oscillations are localized to a scale q, the wiggles in power spectrum are approximately suppressed as exp[-k2Σ2(q)/2], where Σ(q) is rms displacement of particles separated by q, which saturates on large scales, and decreases as q is reduced. No oscillatory features survive past k ~ 0.5h/Mpc at z = 0.

  16. Perturbative quantum field theory in the framework of the fermionic projector

    SciTech Connect

    Finster, Felix

    2014-04-15

    We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergences occur.

  17. On estimating perturbative coefficients in quantum field theory and statistical physics

    SciTech Connect

    Samuel, M.A. |

    1994-05-01

    The authors present a method for estimating perturbative coefficients in quantum field theory and Statistical Physics. They are able to obtain reliable error-bars for each estimate. The results, in all cases, are excellent.

  18. Locomotor stability and adaptation during perturbed walking across the adult female lifespan.

    PubMed

    McCrum, Christopher; Epro, Gaspar; Meijer, Kenneth; Zijlstra, Wiebren; Brüggemann, Gert-Peter; Karamanidis, Kiros

    2016-05-01

    The aim of this work was to examine locomotor stability and adaptation across the adult female lifespan during perturbed walking on the treadmill. 11 young, 11 middle and 14 older-aged female adults (mean and SD: 25.5(2.1), 50.6(6.4) and 69.0(4.7) years old respectively) walked on a treadmill. We applied a sustained perturbation to the swing phase of the right leg for 18 consecutive gait cycles, followed by a step with the resistance unexpectedly removed, via an ankle strap connected to a break-and-release system. The margin of stability (MoS) at foot touchdown was calculated as the difference between the anterior boundary of the base of support (BoS) and extrapolated center of mass. Older participants showed lower MoS adaptation magnitude in the early adaptation phase (steps 1-3) compared to the young and middle-aged groups. However, in the late adaptation phase (steps 16-18) there were no significant differences in adaptation magnitude between the three age groups. After removing the resistance, all three age groups showed similar aftereffects (i.e. increased BoS). The current results suggest that in old age, the ability to recalibrate locomotion to control stability is preserved, but the rate of adaptive improvement in locomotor stability is diminished.

  19. Reciprocity theorem and perturbation theory for photonic crystal waveguides.

    PubMed

    Michaelis, D; Peschel, U; Wächter, C; Bräuer, A

    2003-12-01

    Starting from Maxwell's equations we derive a reciprocity theorem for photonic crystal waveguides. A set of strongly coupled discrete equations results, which can be applied to the simulation of perturbed photonic crystal waveguides. As an example we analytically study the influence of the dispersion of a two level system on the band structure of a photonic crystal waveguide. In particular, the formation of polariton gaps is discussed.

  20. Nonminimal derivative coupling scalar-tensor theories: Odd-parity perturbations and black hole stability

    NASA Astrophysics Data System (ADS)

    Cisterna, Adolfo; Cruz, Miguel; Delsate, Térence; Saavedra, Joel

    2015-11-01

    We derive the odd-parity perturbation equation for the nonminimal kinetic coupling sector of the general Horndeski theory, where the kinetic term is coupled to the metric and the Einstein tensor. We derive the potential of the perturbation, by identifying a master function and switching to tortoise coordinates. We then prove the mode stability under linear odd-parity perturbations of hairy black holes in this sector of Horndeski theory, when a cosmological constant term in the action is included. Finally, we comment on the existence of slowly rotating black hole solutions in this setup and discuss their implications on the physics of compact object configurations, such as neutron stars.

  1. Two-point functions of quenched lattice QCD in Numerical Stochastic Perturbation Theory

    SciTech Connect

    Di Renzo, F.; Ilgenfritz, E.-M.; Perlt, H.; Schiller, A.; Torrero, C.

    2011-05-23

    We summarize the higher-loop perturbative computation of the ghost and gluon propagators in SU(3) Lattice Gauge Theory. Our final aim is to compare with results from lattice simulations in order to expose the genuinely non-perturbative content of the latter. By means of Numerical Stochastic Perturbation Theory we compute the ghost and gluon propagators in Landau gauge up to three and four loops. We present results in the infinite volume and a{yields}0 limits, based on a general fitting strategy.

  2. Formation of model-free motor memories during motor adaptation depends on perturbation schedule.

    PubMed

    Orban de Xivry, Jean-Jacques; Lefèvre, Philippe

    2015-04-01

    Motor adaptation to an external perturbation relies on several mechanisms such as model-based, model-free, strategic, or repetition-dependent learning. Depending on the experimental conditions, each of these mechanisms has more or less weight in the final adaptation state. Here we focused on the conditions that lead to the formation of a model-free motor memory (Huang VS, Haith AM, Mazzoni P, Krakauer JW. Neuron 70: 787-801, 2011), i.e., a memory that does not depend on an internal model or on the size or direction of the errors experienced during the learning. The formation of such model-free motor memory was hypothesized to depend on the schedule of the perturbation (Orban de Xivry JJ, Ahmadi-Pajouh MA, Harran MD, Salimpour Y, Shadmehr R. J Neurophysiol 109: 124-136, 2013). Here we built on this observation by directly testing the nature of the motor memory after abrupt or gradual introduction of a visuomotor rotation, in an experimental paradigm where the presence of model-free motor memory can be identified (Huang VS, Haith AM, Mazzoni P, Krakauer JW. Neuron 70: 787-801, 2011). We found that relearning was faster after abrupt than gradual perturbation, which suggests that model-free learning is reduced during gradual adaptation to a visuomotor rotation. In addition, the presence of savings after abrupt introduction of the perturbation but gradual extinction of the motor memory suggests that unexpected errors are necessary to induce a model-free motor memory. Overall, these data support the hypothesis that different perturbation schedules do not lead to a more or less stabilized motor memory but to distinct motor memories with different attributes and neural representations.

  3. Formation tracker design of multiple mobile robots with wheel perturbations: adaptive output-feedback approach

    NASA Astrophysics Data System (ADS)

    Yoo, Sung Jin

    2016-11-01

    This paper presents a theoretical design approach for output-feedback formation tracking of multiple mobile robots under wheel perturbations. It is assumed that these perturbations are unknown and the linear and angular velocities of the robots are unmeasurable. First, adaptive state observers for estimating unmeasurable velocities of the robots are developed under the robots' kinematics and dynamics including wheel perturbation effects. Then, we derive a virtual-structure-based formation tracker scheme according to the observer dynamic surface design procedure. The main difficulty of the output-feedback control design is to manage the coupling problems between unmeasurable velocities and unknown wheel perturbation effects. These problems are avoided by using the adaptive technique and the function approximation property based on fuzzy logic systems. From the Lyapunov stability analysis, it is shown that point tracking errors of each robot and synchronisation errors for the desired formation converge to an adjustable neighbourhood of the origin, while all signals in the controlled closed-loop system are semiglobally uniformly ultimately bounded.

  4. A novel adaptive controller for two-degree of freedom polar robot with unknown perturbations

    NASA Astrophysics Data System (ADS)

    Faieghi, Mohammad Reza; Delavari, Hadi; Baleanu, Dumitru

    2012-02-01

    In industrial applications, the performance of robot manipulators is always affected due to the presence of uncertainties and disturbances. This paper proposes a novel adaptive control scheme for robust control of robotic manipulators perturbed by unknown uncertainties and disturbances. First, an active sliding mode controller is designed and a sufficient condition is obtained guarantying reachability of the states to hit the sliding surface in finite time. Then, based on a Lyapunov function candidate an adaptive switching gain is derived which make the controller capable to bring the tracking error to zero without any disturbance exerted upon the stability. By virtue of this controller it can be shown that the controller can track the desired trajectories even in the presence of unknown perturbations. For the problem of determining the control parameters Particle Swarm Optimization (PSO) algorithm has been employed. Our theoretic achievements are verified by numerical simulations.

  5. A time-dependent formulation of multi-reference perturbation theory.

    PubMed

    Sokolov, Alexander Yu; Chan, Garnet Kin-Lic

    2016-02-14

    We discuss the time-dependent formulation of perturbation theory in the context of the interacting zeroth-order Hamiltonians that appear in multi-reference situations. As an example, we present a time-dependent formulation and implementation of second-order n-electron valence perturbation theory. The resulting time-dependent n-electron valence second-order perturbation theory (t-NEVPT2) method yields the fully uncontracted n-electron valence perturbation wavefunction and energy, but has a lower computational scaling than the usual contracted variants, and also avoids the construction of high-order density matrices and the diagonalization of metrics. We present results of t-NEVPT2 for the water, nitrogen, carbon, and chromium molecules and outline directions for the future.

  6. Multi-Level Adaptive Techniques (MLAT) for singular-perturbation problems

    NASA Technical Reports Server (NTRS)

    Brandt, A.

    1978-01-01

    The multilevel (multigrid) adaptive technique, a general strategy of solving continuous problems by cycling between coarser and finer levels of discretization is described. It provides very fast general solvers, together with adaptive, nearly optimal discretization schemes. In the process, boundary layers are automatically either resolved or skipped, depending on a control function which expresses the computational goal. The global error decreases exponentially as a function of the overall computational work, in a uniform rate independent of the magnitude of the singular-perturbation terms. The key is high-order uniformly stable difference equations, and uniformly smoothing relaxation schemes.

  7. Adaptive neural control for a class of perturbed strict-feedback nonlinear time-delay systems.

    PubMed

    Wang, Min; Chen, Bing; Shi, Peng

    2008-06-01

    This paper proposes a novel adaptive neural control scheme for a class of perturbed strict-feedback nonlinear time-delay systems with unknown virtual control coefficients. Based on the radial basis function neural network online approximation capability, an adaptive neural controller is presented by combining the backstepping approach and Lyapunov-Krasovskii functionals. The proposed controller guarantees the semiglobal boundedness of all the signals in the closed-loop system and contains minimal learning parameters. Finally, three simulation examples are given to demonstrate the effectiveness and applicability of the proposed scheme.

  8. New Approach for IIR Adaptive Lattice Filter Structure Using Simultaneous Perturbation Algorithm

    NASA Astrophysics Data System (ADS)

    Martinez, Jorge Ivan Medina; Nakano, Kazushi; Higuchi, Kohji

    Adaptive infinite impulse response (IIR), or recursive, filters are less attractive mainly because of the stability and the difficulties associated with their adaptive algorithms. Therefore, in this paper the adaptive IIR lattice filters are studied in order to devise algorithms that preserve the stability of the corresponding direct-form schemes. We analyze the local properties of stationary points, a transformation achieving this goal is suggested, which gives algorithms that can be efficiently implemented. Application to the Steiglitz-McBride (SM) and Simple Hyperstable Adaptive Recursive Filter (SHARF) algorithms is presented. Also a modified version of Simultaneous Perturbation Stochastic Approximation (SPSA) is presented in order to get the coefficients in a lattice form more efficiently and with a lower computational cost and complexity. The results are compared with previous lattice versions of these algorithms. These previous lattice versions may fail to preserve the stability of stationary points.

  9. Adaptive preconditioning in neurological diseases – therapeutic insights from proteostatic perturbations

    PubMed Central

    Mollereau, B.; Rzechorzek, N.M.; Roussel, B.D.; Sedru, M.; Van den Brink, D.M.; Bailly-Maitre, B.; Palladino, F.; Medinas, D.B.; Domingos, P.M.; Hunot, S.; Chandran, S.; Birman, S.; Baron, T.; Vivien, D.; Duarte, C.B.; Ryoo, H.D.; Steller, H.; Urano, F.; Chevet, E.; Kroemer, G.; Ciechanover, A.; Calabrese, E.J.; Kaufman, R.J.; Hetz, C.

    2016-01-01

    In neurological disorders, both acute and chronic neural stress can disrupt cellular proteostasis, resulting in the generation of pathological protein. However in most cases, neurons adapt to these proteostatic perturbations by activating a range of cellular protective and repair responses, thus maintaining cell function. These interconnected adaptive mechanisms comprise a ‘proteostasis network’ and include the unfolded protein response, the ubiquitin proteasome system and autophagy. Interestingly, several recent studies have shown that these adaptive responses can be stimulated by preconditioning treatments, which confer resistance to a subsequent toxic challenge – the phenomenon known as hormesis. In this review we discuss the impact of adaptive stress responses stimulated in diverse human neuropathologies including Parkinson’s disease, Wolfram syndrome, brain ischemia, and brain cancer. Further, we examine how these responses and the molecular pathways they recruit might be exploited for therapeutic gain. PMID:26923166

  10. Perturbative Quantum Gravity as a Double Copy of Gauge Theory and Implications for UV Properties

    NASA Astrophysics Data System (ADS)

    Bern, Zvi

    2015-01-01

    The talk will review recent developments showing that in a precise sense gravity scattering amplitudes are double copies of corresponding gauge theory ones used to describe the strong subnuclear interactions. Underlying this is a correspondence between the color charges and kinematic numerators appearing in gauge theory scattering amplitudes. An application of these ideas will be given, demonstrating that within perturbation theory standard supergravity theories are much tamer in the ultraviolet than had been believed possible.

  11. Perturbative Quantum Gravity as a Double Copy of Gauge Theory

    SciTech Connect

    Bern, Zvi; Carrasco, John Joseph M.; Johansson, Henrik

    2010-08-06

    In a previous paper we observed that (classical) tree-level gauge-theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory diagram numerators. Here we conjecture that this duality persists to all quantum loop orders and can thus be used to obtain multiloop gravity amplitudes easily from gauge-theory ones. As a nontrivial test, we show that the three-loop four-point amplitude of N=4 super-Yang-Mills theory can be arranged into a form satisfying the duality, and by taking double copies of the diagram numerators we obtain the corresponding amplitude of N=8 supergravity. We also remark on a nonsupersymmetric two-loop test based on pure Yang-Mills theory resulting in gravity coupled to an antisymmetric tensor and dilaton.

  12. Perturbative quantum gravity as a double copy of gauge theory.

    PubMed

    Bern, Zvi; Carrasco, John Joseph M; Johansson, Henrik

    2010-08-01

    In a previous paper we observed that (classical) tree-level gauge-theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory diagram numerators. Here we conjecture that this duality persists to all quantum loop orders and can thus be used to obtain multiloop gravity amplitudes easily from gauge-theory ones. As a nontrivial test, we show that the three-loop four-point amplitude of N=4 super-Yang-Mills theory can be arranged into a form satisfying the duality, and by taking double copies of the diagram numerators we obtain the corresponding amplitude of N=8 supergravity. We also remark on a nonsupersymmetric two-loop test based on pure Yang-Mills theory resulting in gravity coupled to an antisymmetric tensor and dilaton.

  13. Integrable perturbations of conformal field theories and Yetter-Drinfeld modules

    SciTech Connect

    Bücher, David; Runkel, Ingo

    2014-11-15

    In this paper we relate a problem in representation theory — the study of Yetter-Drinfeld modules over certain braided Hopf algebras — to a problem in two-dimensional quantum field theory, namely, the identification of integrable perturbations of a conformal field theory. A prescription that parallels Lusztig's construction allows one to read off the quantum group governing the integrable symmetry. As an example, we illustrate how the quantum group for the loop algebra of sl(2) appears in the integrable structure of the perturbed uncompactified and compactified free boson.

  14. Investigation of a Diagnostic for Perturbation Theory: Comparison to the T(sub 1) Diagnostic of Coupled-Cluster Theory

    NASA Technical Reports Server (NTRS)

    Lee, Timothy J.; Head-Gordon, Martin; Rendell, Alistair P.; Langhoff, Stephen R. (Technical Monitor)

    1995-01-01

    A diagnostic for perturbation theory calculations, S(sub 2), is defined and numerical results are compared to the established T(sub 1) diagnostic from coupled-cluster theory. S(sub 2) is the lowest order non-zero contribution to a perturbation expansion of T(sub 1). S(sub 2) is a reasonable estimate of the importance of non-dynamical electron correlation, although not as reliable as T(sub 1). S(sub 2) values less than or equal to 0.012 suggest that low orders of perturbation theory should yield reasonable results; S(sub 2) values between 0.012-0.015 suggest that caution is required in interpreting results from low orders of perturbation theory; S(sub 2) values greater than or equal to 0.015 indicate that low orders of perturbation theory are not reliable for accurate results. Although not required mathematically, S(sub 2) is always less than T(sub 1) for the examples studied here.

  15. Expansion of Perturbation Theory Applied to Shim Rotation Automation of the Advanced Test Reactor

    NASA Astrophysics Data System (ADS)

    Peterson, Joshua Loren

    In 2007, the Department of Energy (DOE) declared the Advanced Test Reactor (ATR) a National Scientific User Facility (NSUF). This declaration expanded the focus of the ATR to include diversified classes of academic and industrial experiments. An essential part of the new suite of more accurate and flexible codes being deployed to support the NSUF is their ability to predict reactor behavior at startup, particularly the position of the outer shim control cylinders (OSCC). The current method used for calculating the OSCC positions during a cycle startup utilizes a heuristic trial and error approach that is impractical with the computationally intensive reactor physics tools, such as NEWT. It is therefore desirable that shim rotation prediction for startup be automated. Shim rotation prediction with perturbation theory was chosen to be investigated as one method for use with startup calculation automation. A modified form of first order perturbation theory, called phase space interpolated perturbation theory, was developed to more accurately model shim rotation prediction. Shim rotation prediction is just one application for this new modified form of perturbation theory. Phase space interpolated perturbation theory can be used on any application where the range of change to the system is known a priori, but the magnitude of change is not known. A cubic regression method was also developed to automate shim rotation prediction by using only forward solutions to the transport equation.

  16. Use of the Halbach perturbation theory for the multipole design of the ALS storage ring sextupole

    SciTech Connect

    Marks, S.

    1995-02-01

    The Advanced Light Source (ALS) storage ring sextupole is a unique multi-purpose magnet. It is designed to operate in the primary or sextupole mode and in three auxiliary trim modes: horizontal steering, vertical steering, and skew quadrupole. Klaus Halbach developed a perturbation theory for iron-dominated magnets which provides the basis for this design. Many magnet designers, certainly those who have been exposed to Klaus, are familiar with this theory and have used it for such things as evaluating the effect of assembly alignment errors. The ALS sextupole design process was somewhat novel in its use of the perturbation theory to design essential features of the magnet. In particular, the steering and skew quadrupole functions are produced by violating sextupole symmetry and are thus perturbations of the normal sextupole excitation. The magnet was designed such that all four modes are decoupled and can be excited independently. This paper discusses the use of Halbach`s perturbation theory to design the trim functions and to evaluate the primary asymmetry in the sextupole mode, namely, a gap in the return yoke to accommodate the vacuum chamber. Prototype testing verified all operating modes of the magnet and confirmed the expected performance from calculations based upon the Halbach perturbation theory. A total of 48 sextupole magnets of this design are now installed and operating successfully in the ALS storage ring.

  17. Temporal features of postural adaptation strategy to prolonged and repeatable balance perturbation.

    PubMed

    Schmid, Micaela; Sozzi, Stefania

    2016-08-15

    Aim of this study was to get insight into the features of the postural adaptation process, occurring during a continuous 3-min and 0.6Hz horizontal sinusoidal oscillation of the body support base. We hypothesized an ongoing temporal organization of the balancing strategy that gradually becomes fine-tuned and more coordinated with the platform movement. The trial was divided into oscillation cycles and for each cycle: leg muscles activity and temporal relationship between Centre of Mass and Centre of Pressure A-P position were analyzed. The results of each cycle were grouped in time-windows of 10 successive cycles (time windows of 16.6s). Muscle activity was initially prominent and diminished progressively. The major burst of Tibialis Anterior (TA) muscle always occurred at the same time instant of the platform oscillation cycle, in advance with respect to the platform posterior turning point. This burst produced a body forward rotation that was delayed throughout the task. During prolonged and repeatable balance perturbation, an ongoing postural adaptation process occurs. When the effects of the perturbation become predictable, the CNS scales the level of muscle activity to counteracting the destabilizing effects of the perturbations. Furthermore, the CNS tunes the kinematics and the kinetic responses optimally by slightly delaying the onset of the body forward rotation, maintaining unchanged the time-pattern of postural muscle activation. PMID:27291456

  18. Temporal features of postural adaptation strategy to prolonged and repeatable balance perturbation.

    PubMed

    Schmid, Micaela; Sozzi, Stefania

    2016-08-15

    Aim of this study was to get insight into the features of the postural adaptation process, occurring during a continuous 3-min and 0.6Hz horizontal sinusoidal oscillation of the body support base. We hypothesized an ongoing temporal organization of the balancing strategy that gradually becomes fine-tuned and more coordinated with the platform movement. The trial was divided into oscillation cycles and for each cycle: leg muscles activity and temporal relationship between Centre of Mass and Centre of Pressure A-P position were analyzed. The results of each cycle were grouped in time-windows of 10 successive cycles (time windows of 16.6s). Muscle activity was initially prominent and diminished progressively. The major burst of Tibialis Anterior (TA) muscle always occurred at the same time instant of the platform oscillation cycle, in advance with respect to the platform posterior turning point. This burst produced a body forward rotation that was delayed throughout the task. During prolonged and repeatable balance perturbation, an ongoing postural adaptation process occurs. When the effects of the perturbation become predictable, the CNS scales the level of muscle activity to counteracting the destabilizing effects of the perturbations. Furthermore, the CNS tunes the kinematics and the kinetic responses optimally by slightly delaying the onset of the body forward rotation, maintaining unchanged the time-pattern of postural muscle activation.

  19. Inverse-scattering theory and the density perturbations from inflation.

    PubMed

    Habib, Salman; Heitmann, Katrin; Jungman, Gerard

    2005-02-18

    We show how to use inverse-scattering theory as the basis for the inflationary reconstruction program, the goal of which is to gain information about the physics which drives inflation. Inverse-scattering theory provides an effective and well-motivated procedure, having a sound mathematical basis and being of sufficient generality that it can be considered the foundation for a nonparametric reconstruction program. We show how simple properties of the power spectrum translate directly into statements about the evolution of the background geometry during inflation. PMID:15783718

  20. Diagrammatic perturbation theory applied to the ground state of the water molecule

    NASA Technical Reports Server (NTRS)

    Silver, D. M.; Wilson, S.

    1977-01-01

    The diagrammatic many-body perturbation theory is applied to the ground state of the water molecule within the algebraic approximation. Using four different basis sets, the total energy, the equilibrium OH bond length, and the equilibrium HOH bond angle are examined. The latter is found to be a particularly sensitive test of the convergence of perturbation expansions. Certain third-order results, which incorporate all two-, three-, and four-body effects, show evidence of good convergence properties.

  1. Revisiting Hartle's model using perturbed matching theory to second order: amending the change in mass

    NASA Astrophysics Data System (ADS)

    Reina, Borja; Vera, Raül

    2015-08-01

    Hartle's model describes the equilibrium configuration of a rotating isolated compact body in perturbation theory up to second order in general relativity. The interior of the body is a perfect fluid with a barotropic equation of state, no convective motions and rigid rotation. That interior is matched across its surface to an asymptotically flat vacuum exterior. Perturbations are taken to second order around a static and spherically symmetric background configuration. Apart from the explicit assumptions, the perturbed configuration is constructed upon some implicit premises, in particular the continuity of the functions describing the perturbation in terms of some background radial coordinate. In this work we revisit the model within a modern general and consistent theory of perturbative matchings to second order, which is independent of the coordinates and gauges used to describe the two regions to be joined. We explore the matching conditions up to second order in full. The main particular result we present is that the radial function m0 (in the setting of the original work) of the second order perturbation tensor, contrary to the original assumption, presents a jump at the surface of the star, which is proportional to the value of the energy density of the background configuration there. As a consequence, the change in mass δ M needed by the perturbed configuration to keep the value of the central energy density unchanged must be amended. We also discuss some subtleties that arise when studying the deformation of the star.

  2. Kohn-Sham density-functional theory and renormalization of many-body perturbation expansions

    NASA Astrophysics Data System (ADS)

    Valiev, Marat

    1998-03-01

    Numerous practical applications provide strong evidence that despite its simplicity and crude approximations, density-functional theory leads to a rather accurate description of ground state properties of various condensed matter systems. Although well documented numerically, to our knowledge a theoretical explanation of the accuracy of density-functional theory has not been given. This issue is clarified in this work by demonstrating that density-functional theory represents a particular renormalization procedure of a many-body perturbation expansion. In other words, it is shown that density-functional theory is a many-body perturbation theory whose convergence properties have been optimized. The realization of this fact brings new meaning into density-functional theory and explains the success of density-functional based calculations. For more information go to http://alchemy.ucsd.edu/marat/ .

  3. Optical tweezers theory near a flat surface: a perturbative method

    NASA Astrophysics Data System (ADS)

    Flyvbjerg, Henrik; Dutra, Rafael S.; Maia Neto, Paolo A.; Nussenzveig, H. Moyses

    We propose a perturbative calculation of the optical force exercised by a focused laser beam on a microsphere of arbitrary radius that is localized near a flat glass surface in a standard optical tweezers setup. Starting from the Mie-Debye representation for the electric field of a Gaussian laser beam, focused by an objective of high numerical aperture, we derive a recursive series that represents the multiple reflections that describe the reverberation of laser light between the microsphere and the glass slide. We present numerical results for the axial component of the optical force and the axial trap stiffness. Numerical results for a configuration typical in biological applications--a microsphere of 0.5 µm radius at a distance around 0.25 µm from the surface--show a 37 [1] Viana N B, Rocha M S. Mesquita O N, et al. (2007) Towards absolute calibration of optical tweezers. Phys Rev E 75:021914-1-14. [2] Dutra R S, Viana N B, Maia Neto P A, et al. (2014) Absolute calibration of forces in optical tweezers. Phys Rev A 90:013825-1-13. Rafael S. Dutra thanks the Brazilian ``Science without Borders'' program for a postdoctoral scholarship.

  4. Self-consistent perturbation theory for two dimensional twisted bilayers

    NASA Astrophysics Data System (ADS)

    Shirodkar, Sharmila N.; Tritsaris, Georgios A.; Kaxiras, Efthimios

    Theoretical modeling and ab-initio simulations of two dimensional heterostructures with arbitrary angles of rotation between layers involve unrealistically large and expensive calculations. To overcome this shortcoming, we develop a methodology for weakly interacting heterostructures that treats the effect of one layer on the other as perturbation, and restricts the calculations to their primitive cells. Thus, avoiding computationally expensive supercells. We start by approximating the interaction potential between the twisted bilayers to that of a hypothetical configuration (viz. ideally stacked untwisted layers), which produces band structures in reasonable agreement with full-scale ab-initio calculations for commensurate and twisted bilayers of graphene (Gr) and Gr/hexagonal boron nitride (h-BN) heterostructures. We then self-consistently calculate the charge density and hence, interaction potential of the heterostructures. In this work, we test our model for bilayers of various combinations of Gr, h-BN and transition metal dichalcogenides, and discuss the advantages and shortcomings of the self-consistently calculated interaction potential. Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.

  5. Evolution of tensor perturbations in scalar-tensor theories of gravity

    SciTech Connect

    Carloni, Sante; Dunsby, Peter K. S.

    2007-03-15

    The evolution equations for tensor perturbations in a generic scalar-tensor theory of gravity are presented. Exact solutions are given for a specific class of theories and Friedmann-Lemaitre-Robertson-Walker backgrounds. In these cases it is shown that, although the evolution of tensor models depends on the choice of parameters of the theory, no amplification is possible if the gravitational interaction is attractive.

  6. Time-reversed adapted-perturbation (TRAP) optical focusing onto dynamic objects inside scattering media

    PubMed Central

    Ma, Cheng; Xu, Xiao; Liu, Yan; Wang, Lihong V.

    2014-01-01

    The ability to steer and focus light inside scattering media has long been sought for a multitude of applications. To form optical foci inside scattering media, the only feasible strategy at present is to guide photons by using either implanted1 or virtual2–4 guide stars, which can be inconvenient and limits potential applications. Here, we report a scheme for focusing light inside scattering media by employing intrinsic dynamics as guide stars. By time-reversing the perturbed component of the scattered light adaptively, we show that it is possible to focus light to the origin of the perturbation. Using the approach, we demonstrate non-invasive dynamic light focusing onto moving targets and imaging of a time-variant object obscured by highly scattering media. Anticipated applications include imaging and photoablation of angiogenic vessels in tumours as well as other biomedical uses. PMID:25530797

  7. Perturbation theory for the refractive index mismatch between the inclusion and the surrounding tissues

    NASA Astrophysics Data System (ADS)

    Chai, Chenggang; Liu, Quan

    2016-08-01

    Tissue refractive index is one optical contrast mechanism with diagnostic potential, it is very important to investigate the effect of the refractive index mismatch on light propagation through diffusive regions. Here, we present a new analytical solution of perturbation theory for the refractive index mismatch between the small spherical inclusion and the surrounding tissues. The solution has been used to implement fitting procedures in order to obtain the optical properties of a heterogeneous sphere in semi-infinite medium from measurements of diffuse reflectance. Finally, perturbation theory has been validated by comparisons with the results of Monte Carlo simulation. The new perturbation theory would provide a basis for allowing early disease diagnosis and automatic screening.

  8. Integrated perturbation theory and one-loop power spectra of biased tracers

    NASA Astrophysics Data System (ADS)

    Matsubara, Takahiko

    2014-08-01

    General and explicit predictions from the integrated perturbation theory (iPT) for power spectra and correlation functions of biased tracers are derived and presented in the one-loop approximation. The iPT is a general framework of the nonlinear perturbation theory of cosmological density fields in the presence of nonlocal bias, redshift-space distortions, and primordial non-Gaussianity. Analytic formulas of auto and cross power spectra of nonlocally biased tracers in both real and redshift spaces are derived and the results are comprehensively summarized. The main difference from previous formulas derived by the present author is to include the effects of generally nonlocal Lagrangian bias and primordial non-Gaussianity, and the derivation method of the new formula is fundamentally different from the previous one. Relations to recent work on improved methods of nonlinear perturbation theory in the literature are clarified and discussed.

  9. The application of the thermodynamic perturbation theory to study the hydrophobic hydration

    PubMed Central

    Mohorič, Tomaž; Urbic, Tomaz; Hribar-Lee, Barbara

    2013-01-01

    The thermodynamic perturbation theory was tested against newly obtained Monte Carlo computer simulations to describe the major features of the hydrophobic effect in a simple 3D-Mercedes-Benz water model: the temperature and hydrophobe size dependence on entropy, enthalpy, and free energy of transfer of a simple hydrophobic solute into water. An excellent agreement was obtained between the theoretical and simulation results. Further, the thermodynamic perturbation theory qualitatively correctly (with respect to the experimental data) describes the solvation thermodynamics under conditions where the simulation results are difficult to obtain with good enough accuracy, e.g., at high pressures. PMID:23862923

  10. The application of the thermodynamic perturbation theory to study the hydrophobic hydration

    NASA Astrophysics Data System (ADS)

    Mohorič, Tomaž; Urbic, Tomaz; Hribar-Lee, Barbara

    2013-07-01

    The thermodynamic perturbation theory was tested against newly obtained Monte Carlo computer simulations to describe the major features of the hydrophobic effect in a simple 3D-Mercedes-Benz water model: the temperature and hydrophobe size dependence on entropy, enthalpy, and free energy of transfer of a simple hydrophobic solute into water. An excellent agreement was obtained between the theoretical and simulation results. Further, the thermodynamic perturbation theory qualitatively correctly (with respect to the experimental data) describes the solvation thermodynamics under conditions where the simulation results are difficult to obtain with good enough accuracy, e.g., at high pressures.

  11. The application of the thermodynamic perturbation theory to study the hydrophobic hydration.

    PubMed

    Mohoric, Tomaz; Urbic, Tomaz; Hribar-Lee, Barbara

    2013-07-14

    The thermodynamic perturbation theory was tested against newly obtained Monte Carlo computer simulations to describe the major features of the hydrophobic effect in a simple 3D-Mercedes-Benz water model: the temperature and hydrophobe size dependence on entropy, enthalpy, and free energy of transfer of a simple hydrophobic solute into water. An excellent agreement was obtained between the theoretical and simulation results. Further, the thermodynamic perturbation theory qualitatively correctly (with respect to the experimental data) describes the solvation thermodynamics under conditions where the simulation results are difficult to obtain with good enough accuracy, e.g., at high pressures.

  12. Long-term evolution of Galileo operational orbits by canonical perturbation theory

    NASA Astrophysics Data System (ADS)

    Lara, Martin; San-Juan, Juan F.; López-Ochoa, Luis M.; Cefola, Paul

    2014-02-01

    Galileo operational orbits are slightly affected by the 3 to 5 tesseral resonance, an effect that can be much more important in the case of disposal orbits. Proceeding by canonical perturbation theory we show that the part of the long-term Hamiltonian corresponding to the non-centralities of the Earth's gravitational potential can be replaced by an intermediary that shows the pendulum dynamics of the 3 to 5 tesseral resonance problem. Inclusion of lunisolar perturbations requires a semi-analytical integration, which is compared with the corresponding results from the well-established Draper Semi-analytical Satellite Theory.

  13. Relativistic multireference many-body perturbation theory calculations on Au64+ - Au69+ ions

    SciTech Connect

    Vilkas, M J; Ishikawa, Y; Trabert, E

    2006-03-31

    Many-body perturbation theory (MBPT) calculations are an adequate tool for the description of the structure of highly charged multi-electron ions and for the analysis of their spectra. They demonstrate this by way of a re-investigation of n=3, {Delta}n=0 transitions in the EUV spectra of Na-, Mg-, Al-like, and Si-like ions of Au that have been obtained previously by heavy-ion accelerator based beam-foil spectroscopy. They discuss the evidence and propose several revisions on the basis of the multi-reference many-body perturbation theory calculations of Ne- through P-like ions of Au.

  14. Radiation reaction from QED: Lightfront perturbation theory in a plane wave background

    NASA Astrophysics Data System (ADS)

    Ilderton, Anton; Torgrimsson, Greger

    2013-07-01

    We derive dynamical, real time radiation reaction effects from lightfront QED. Combining the Hamiltonian formalism with a plane wave background field, the calculation is performed in the Furry picture for which the background is treated exactly while interactions between quantum fields are treated in perturbation theory as normal. We work to a fixed order in perturbation theory, but no other approximation is made. The literature contains many proposals for the correct classical equation describing a radiating particle; we take the classical limit of our results and identify which equations are consistent with QED.

  15. The application of the thermodynamic perturbation theory to study the hydrophobic hydration.

    PubMed

    Mohoric, Tomaz; Urbic, Tomaz; Hribar-Lee, Barbara

    2013-07-14

    The thermodynamic perturbation theory was tested against newly obtained Monte Carlo computer simulations to describe the major features of the hydrophobic effect in a simple 3D-Mercedes-Benz water model: the temperature and hydrophobe size dependence on entropy, enthalpy, and free energy of transfer of a simple hydrophobic solute into water. An excellent agreement was obtained between the theoretical and simulation results. Further, the thermodynamic perturbation theory qualitatively correctly (with respect to the experimental data) describes the solvation thermodynamics under conditions where the simulation results are difficult to obtain with good enough accuracy, e.g., at high pressures. PMID:23862923

  16. Second order classical perturbation theory for the sticking probability of heavy atoms scattered on surfaces

    SciTech Connect

    Sahoo, Tapas; Pollak, Eli

    2015-08-14

    A second order classical perturbation theory is developed to calculate the sticking probability of a particle scattered from an uncorrugated thermal surface. An analytic expression for the temperature dependent energy loss of the particle to the surface is derived by employing a one-dimensional generalized Langevin equation. The surface temperature reduces the energy loss, since the thermal surface transfers energy to the particle. Using a Gaussian energy loss kernel and the multiple collision theory of Fan and Manson [J. Chem. Phys. 130, 064703 (2009)], enables the determination of the fraction of particles trapped on the surface after subsequent momentum reversals of the colliding particle. This then leads to an estimate of the trapping probability. The theory is tested for the model scattering of Ar on a LiF(100) surface. Comparison with numerical simulations shows excellent agreement of the analytical theory with simulations, provided that the energy loss is determined by the second order perturbation theory.

  17. Non-perturbative selection rules in F-theory

    NASA Astrophysics Data System (ADS)

    Martucci, Luca; Weigand, Timo

    2015-09-01

    We discuss the structure of charged matter couplings in 4-dimensional F-theory compactifications. Charged matter is known to arise from M2-branes wrapping fibral curves on an elliptic or genus-one fibration Y . If a set of fibral curves satisfies a homological relation in the fibre homology, a coupling involving the states can arise without exponential volume suppression due to a splitting and joining of the M2-branes. If the fibral curves only sum to zero in the integral homology of the full fibration, no such coupling is possible. In this case an M2-instanton wrapping a 3-chain bounded by the fibral matter curves can induce a D-term which is volume suppressed. We elucidate the consequences of this pattern for the appearance of massive U(1) symmetries in F-theory and analyse the structure of discrete selection rules in the coupling sector. The weakly coupled analogue of said M2-instantons is worked out to be given by D1-F1 instantons. The generation of an exponentially suppressed F-term requires the formation of half-BPS bound states of M2 and M5-instantons. This effect and its description in terms of fluxed M5-instantons is discussed in a companion paper.

  18. Plantar tactile perturbations enhance transfer of split-belt locomotor adaptation

    PubMed Central

    Mukherjee, Mukul; Eikema, Diderik Jan A.; Chien, Jung Hung; Myers, Sara A.; Scott-Pandorf, Melissa; Bloomberg, Jacob J.; Stergiou, Nicholas

    2015-01-01

    Patterns of human locomotion are highly adaptive and flexible, and depend on the environmental context. Locomotor adaptation requires the use of multisensory information to perceive altered environmental dynamics and generate an appropriate movement pattern. In this study, we investigated the use of multisensory information during locomotor learning. Proprioceptive perturbations were induced by vibrating tactors, placed bilaterally over the plantar surfaces. Under these altered sensory conditions, participants were asked to perform a split-belt locomotor task representative of motor learning. Twenty healthy young participants were separated into two groups: no-tactors (NT) and tactors (TC). All participants performed an overground walking trial, followed by treadmill walking including 18 minutes of split-belt adaptation and an overground trial to determine transfer effects. Interlimb coordination was quantified by symmetry indices and analyzed using mixed repeated measures ANOVAs. Both groups adapted to the locomotor task, indicated by significant reductions in gait symmetry during the split-belt task. No significant group differences in spatiotemporal and kinetic parameters were observed on the treadmill. However, significant groups differences were observed overground. Step and swing time asymmetries learned on the split belt treadmill, were retained and decayed more slowly overground in the TC group whereas in NT, asymmetries were rapidly lost. These results suggest that tactile stimulation contributed to increased lower limb proprioceptive gain. High proprioceptive gain allows for more persistent overground after-effects, at the cost of reduced adaptability. Such persistence may be utilized in populations displaying pathologic asymmetric gait by retraining a more symmetric pattern. PMID:26169104

  19. Plantar tactile perturbations enhance transfer of split-belt locomotor adaptation.

    PubMed

    Mukherjee, Mukul; Eikema, Diderik Jan A; Chien, Jung Hung; Myers, Sara A; Scott-Pandorf, Melissa; Bloomberg, Jacob J; Stergiou, Nicholas

    2015-10-01

    Patterns of human locomotion are highly adaptive and flexible and depend on the environmental context. Locomotor adaptation requires the use of multisensory information to perceive altered environmental dynamics and generate an appropriate movement pattern. In this study, we investigated the use of multisensory information during locomotor learning. Proprioceptive perturbations were induced by vibrating tactors, placed bilaterally over the plantar surfaces. Under these altered sensory conditions, participants were asked to perform a split-belt locomotor task representative of motor learning. Twenty healthy young participants were separated into two groups: no-tactors (NT) and tactors (TC). All participants performed an overground walking trial, followed by treadmill walking including 18 min of split-belt adaptation and an overground trial to determine transfer effects. Interlimb coordination was quantified by symmetry indices and analyzed using mixed repeated-measures ANOVAs. Both groups adapted to the locomotor task, indicated by significant reductions in gait symmetry during the split-belt task. No significant group differences in spatiotemporal and kinetic parameters were observed on the treadmill. However, significant group differences were observed overground. Step and swing time asymmetries learned on the split-belt treadmill were retained and decayed more slowly overground in the TC group whereas in NT, asymmetries were rapidly lost. These results suggest that tactile stimulation contributed to increased lower limb proprioceptive gain. High proprioceptive gain allows for more persistent overground after effects, at the cost of reduced adaptability. Such persistence may be utilized in populations displaying pathologic asymmetric gait by retraining a more symmetric pattern.

  20. Adaptive robust maximum power point tracking control for perturbed photovoltaic systems with output voltage estimation.

    PubMed

    Koofigar, Hamid Reza

    2016-01-01

    The problem of maximum power point tracking (MPPT) in photovoltaic (PV) systems, despite the model uncertainties and the variations in environmental circumstances, is addressed. Introducing a mathematical description, an adaptive sliding mode control (ASMC) algorithm is first developed. Unlike many previous investigations, the output voltage is not required to be sensed and the upper bound of system uncertainties and the variations of irradiance and temperature are not required to be known. Estimating the output voltage by an update law, an adaptive-based H∞ tracking algorithm is then developed for the case the perturbations are energy-bounded. The stability analysis is presented for the proposed tracking control schemes, based on the Lyapunov stability theorem. From a comparison viewpoint, some numerical and experimental studies are also presented and discussed. PMID:26606851

  1. Adaptive robust maximum power point tracking control for perturbed photovoltaic systems with output voltage estimation.

    PubMed

    Koofigar, Hamid Reza

    2016-01-01

    The problem of maximum power point tracking (MPPT) in photovoltaic (PV) systems, despite the model uncertainties and the variations in environmental circumstances, is addressed. Introducing a mathematical description, an adaptive sliding mode control (ASMC) algorithm is first developed. Unlike many previous investigations, the output voltage is not required to be sensed and the upper bound of system uncertainties and the variations of irradiance and temperature are not required to be known. Estimating the output voltage by an update law, an adaptive-based H∞ tracking algorithm is then developed for the case the perturbations are energy-bounded. The stability analysis is presented for the proposed tracking control schemes, based on the Lyapunov stability theorem. From a comparison viewpoint, some numerical and experimental studies are also presented and discussed.

  2. Taming Landau singularities in QCD perturbation theory: The analytic approach 2.0

    NASA Astrophysics Data System (ADS)

    Stefanis, N. G.

    2013-05-01

    The aim of this topical article is to outline the fundamental ideas underlying the recently developed Fractional Analytic Perturbation Theory (FAPT) of QCD and present its main calculational tools together with key applications. For this, it is first necessary to review previous methods to apply QCD perturbation theory at low spacelike momentum scales, where the influence of the Landau singularities becomes inevitable. Several concepts are considered and their limitations are pointed out. The usefulness of FAPT is discussed in terms of two characteristic hadronic quantities: the perturbatively calculable part of the pion's electromagnetic form factor in the spacelike region and the Higgs-boson decay into a b bar b pair in the timelike region. In the first case, the focus is on the optimization of the prediction with respect to the choice of the renormalization scheme and the dependence on the renormalization and the factorization scales. The second case serves to show that the application of FAPT to this reaction reaches already at the four-loop level an accuracy of the order of 1%, avoiding difficulties inherent in the standard perturbative expansion. The obtained results are compared with estimates from fixed-order and contour-improved QCD perturbation theory. Using the brand-new Higgs mass value of about 125 GeV, measured at the Large Hadron Collider (CERN), a prediction for Γ _{H to bbar b} = 2.4 ± 0.15 MeV is extracted.

  3. Application of the lie-transform perturbation theory for the turn-by-turn data analysis

    SciTech Connect

    Alexahin, Y.; /Fermilab

    2006-06-01

    Harmonic analysis of turn-by-turn BPM data is a rich source of information on linear and nonlinear optics in circular machines. In the present report the normal form approach first introduced by R. Bartolini and F. Schmidt is extended on the basis of the Lie-transform perturbation theory to provide direct relation between the sources of perturbation and observable spectra of betatron oscillations. The goal is to localize strong perturbing elements, find the resonance driving terms--both absolute value and phase--that are necessary for calculation of the required adjustments in correction magnet circuits: e.g. skew-quadrupoles for linear coupling correction. The theory is nonlinear and permits to analyze higher order effects, such as coupling contribution to beta-beating and nonlinear sum resonances.

  4. Extended Møller-Plesset perturbation theory for dynamical and static correlations

    SciTech Connect

    Tsuchimochi, Takashi Van Voorhis, Troy

    2014-10-28

    We present a novel method that appropriately handles both dynamical and static electron correlations in a balanced manner, using a perturbation theory on a spin-extended Hartree-Fock (EHF) wave function reference. While EHF is a suitable candidate for degenerate systems where static correlation is ubiquitous, it is known that most of dynamical correlation is neglected in EHF. In this work, we derive a perturbative correction to a fully spin-projected self-consistent wave function based on second-order Møller-Plesset perturbation theory (MP2). The proposed method efficiently captures the ability of EHF to describe static correlation in degeneracy, combined with MP2's ability to treat dynamical correlation effects. We demonstrate drastic improvements on molecular ground state and excited state potential energy curves and singlet-triplet splitting energies over both EHF and MP2 with similar computational effort to the latter.

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

    PubMed

    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.

  6. The Feynman integrand as a white noise distribution beyond perturbation theory

    SciTech Connect

    Grothaus, Martin; Vogel, Anna

    2008-06-18

    In this note the concepts of path integrals and techniques how to construct them are presented. Here we concentrate on a White Noise approach. Combining White Noise techniques with a generalized time-dependent Doss' formula Feynman integrands are constructed as white noise distributions beyond perturbation theory.

  7. Meta-stable Supersymmetry Breaking in an N = 1 Perturbed Seiberg-Witten Theory

    SciTech Connect

    Sasaki, Shin; Arai, Masato; Montonen, Claus; Okada, Nobuchika

    2008-11-23

    In this contribution, we discuss the possibility of meta-stable supersymmetry (SUSY) breaking vacua in a perturbed Seiberg-Witten theory with Fayet-Iliopoulos (FI) term. We found meta-stable SUSY breaking vacua at the degenerated dyon and monopole singular points in the moduli space at the nonperturbative level.

  8. Advanced Small Perturbation Potential Flow Theory for Unsteady Aerodynamic and Aeroelastic Analyses

    NASA Technical Reports Server (NTRS)

    Batina, John T.

    2005-01-01

    An advanced small perturbation (ASP) potential flow theory has been developed to improve upon the classical transonic small perturbation (TSP) theories that have been used in various computer codes. These computer codes are typically used for unsteady aerodynamic and aeroelastic analyses in the nonlinear transonic flight regime. The codes exploit the simplicity of stationary Cartesian meshes with the movement or deformation of the configuration under consideration incorporated into the solution algorithm through a planar surface boundary condition. The new ASP theory was developed methodically by first determining the essential elements required to produce full-potential-like solutions with a small perturbation approach on the requisite Cartesian grid. This level of accuracy required a higher-order streamwise mass flux and a mass conserving surface boundary condition. The ASP theory was further developed by determining the essential elements required to produce results that agreed well with Euler solutions. This level of accuracy required mass conserving entropy and vorticity effects, and second-order terms in the trailing wake boundary condition. Finally, an integral boundary layer procedure, applicable to both attached and shock-induced separated flows, was incorporated for viscous effects. The resulting ASP potential flow theory, including entropy, vorticity, and viscous effects, is shown to be mathematically more appropriate and computationally more accurate than the classical TSP theories. The formulaic details of the ASP theory are described fully and the improvements are demonstrated through careful comparisons with accepted alternative results and experimental data. The new theory has been used as the basis for a new computer code called ASP3D (Advanced Small Perturbation - 3D), which also is briefly described with representative results.

  9. Individuals with medial knee osteoarthritis show neuromuscular adaptation when perturbed during walking despite functional and structural impairments.

    PubMed

    Kumar, Deepak; Swanik, Charles Buz; Reisman, Darcy S; Rudolph, Katherine S

    2014-01-01

    Neuromuscular control relies on sensory feedback that influences responses to changing external demands, and the normal response is for movement and muscle activation patterns to adapt to repeated perturbations. People with knee osteoarthritis (OA) are known to have pain, quadriceps weakness, and neuromotor deficits that could affect adaption to external perturbations. The aim of this study was to analyze neuromotor adaptation during walking in people with knee OA (n = 38) and controls (n = 23). Disability, quadriceps strength, joint space width, malalignment, and proprioception were assessed. Kinematic and EMG data were collected during undisturbed walking and during perturbations that caused lateral translation of the foot at initial contact. Knee excursions and EMG magnitudes were analyzed. Subjects with OA walked with less knee motion and higher muscle activation and had greater pain, limitations in function, quadriceps weakness, and malalignment, but no difference was observed in proprioception. Both groups showed increased EMG and decreased knee motion in response to the first perturbation, followed by progressively decreased EMG activity and increased knee motion during midstance over the first five perturbations, but no group differences were observed. Over 30 trials, EMG levels returned to those of normal walking. The results illustrate that people with knee OA respond similarly to healthy individuals when exposed to challenging perturbations during functional weight-bearing activities despite structural, functional, and neuromotor impairments. Mechanisms underlying the adaptive response in people with knee OA need further study. PMID:24072409

  10. Band alignment of semiconductors from density-functional theory and many-body perturbation theory

    NASA Astrophysics Data System (ADS)

    Hinuma, Yoyo; Grüneis, Andreas; Kresse, Georg; Oba, Fumiyasu

    2014-10-01

    The band lineup, or alignment, of semiconductors is investigated via first-principles calculations based on density functional theory (DFT) and many-body perturbation theory (MBPT). Twenty-one semiconductors including C, Si, and Ge in the diamond structure, BN, AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb, ZnS, ZnSe, ZnTe, CdS, CdSe, and CdTe in the zinc-blende structure, and GaN and ZnO in the wurtzite structure are considered in view of their fundamental and technological importance. Band alignments are determined using the valence and conduction band offsets from heterointerface calculations, the ionization potential (IP) and electron affinity (EA) from surface calculations, and the valence band maximum and conduction band minimum relative to the branch point energy, or charge neutrality level, from bulk calculations. The performance of various approximations to DFT and MBPT, namely the Perdew-Burke-Ernzerhof (PBE) semilocal functional, the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional, and the GW approximation with and without vertex corrections in the screened Coulomb interaction, is assessed using the GWΓ1 approximation as a reference, where first-order vertex corrections are included in the self-energy. The experimental IPs, EAs, and band offsets are well reproduced by GWΓ1 for most of the semiconductor surfaces and heterointerfaces considered in this study. The PBE and HSE functionals show sizable errors in the IPs and EAs, in particular for group II-VI semiconductors with wide band gaps, but are much better in the prediction of relative band positions or band offsets due to error cancellation. The performance of the GW approximation is almost on par with GWΓ1 as far as relative band positions are concerned. The band alignments based on average interfacial band offsets for all pairs of 17 semiconductors and branch point energies agree with explicitly calculated interfacial band offsets with small mean absolute errors of both ˜0.1eV, indicating a

  11. Similarity-transformed perturbation theory on top of truncated local coupled cluster solutions: Theory and applications to intermolecular interactions

    SciTech Connect

    Azar, Richard Julian Head-Gordon, Martin

    2015-05-28

    Your correspondents develop and apply fully nonorthogonal, local-reference perturbation theories describing non-covalent interactions. Our formulations are based on a Löwdin partitioning of the similarity-transformed Hamiltonian into a zeroth-order intramonomer piece (taking local CCSD solutions as its zeroth-order eigenfunction) plus a first-order piece coupling the fragments. If considerations are limited to a single molecule, the proposed intermolecular similarity-transformed perturbation theory represents a frozen-orbital variant of the “(2)”-type theories shown to be competitive with CCSD(T) and of similar cost if all terms are retained. Different restrictions on the zeroth- and first-order amplitudes are explored in the context of large-computation tractability and elucidation of non-local effects in the space of singles and doubles. To accurately approximate CCSD intermolecular interaction energies, a quadratically growing number of variables must be included at zeroth-order.

  12. Constructing perturbation theory kernels for large-scale structure in generalized cosmologies

    NASA Astrophysics Data System (ADS)

    Taruya, Atsushi

    2016-07-01

    We present a simple numerical scheme for perturbation theory (PT) calculations of large-scale structure. Solving the evolution equations for perturbations numerically, we construct the PT kernels as building blocks of statistical calculations, from which the power spectrum and/or correlation function can be systematically computed. The scheme is especially applicable to the generalized structure formation including modified gravity, in which the analytic construction of PT kernels is intractable. As an illustration, we show several examples for power spectrum calculations in f (R ) gravity and Λ CDM models.

  13. Diagrammatic perturbation theory - N2 X1 Sigma/plus/g

    NASA Technical Reports Server (NTRS)

    Wilson, S.; Silver, D. M.

    1977-01-01

    The diagrammatic many-body perturbation theory is used to calculate the correlation energy of the nitrogen molecule in its electronic ground state. Using the algebraic approximation, the energy is evaluated through third order, including all many-body effects. (2/1) Pade approximants and variational upper bounds are constructed. For one of the perturbation expansions considered, the (2/1) Pade approximant leads to the recovery of 79.5 percent of the empirical correlation energy, while the variational upper bound recovers 72.0 percent. Three-body effects are examined in some detail. The relationships with previous work on N2 are discussed.

  14. Corrections to the Born-Oppenheimer approximation by means of perturbation theory

    SciTech Connect

    Fernandez, F.M. )

    1994-10-01

    We develop an efficient method for the calculation of corrections to the Born-Oppenheimer approximation by means of perturbation theory. The perturbation terms through sixth order in the small parameter [kappa]=([ital m]/[ital M])[sup 1/4], where [ital m] and [ital M] are, respectively, electronic and nuclear masses, allow the construction of an effective vibrational Hamiltonian that takes into account adiabatic and nonadiabatic effects. The latter is negative and linearly dependent on the vibrational quantum numbers. We illustrate the application of the main equations and verify the general results by means of an exactly solvable model of two coupled harmonic oscillators.

  15. Density matrix perturbation theory for magneto-optical response of periodic insulators

    NASA Astrophysics Data System (ADS)

    Lebedeva, Irina; Tokatly, Ilya; Rubio, Angel

    2015-03-01

    Density matrix perturbation theory offers an ideal theoretical framework for the description of response of solids to arbitrary electromagnetic fields. In particular, it allows to consider perturbations introduced by uniform electric and magnetic fields under periodic boundary conditions, though the corresponding potentials break the translational invariance of the Hamiltonian. We have implemented the density matrix perturbation theory in the open-source Octopus code on the basis of the efficient Sternheimer approach. The procedures for responses of different order to electromagnetic fields, including electric polarizability, orbital magnetic susceptibility and magneto-optical response, have been developed and tested by comparison with the results for finite systems and for wavefunction-based perturbation theory, which is already available in the code. Additional analysis of the orbital magneto-optical response is performed on the basis of analytical models. Symmetry limitations to observation of the magneto-optical response are discussed. The financial support from the Marie Curie Fellowship PIIF-GA-2012-326435 (RespSpatDisp) is gratefully acknowledged.

  16. Dual Ginzburg-Landau Theory on Non-Perturbative QCD Phenomena

    NASA Astrophysics Data System (ADS)

    Toki, H.

    The fundamental building blocks of matter are quarks. They are the elementary particles in the standard theory together with the leptons. Hence, it is fundamental to describe hadrons and nuclei in terms of quarks and gluons, the subject of which is called Quark Nuclear Physics. The quark-gluon dynamics is described by quantum chromodynamics (QCD). Our interest is the non-perturbative aspect of QCD as confinement, chiral symmetry breaking, hadronization, etc. We introduce the dual Ginzburg-Landau theory (DGL), where the color monopole fields and their condensation in the QCD vacuum play essential roles in describing these non-perturbative phenomena. We discuss the connection of the monopole fields with instantons, which are the classical solutions of the non-abelian gauge theory.

  17. Plantar tactile perturbations enhance transfer of split-belt locomotor adaptation.

    PubMed

    Mukherjee, Mukul; Eikema, Diderik Jan A; Chien, Jung Hung; Myers, Sara A; Scott-Pandorf, Melissa; Bloomberg, Jacob J; Stergiou, Nicholas

    2015-10-01

    Patterns of human locomotion are highly adaptive and flexible and depend on the environmental context. Locomotor adaptation requires the use of multisensory information to perceive altered environmental dynamics and generate an appropriate movement pattern. In this study, we investigated the use of multisensory information during locomotor learning. Proprioceptive perturbations were induced by vibrating tactors, placed bilaterally over the plantar surfaces. Under these altered sensory conditions, participants were asked to perform a split-belt locomotor task representative of motor learning. Twenty healthy young participants were separated into two groups: no-tactors (NT) and tactors (TC). All participants performed an overground walking trial, followed by treadmill walking including 18 min of split-belt adaptation and an overground trial to determine transfer effects. Interlimb coordination was quantified by symmetry indices and analyzed using mixed repeated-measures ANOVAs. Both groups adapted to the locomotor task, indicated by significant reductions in gait symmetry during the split-belt task. No significant group differences in spatiotemporal and kinetic parameters were observed on the treadmill. However, significant group differences were observed overground. Step and swing time asymmetries learned on the split-belt treadmill were retained and decayed more slowly overground in the TC group whereas in NT, asymmetries were rapidly lost. These results suggest that tactile stimulation contributed to increased lower limb proprioceptive gain. High proprioceptive gain allows for more persistent overground after effects, at the cost of reduced adaptability. Such persistence may be utilized in populations displaying pathologic asymmetric gait by retraining a more symmetric pattern. PMID:26169104

  18. Congenitally blind individuals rapidly adapt to coriolis force perturbations of their reaching movements.

    PubMed

    DiZio, P; Lackner, J R

    2000-10-01

    Reaching movements made to visual targets in a rotating room are initially deviated in path and endpoint in the direction of transient Coriolis forces generated by the motion of the arm relative to the rotating environment. With additional reaches, movements become progressively straighter and more accurate. Such adaptation can occur even in the absence of visual feedback about movement progression or terminus. Here we examined whether congenitally blind and sighted subjects without visual feedback would demonstrate adaptation to Coriolis forces when they pointed to a haptically specified target location. Subjects were tested pre-, per-, and postrotation at 10 rpm counterclockwise. Reaching to straight ahead targets prerotation, both groups exhibited slightly curved paths. Per-rotation, both groups showed large initial deviations of movement path and curvature but within 12 reaches on average had returned to prerotation curvature levels and endpoints. Postrotation, both groups showed mirror image patterns of curvature and endpoint to the per-rotation pattern. The groups did not differ significantly on any of the performance measures. These results provide compelling evidence that motor adaptation to Coriolis perturbations can be achieved on the basis of proprioceptive, somatosensory, and motor information in the complete absence of visual experience.

  19. Congenitally blind individuals rapidly adapt to coriolis force perturbations of their reaching movements

    NASA Technical Reports Server (NTRS)

    DiZio, P.; Lackner, J. R.

    2000-01-01

    Reaching movements made to visual targets in a rotating room are initially deviated in path and endpoint in the direction of transient Coriolis forces generated by the motion of the arm relative to the rotating environment. With additional reaches, movements become progressively straighter and more accurate. Such adaptation can occur even in the absence of visual feedback about movement progression or terminus. Here we examined whether congenitally blind and sighted subjects without visual feedback would demonstrate adaptation to Coriolis forces when they pointed to a haptically specified target location. Subjects were tested pre-, per-, and postrotation at 10 rpm counterclockwise. Reaching to straight ahead targets prerotation, both groups exhibited slightly curved paths. Per-rotation, both groups showed large initial deviations of movement path and curvature but within 12 reaches on average had returned to prerotation curvature levels and endpoints. Postrotation, both groups showed mirror image patterns of curvature and endpoint to the per-rotation pattern. The groups did not differ significantly on any of the performance measures. These results provide compelling evidence that motor adaptation to Coriolis perturbations can be achieved on the basis of proprioceptive, somatosensory, and motor information in the complete absence of visual experience.

  20. Probing non-perturbative effects in M-theory on orientifolds

    NASA Astrophysics Data System (ADS)

    Okuyama, Kazumi

    2016-01-01

    Using holography, we study non-perturbative effects in M-theory on orientifolds from the analysis of the S 3 partition functions of dual field theories. We consider the S 3 partition functions of N=4 Yang-Mills theory with O( n) gauge symmetry coupled to one (anti)symmetric and N f fundamental hypermultiplets from the Fermi gas approach. In addition to the worldsheet instanton and membrane instanton corrections to the grand potential, which are also present in the U( n) Yang-Mills case, we find that there exist "half instanton" corrections coming from the effect of orientifold plane.

  1. Perturbation theory for fractional Brownian motion in presence of absorbing boundaries

    NASA Astrophysics Data System (ADS)

    Wiese, Kay Jörg; Majumdar, Satya N.; Rosso, Alberto

    2011-06-01

    Fractional Brownian motion is a Gaussian process x(t) with zero mean and two-time correlations =D(t12H+t22H-|t1-t2|2H), where H, with 0perturbation theory around this limit, setting H=1/2+ɛ, to calculate the scaling function R+(y) to first order in ɛ. We find that R+(y) behaves as R+(y)~yϕ as y→0 (near the absorbing boundary), while R+(y)~yγexp(-y2/2) as y→∞, with ϕ=1-4ɛ+O(ɛ2) and γ=1-2ɛ+O(ɛ2). Our ɛ-expansion result confirms the scaling relation ϕ=(1-H)/H proposed in Zoia, Rosso, and Majumdar [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.102.120602 102, 120602 (2009)]. We verify our findings via numerical simulations for H=2/3. The tools developed here are versatile, powerful, and adaptable to different situations.

  2. A projected approximation to strongly contracted N-electron valence perturbation theory for DMRG wavefunctions

    NASA Astrophysics Data System (ADS)

    Roemelt, Michael; Guo, Sheng; Chan, Garnet K.-L.

    2016-05-01

    A novel approach to strongly contracted N-electron valence perturbation theory (SC-NEVPT2) as a means of describing dynamic electron correlation for quantum chemical density matrix renormalization group (DMRG) calculations is presented. In this approach the strongly contracted perturber functions are projected onto a renormalized Hilbert space. Compared to a straightforward implementation of SC-NEVPT2 with DMRG wavefunctions, the computational scaling and storage requirements are reduced. This favorable scaling opens up the possibility of calculations with larger active spaces. A specially designed renormalization scheme ensures that both the electronic ground state and the perturber functions are well represented in the renormalized Hilbert space. Test calculations on the N2 and [Cu2O2(en)2]2+ demonstrate some key properties of the method and indicate its capabilities.

  3. A projected approximation to strongly contracted N-electron valence perturbation theory for DMRG wavefunctions.

    PubMed

    Roemelt, Michael; Guo, Sheng; Chan, Garnet K-L

    2016-05-28

    A novel approach to strongly contracted N-electron valence perturbation theory (SC-NEVPT2) as a means of describing dynamic electron correlation for quantum chemical density matrix renormalization group (DMRG) calculations is presented. In this approach the strongly contracted perturber functions are projected onto a renormalized Hilbert space. Compared to a straightforward implementation of SC-NEVPT2 with DMRG wavefunctions, the computational scaling and storage requirements are reduced. This favorable scaling opens up the possibility of calculations with larger active spaces. A specially designed renormalization scheme ensures that both the electronic ground state and the perturber functions are well represented in the renormalized Hilbert space. Test calculations on the N2 and [Cu2O2(en)2](2+) demonstrate some key properties of the method and indicate its capabilities. PMID:27250285

  4. Three new branched chain equations of state based on Wertheim's perturbation theory

    NASA Astrophysics Data System (ADS)

    Marshall, Bennett D.; Chapman, Walter G.

    2013-05-01

    In this work, we present three new branched chain equations of state (EOS) based on Wertheim's perturbation theory. The first represents a slightly approximate general branched chain solution of Wertheim's second order perturbation theory (TPT2) for athermal hard chains, and the second represents the extension of first order perturbation theory with a dimer reference fluid (TPT1-D) to branched athermal hard chain molecules. Each athermal branched chain EOS was shown to give improved results over their linear counterparts when compared to simulation data for branched chain molecules with the branched TPT1-D EOS being the most accurate. Further, it is shown that the branched TPT1-D EOS can be extended to a Lennard-Jones dimer reference system to obtain an equation of state for branched Lennard-Jones chains. The theory is shown to accurately predict the change in phase diagram and vapor pressure which results from branching as compared to experimental data for n-octane and corresponding branched isomers.

  5. Exploring arbitrarily high orders of optimized perturbation theory in QCD with nf → 161/2

    NASA Astrophysics Data System (ADS)

    Stevenson, P. M.

    2016-09-01

    Perturbative QCD with nf flavours of massless quarks becomes simple in the hypothetical limit nf → 161/2, where the leading β-function coefficient vanishes. The Banks-Zaks (BZ) expansion in a0 ≡8/321 (161/2 -nf) is straightforward to obtain from perturbative results in MS ‾ or any renormalization scheme (RS) whose nf dependence is 'regular'. However, 'irregular' RS's are perfectly permissible and should ultimately lead to the same BZ results. We show here that the 'optimal' RS determined by the Principle of Minimal Sensitivity does yield the same BZ-expansion results when all orders of perturbation theory are taken into account. The BZ limit provides an arena for exploring optimized perturbation theory at arbitrarily high orders. These explorations are facilitated by a 'master equation' expressing the optimization conditions in the fixed-point limit. We find an intriguing strong/weak coupling duality a →a*2 / a about the fixed point a*.

  6. Thermodynamic perturbation theory for associating fluids confined in a one-dimensional pore

    SciTech Connect

    Marshall, Bennett D.

    2015-06-21

    In this paper, a new theory is developed for the self-assembly of associating molecules confined to a single spatial dimension, but allowed to explore all orientation angles. The interplay of the anisotropy of the pair potential and the low dimensional space results in orientationally ordered associated clusters. This local order enhances association due to a decrease in orientational entropy. Unlike bulk 3D fluids which are orientationally homogeneous, association in 1D necessitates the self-consistent calculation of the orientational distribution function. To test the new theory, Monte Carlo simulations are performed and the theory is found to be accurate. It is also shown that the traditional treatment in first order perturbation theory fails to accurately describe this system. The theory developed in this paper may be used as a tool to study hydrogen bonding of molecules in 1D zeolites as well as the hydrogen bonding of molecules in carbon nanotubes.

  7. Second-order many-body perturbation theory: an eternal frontier.

    PubMed

    Hirata, So; He, Xiao; Hermes, Matthew R; Willow, Soohaeng Y

    2014-01-30

    Second-order many-body perturbation theory [MBPT(2)] is the lowest-ranked member of a systematic series of approximations convergent at the exact solutions of the Schrödinger equations. It has served and continues to serve as the testing ground for new approximations, algorithms, and even theories. This article introduces this basic theory from a variety of viewpoints including the Rayleigh-Schrödinger perturbation theory, the many-body Green's function theory based on the Dyson equation, and the related Feynman-Goldstone diagrams. It also explains the important properties of MBPT(2) such as size consistency, its ability to describe dispersion interactions, and divergence in metals. On this basis, this article surveys three major advances made recently by the authors to this theory. They are a finite-temperature extension of MBPT(2) and the resolution of the Kohn-Luttinger conundrum, a stochastic evaluation of the correlation and self-energies of MBPT(2) using the Monte Carlo integration of their Laplace-transformed expressions, and an extension to anharmonic vibrational zero-point energies and transition frequencies based on the Dyson equation.

  8. Second-order many-body perturbation theory: an eternal frontier.

    PubMed

    Hirata, So; He, Xiao; Hermes, Matthew R; Willow, Soohaeng Y

    2014-01-30

    Second-order many-body perturbation theory [MBPT(2)] is the lowest-ranked member of a systematic series of approximations convergent at the exact solutions of the Schrödinger equations. It has served and continues to serve as the testing ground for new approximations, algorithms, and even theories. This article introduces this basic theory from a variety of viewpoints including the Rayleigh-Schrödinger perturbation theory, the many-body Green's function theory based on the Dyson equation, and the related Feynman-Goldstone diagrams. It also explains the important properties of MBPT(2) such as size consistency, its ability to describe dispersion interactions, and divergence in metals. On this basis, this article surveys three major advances made recently by the authors to this theory. They are a finite-temperature extension of MBPT(2) and the resolution of the Kohn-Luttinger conundrum, a stochastic evaluation of the correlation and self-energies of MBPT(2) using the Monte Carlo integration of their Laplace-transformed expressions, and an extension to anharmonic vibrational zero-point energies and transition frequencies based on the Dyson equation. PMID:24328153

  9. Development, implementation, and verification of multicycle depletion perturbation theory for reactor burnup analysis

    SciTech Connect

    White, J.R.

    1980-08-01

    A generalized depletion perturbation formulation based on the quasi-static method for solving realistic multicycle reactor depletion problems is developed and implemented within the VENTURE/BURNER modular code system. The present development extends the original formulation derived by M.L. Williams to include nuclide discontinuities such as fuel shuffling and discharge. This theory is first described in detail with particular emphasis given to the similarity of the forward and adjoint quasi-static burnup equations. The specific algorithm and computational methods utilized to solve the adjoint problem within the newly developed DEPTH (Depletion Perturbation Theory) module are then briefly discussed. Finally, the main features and computational accuracy of this new method are illustrated through its application to several representative reactor depletion problems.

  10. Spatially covariant theories of gravity: disformal transformation, cosmological perturbations and the Einstein frame

    NASA Astrophysics Data System (ADS)

    Fujita, Tomohiro; Gao, Xian; Yokoyama, Jun'ichi

    2016-02-01

    We investigate the cosmological background evolution and perturbations in a general class of spatially covariant theories of gravity, which propagates two tensor modes and one scalar mode. We show that the structure of the theory is preserved under the disformal transformation. We also evaluate the primordial spectra for both the gravitational waves and the curvature perturbation, which are invariant under the disformal transformation. Due to the existence of higher spatial derivatives, the quadratic Lagrangian for the tensor modes itself cannot be transformed to the form in the Einstein frame. Nevertheless, there exists a one-parameter family of frames in which the spectrum of the gravitational waves takes the standard form in the Einstein frame.

  11. Testing tree-level perturbation theory for large-scale structure with the local Lagrangian approximation

    NASA Astrophysics Data System (ADS)

    Protogeros, Zacharias A. M.; Melott, Adrian L.; Scherrer, Robert J.

    1997-09-01

    We test tree-level perturbation theory for Gaussian initial conditions with power spectra P(k)~k^n by comparing the probability distribution function (PDF) for the density predicted by the local Lagrangian approximation (LLA) with the results of numerical gravitational clustering simulations. Our results indicate that our approximation correctly reproduces the evolved density PDF for n=-1 and -2 power spectra up to the weakly non-linear regime, while it shows marginal agreement for power indices n=0 and +1 in the linear regime and poor agreement beyond this point. This suggests that tree-level perturbation theory (as realized in the LLA) can accurately predict the density distribution function for n<=-1, but fails for n>=0.

  12. Apparently noninvariant terms of nonlinear sigma models in lattice perturbation theory

    SciTech Connect

    Harada, Koji; Hattori, Nozomu; Kubo, Hirofumi; Yamamoto, Yuki

    2009-03-15

    Apparently noninvariant terms (ANTs) that appear in loop diagrams for nonlinear sigma models are revisited in lattice perturbation theory. The calculations have been done mostly with dimensional regularization so far. In order to establish that the existence of ANTs is independent of the regularization scheme, and of the potential ambiguities in the definition of the Jacobian of the change of integration variables from group elements to 'pion' fields, we employ lattice regularization, in which everything (including the Jacobian) is well defined. We show explicitly that lattice perturbation theory produces ANTs in the four-point functions of the pion fields at one-loop and the Jacobian does not play an important role in generating ANTs.

  13. FAST-PT: a novel algorithm to calculate convolution integrals in cosmological perturbation theory

    NASA Astrophysics Data System (ADS)

    McEwen, Joseph E.; Fang, Xiao; Hirata, Christopher M.; Blazek, Jonathan A.

    2016-09-01

    We present a novel algorithm, FAST-PT, for performing convolution or mode-coupling integrals that appear in nonlinear cosmological perturbation theory. The algorithm uses several properties of gravitational structure formation—the locality of the dark matter equations and the scale invariance of the problem—as well as Fast Fourier Transforms to describe the input power spectrum as a superposition of power laws. This yields extremely fast performance, enabling mode-coupling integral computations fast enough to embed in Monte Carlo Markov Chain parameter estimation. We describe the algorithm and demonstrate its application to calculating nonlinear corrections to the matter power spectrum, including one-loop standard perturbation theory and the renormalization group approach. We also describe our public code (in Python) to implement this algorithm. The code, along with a user manual and example implementations, is available at https://github.com/JoeMcEwen/FAST-PT.

  14. Inflationary Dilatonic de Sitter Universe from { N} = 4 Super-Yang Mills Theory Perturbed by Scalars

    NASA Astrophysics Data System (ADS)

    Hurtado, John Quiroga

    In this paper a quantum { N} = 4 super-Yang Mills theory perturbed by dilaton-coupled scalars, is considered. The induced effective action for such a theory is calculated on a dilaton-gravitational background using the conformal anomaly found via AdS/CFT correspondence. Considering such an effective action (using the large N method) as a quantum correction to the classical gravity action with cosmological constant we study the effect from dilaton to the scale factor (which corresponds to the inflationary universe without dilaton). It is shown that, depending on the initial conditions for the dilaton, the dilaton may slow down, or accelerate, the inflation process. At late times, the dilaton is decaying exponentially. At the end of this work, we consider the question how the perturbation of the solution for the scale factor affects the stability of the solution for the equations of motion and therefore the stability of the Inflationary Universe, which could be eternal.

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

    PubMed

    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.

  16. Periodic orbits of perturbed elliptic oscillators in 6D via averaging theory

    NASA Astrophysics Data System (ADS)

    Lembarki, Fatima Ezzahra; Llibre, Jaume

    2016-10-01

    We provide sufficient conditions on the energy levels to guarantee the existence of periodic orbits for the perturbed elliptic oscillators in 6D using the averaging theory. We give also an analytical estimation of the shape of these periodic orbits parameterized by the energy. The Hamiltonian system here studied comes either from the analysis of the galactic dynamics, or from the motion of the atomic particles in physics.

  17. A simplified perturbation theory for equilibrium properties of triangular-well fluids

    NASA Astrophysics Data System (ADS)

    Largo, J.; Solana, J. R.

    2000-09-01

    A simple expression for the first coordination shell of the radial distribution function of the reference hard-sphere fluid is used in combination with Barker-Henderson perturbation theory to obtain the thermodynamic properties of triangular-well fluids. These properties are expressed analytically in terms of density, temperature, and range of the potential. It is found that the results are accurate for a wide range of densities and temperatures in comparison with existing simulation data.

  18. Nucleon-to-{delta} axial transition form factors in relativistic baryon chiral perturbation theory

    SciTech Connect

    Geng, L. S.; Camalich, J. Martin; Alvarez-Ruso, L.; Vacas, M. J. Vicente

    2008-07-01

    We report a theoretical study of the axial nucleon-to-delta (1232) (N{yields}{delta}) transition form factors up to one-loop order in relativistic baryon chiral perturbation theory. We adopt a formalism in which the {delta} couplings obey the spin-3/2 gauge symmetry and, therefore, decouple the unphysical spin-1/2 fields. We compare the results with phenomenological form factors obtained from neutrino bubble-chamber data and in quark models.

  19. Rare decay {eta}{r_arrow}{pi}{pi}{gamma}{gamma} in chiral perturbation theory

    SciTech Connect

    Knoechlein, G.; Scherer, S.; Drechsel, D.

    1996-04-01

    We investigate the rare radiative {eta} decay modes {eta}{r_arrow}{pi}{sup +}{pi}{sup {minus}}{gamma}{gamma} and {eta}{r_arrow}{pi}{sup 0}{pi}{sup 0}{gamma}{gamma} within the framework of chiral perturbation theory at {ital O}({ital p}{sup 4}). We present photon spectra and partial decay rates for both processes as well as a Dalitz contour plot for the charged decay. {copyright} {ital 1996 The American Physical Society.}

  20. Excited D{sub s} (and Pentaquarks) in Chiral Perturbation Theory

    SciTech Connect

    Thomas Mehen

    2005-01-01

    I present results of a heavy hadron chiral perturbation theory analysis of the decays and masses of the recently discovered excited charm mesons. The present data on the electromagnetic branching ratios are consistent with heavy quark symmetry predictions and disfavor a molecular interpretation of these states. I also discuss model independent predictions for the strong decays of pentaquarks in the 10-bar representation of SU(3) which can be used to constrain the angular momentum and parity quantum numbers of these states.

  1. Vibrational Corrections to Molecular Properties: Second-Order Vibrational Perturbation Theory VS Variational Computations

    NASA Astrophysics Data System (ADS)

    Harding, Michael E.; Vázquez, Juana; Stanton, John F.; Diezemann, Gregor; Gauss, Jürgen

    2011-06-01

    For a small set of linear and non-linear molecules, a detailed comparison of two different procedures for predicting vibrationally averaged molecular properties, i.e., second-order vibrational perturbation theory (VPT2) and a variational approach, is carried out. Results for vibrational corrections to dipole and quadrupole moments, nuclear quadrupole moments, static electric-dipole polarizabilities, NMR chemical shielding tensors, nuclear spin-rotation tensors, magnetizabilities, and rotational g-tensors are reported.

  2. Brillouin-zone integration scheme for many-body density of states: Tetrahedron method combined with cluster perturbation theory

    NASA Astrophysics Data System (ADS)

    Seki, K.; Yunoki, S.

    2016-06-01

    By combining the tetrahedron method with the cluster perturbation theory (CPT), we present an accurate method to numerically calculate the density of states of interacting fermions without introducing the Lorentzian broadening parameter η or the numerical extrapolation of η →0 . The method is conceptually based on the notion of the effective single-particle Hamiltonian which can be subtracted in the Lehmann representation of the single-particle Green's function within the CPT. Indeed, we show the general correspondence between the self-energy and the effective single-particle Hamiltonian which describes exactly the single-particle excitation energies of interacting fermions. The detailed formalism is provided for two-dimensional multiorbital systems and a benchmark calculation is performed for the two-dimensional single-band Hubbard model. The method can be adapted straightforwardly to symmetry-broken states, three-dimensional systems, and finite-temperature calculations.

  3. Time-sliced perturbation theory for large scale structure I: general formalism

    NASA Astrophysics Data System (ADS)

    Blas, Diego; Garny, Mathias; Ivanov, Mikhail M.; Sibiryakov, Sergey

    2016-07-01

    We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the cosmological observables at a given moment of time. Expanding the distribution function around the Gaussian weight we formulate a perturbative technique to calculate non-linear corrections to cosmological correlators, similar to the diagrammatic expansion in a three-dimensional Euclidean quantum field theory, with time playing the role of an external parameter. For the physically relevant case of cold dark matter in an Einstein-de Sitter universe, the time evolution of the distribution function can be found exactly and is encapsulated by a time-dependent coupling constant controlling the perturbative expansion. We show that all building blocks of the expansion are free from spurious infrared enhanced contributions that plague the standard cosmological perturbation theory. This paves the way towards the systematic resummation of infrared effects in large scale structure formation. We also argue that the approach proposed here provides a natural framework to account for the influence of short-scale dynamics on larger scales along the lines of effective field theory.

  4. Coarse-grained cosmological perturbation theory: Stirring up the dust model

    NASA Astrophysics Data System (ADS)

    Uhlemann, Cora; Kopp, Michael

    2015-04-01

    We study the effect of coarse graining the dynamics of a pressureless self-gravitating fluid (coarse-grained dust) in the context of cosmological perturbation theory, in both the Eulerian and Lagrangian frameworks. We obtain recursion relations for the Eulerian perturbation kernels of the coarse-grained dust model by relating them to those of the standard pressureless fluid model. The effect of the coarse graining is illustrated by means of power and cross spectra for the density and velocity, which are computed up to one-loop order. In particular, the large-scale vorticity power spectrum that arises naturally from a mass-weighted velocity is derived from first principles. We find qualitatively good agreement for the magnitude, shape, and spectral index of the vorticity power spectrum with recent measurements from N -body simulations and results from the effective field theory of large-scale structure. To lay the ground for applications in the context of Lagrangian perturbation theory, we finally describe how the kernels obtained in Eulerian space can be mapped to Lagrangian ones.

  5. Nonlinear stochastic biasing of halos: Analysis of cosmological N-body simulations and perturbation theories

    NASA Astrophysics Data System (ADS)

    Sato, Masanori; Matsubara, Takahiko

    2013-06-01

    It is crucial to understand and model a behavior of galaxy biasing for future ambitious galaxy redshift surveys. Using 40 large cosmological N-body simulations for a standard ΛCDM cosmology, we study the cross-correlation coefficient between matter and the halo density field, which is an indicator of the stochasticity of bias, over a wide redshift range 0≤z≤3. The cross-correlation coefficient is important to extract information on the matter density field, e.g., by combining galaxy clustering and galaxy-galaxy lensing measurements. We compare the simulation results with integrated perturbation theory (iPT) proposed by one of the present authors and standard perturbation theory combined with a phenomenological model of local bias. The cross-correlation coefficient derived from the iPT agrees with N-body simulation results down to r˜15(10)h-1Mpc within 0.5 (1.0)% for all redshifts and halo masses we consider. The standard perturbation theory with local bias does not explain complicated behaviors on quasilinear scales at low redshifts, while roughly reproduces the general behavior of the cross-correlation coefficient on fully nonlinear scales. The iPT is powerful to predict the cross-correlation coefficient down to quasilinear regimes with a high precision.

  6. Elimination of translational and rotational motions in nuclear orbital plus molecular orbital theory: application of Moller-Plesset perturbation theory.

    PubMed

    Hoshino, Minoru; Nakai, Hiromi

    2006-05-21

    The translation- and rotation-free nuclear orbital plus molecular orbital (TRF-NOMO) theory was developed to determine the nonadiabatic nuclear and electronic wave functions. This study presents a formulation of TRF-NOMO second-order Moller-Plesset (MP2) perturbation and Epstein-Nesbet (EN) theory with the use of the TRF Hamiltonian. Numerical assessment of the TRF-NOMO/MP2 and EN is performed for several molecules. We confirm the importance of the elimination of translational and rotational motions in the many-body calculations. PMID:16729806

  7. Thermodynamics of technetium: Reconciling theory and experiment using density functional perturbation analysis

    SciTech Connect

    Weck, Philippe F.; Kim, Eunja

    2015-06-11

    The structure, lattice dynamics and thermodynamic properties of bulk technetium were investigated within the framework of density functional theory. The phonon density of states spectrum computed with density functional perturbation theory closely matches inelastic coherent neutron scattering measurements. The thermal properties of technetium were derived from phonon frequencies calculated within the quasi-harmonic approximation (QHA), which introduces a volume dependence of phonon frequencies as a part of the anharmonic effect. As a result, the predicted thermal expansion and isobaric heat capacity of technetium are in excellent agreement with available experimental data for temperatures up to ~1600 K.

  8. Communication: Semiclassical perturbation theory for the quantum diffractive scattering of atoms on thermal surfaces

    NASA Astrophysics Data System (ADS)

    Daon, Shauli; Pollak, Eli; Miret-Artés, S.

    2012-11-01

    Inspired by the semiclassical perturbation theory of Hubbard and Miller [J. Chem. Phys. 80, 5827 (1984), 10.1063/1.446609], we derive explicit expressions for the angular distribution of particles scattered from thermal surfaces. At very low surface temperature, the observed experimental background scattering is proportional to the spectral density of the phonons. The angular distribution is a sum of diffraction peaks and a broad background reflecting the spectral density. The theory is applied to measured angular distributions of Ne, Ar, and Kr scattered from a Cu(111) surface.

  9. Perturbative treatment of spin-orbit coupling within spin-free exact two-component theory

    SciTech Connect

    Cheng, Lan; Gauss, Jürgen

    2014-10-28

    This work deals with the perturbative treatment of spin-orbit-coupling (SOC) effects within the spin-free exact two-component theory in its one-electron variant (SFX2C-1e). We investigate two schemes for constructing the SFX2C-1e SOC matrix: the SFX2C-1e+SOC [der] scheme defines the SOC matrix elements based on SFX2C-1e analytic-derivative theory, hereby treating the SOC integrals as the perturbation; the SFX2C-1e+SOC [fd] scheme takes the difference between the X2C-1e and SFX2C-1e Hamiltonian matrices as the SOC perturbation. Furthermore, a mean-field approach in the SFX2C-1e framework is formulated and implemented to efficiently include two-electron SOC effects. Systematic approximations to the two-electron SOC integrals are also proposed and carefully assessed. Based on benchmark calculations of the second-order SOC corrections to the energies and electrical properties for a set of diatomic molecules, we show that the SFX2C-1e+SOC [der] scheme performs very well in the computation of perturbative SOC corrections and that the “2eSL” scheme, which neglects the (SS|SS)-type two-electron SOC integrals, is both efficient and accurate. In contrast, the SFX2C-1e+SOC [fd] scheme turns out to be incompatible with a perturbative treatment of SOC effects. Finally, as a first chemical application, we report high-accuracy calculations of the {sup 201}Hg quadrupole-coupling parameters of the recently characterized ethylmercury hydride (HHgCH{sub 2}CH{sub 3}) molecule based on SFX2C-1e coupled-cluster calculations augmented with second-order SOC corrections obtained at the Hartree-Fock level using the SFX2C-1e+SOC [der]/2eSL scheme.

  10. Disformal invariance of cosmological perturbations in a generalized class of Horndeski theories

    NASA Astrophysics Data System (ADS)

    Tsujikawa, Shinji

    2015-04-01

    It is known that Horndeski theories can be transformed to a sub-class of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories under the disformal transformation of the metric gμ ν → Ω2(phi)gμ ν+Γ (phi,X) ∇μ phi ∇ν phi, where Ω is a function of a scalar field phi and Γ is another function depending on both phi and X=gμ ν∇μ phi ∇ν phi. We show that, with the choice of unitary gauge, both curvature and tensor perturbations on the flat isotropic cosmological background are generally invariant under the disformal transformation. By means of the effective field theories encompassing Horndeski and GLPV theories, we obtain the second-order actions of scalar/tensor perturbations and present the relations for physical quantities between the two frames. The invariance of the inflationary power spectra under the disformal transformation is explicitly proved up to next-to-leading order in slow-roll. In particular, we identify the existence of the Einstein frame in which the tensor power spectrum is of the same form as that in General Relativity and derive the condition under which the spectrum of gravitational waves in GLPV theories is red-tilted.

  11. Disformal invariance of cosmological perturbations in a generalized class of Horndeski theories

    SciTech Connect

    Tsujikawa, Shinji

    2015-04-01

    It is known that Horndeski theories can be transformed to a sub-class of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories under the disformal transformation of the metric g{sub μ ν} → Ω{sup 2}(φ)g{sub μ ν}+Γ (φ,X) ∇{sub μ} φ ∇{sub ν} φ, where Ω is a function of a scalar field φ and Γ is another function depending on both φ and X=g{sup μ ν}∇{sub μ} φ ∇{sub ν} φ. We show that, with the choice of unitary gauge, both curvature and tensor perturbations on the flat isotropic cosmological background are generally invariant under the disformal transformation. By means of the effective field theories encompassing Horndeski and GLPV theories, we obtain the second-order actions of scalar/tensor perturbations and present the relations for physical quantities between the two frames. The invariance of the inflationary power spectra under the disformal transformation is explicitly proved up to next-to-leading order in slow-roll. In particular, we identify the existence of the Einstein frame in which the tensor power spectrum is of the same form as that in General Relativity and derive the condition under which the spectrum of gravitational waves in GLPV theories is red-tilted.

  12. Disformal invariance of cosmological perturbations in a generalized class of Horndeski theories

    SciTech Connect

    Tsujikawa, Shinji

    2015-04-27

    It is known that Horndeski theories can be transformed to a sub-class of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories under the disformal transformation of the metric g{sub μν}→Ω{sup 2}(ϕ)g{sub μν}+Γ(ϕ,X)∇{sub μ}ϕ∇{sub ν}ϕ, where Ω is a function of a scalar field ϕ and Γ is another function depending on both ϕ and X=g{sup μν}∇{sub μ}ϕ∇{sub ν}ϕ. We show that, with the choice of unitary gauge, both curvature and tensor perturbations on the flat isotropic cosmological background are generally invariant under the disformal transformation. By means of the effective field theories encompassing Horndeski and GLPV theories, we obtain the second-order actions of scalar/tensor perturbations and present the relations for physical quantities between the two frames. The invariance of the inflationary power spectra under the disformal transformation is explicitly proved up to next-to-leading order in slow-roll. In particular, we identify the existence of the Einstein frame in which the tensor power spectrum is of the same form as that in General Relativity and derive the condition under which the spectrum of gravitational waves in GLPV theories is red-tilted.

  13. Gravitoinertial force background level affects adaptation to coriolis force perturbations of reaching movements.

    PubMed

    Lackner, J R; Dizio, P

    1998-08-01

    We evaluated the combined effects on reaching movements of the transient, movement-dependent Coriolis forces and the static centrifugal forces generated in a rotating environment. Specifically, we assessed the effects of comparable Coriolis force perturbations in different static force backgrounds. Two groups of subjects made reaching movements toward a just-extinguished visual target before rotation began, during 10 rpm counterclockwise rotation, and after rotation ceased. One group was seated on the axis of rotation, the other 2.23 m away. The resultant of gravity and centrifugal force on the hand was 1.0 g for the on-center group during 10 rpm rotation, and 1.031 g for the off-center group because of the 0.25 g centrifugal force present. For both groups, rightward Coriolis forces, approximately 0.2 g peak, were generated during voluntary arm movements. The endpoints and paths of the initial per-rotation movements were deviated rightward for both groups by comparable amounts. Within 10 subsequent reaches, the on-center group regained baseline accuracy and straight-line paths; however, even after 40 movements the off-center group had not resumed baseline endpoint accuracy. Mirror-image aftereffects occurred when rotation stopped. These findings demonstrate that manual control is disrupted by transient Coriolis force perturbations and that adaptation can occur even in the absence of visual feedback. An increase, even a small one, in background force level above normal gravity does not affect the size of the reaching errors induced by Coriolis forces nor does it affect the rate of reacquiring straight reaching paths; however, it does hinder restoration of reaching accuracy.

  14. Gravitoinertial force background level affects adaptation to coriolis force perturbations of reaching movements

    NASA Technical Reports Server (NTRS)

    Lackner, J. R.; Dizio, P.

    1998-01-01

    We evaluated the combined effects on reaching movements of the transient, movement-dependent Coriolis forces and the static centrifugal forces generated in a rotating environment. Specifically, we assessed the effects of comparable Coriolis force perturbations in different static force backgrounds. Two groups of subjects made reaching movements toward a just-extinguished visual target before rotation began, during 10 rpm counterclockwise rotation, and after rotation ceased. One group was seated on the axis of rotation, the other 2.23 m away. The resultant of gravity and centrifugal force on the hand was 1.0 g for the on-center group during 10 rpm rotation, and 1.031 g for the off-center group because of the 0.25 g centrifugal force present. For both groups, rightward Coriolis forces, approximately 0.2 g peak, were generated during voluntary arm movements. The endpoints and paths of the initial per-rotation movements were deviated rightward for both groups by comparable amounts. Within 10 subsequent reaches, the on-center group regained baseline accuracy and straight-line paths; however, even after 40 movements the off-center group had not resumed baseline endpoint accuracy. Mirror-image aftereffects occurred when rotation stopped. These findings demonstrate that manual control is disrupted by transient Coriolis force perturbations and that adaptation can occur even in the absence of visual feedback. An increase, even a small one, in background force level above normal gravity does not affect the size of the reaching errors induced by Coriolis forces nor does it affect the rate of reacquiring straight reaching paths; however, it does hinder restoration of reaching accuracy.

  15. Perturbation theory for multicomponent fluids based on structural properties of hard-sphere chain mixtures

    NASA Astrophysics Data System (ADS)

    Hlushak, Stepan

    2015-09-01

    An analytical expression for the Laplace transform of the radial distribution function of a mixture of hard-sphere chains of arbitrary segment size and chain length is used to rigorously formulate the first-order Barker-Henderson perturbation theory for the contribution of the segment-segment dispersive interactions into thermodynamics of the Lennard-Jones chain mixtures. Based on this approximation, a simple variant of the statistical associating fluid theory is proposed and used to predict properties of several mixtures of chains of different lengths and segment sizes. The theory treats the dispersive interactions more rigorously than the conventional theories and provides means for more accurate description of dispersive interactions in the mixtures of highly asymmetric components.

  16. Perturbation theory for multicomponent fluids based on structural properties of hard-sphere chain mixtures

    SciTech Connect

    Hlushak, Stepan

    2015-09-28

    An analytical expression for the Laplace transform of the radial distribution function of a mixture of hard-sphere chains of arbitrary segment size and chain length is used to rigorously formulate the first-order Barker-Henderson perturbation theory for the contribution of the segment-segment dispersive interactions into thermodynamics of the Lennard-Jones chain mixtures. Based on this approximation, a simple variant of the statistical associating fluid theory is proposed and used to predict properties of several mixtures of chains of different lengths and segment sizes. The theory treats the dispersive interactions more rigorously than the conventional theories and provides means for more accurate description of dispersive interactions in the mixtures of highly asymmetric components.

  17. Second order classical perturbation theory for atom surface scattering: Analysis of asymmetry in the angular distribution

    SciTech Connect

    Zhou, Yun Pollak, Eli; Miret-Artés, Salvador

    2014-01-14

    A second order classical perturbation theory is developed and applied to elastic atom corrugated surface scattering. The resulting theory accounts for experimentally observed asymmetry in the final angular distributions. These include qualitative features, such as reduction of the asymmetry in the intensity of the rainbow peaks with increased incidence energy as well as the asymmetry in the location of the rainbow peaks with respect to the specular scattering angle. The theory is especially applicable to “soft” corrugated potentials. Expressions for the angular distribution are derived for the exponential repulsive and Morse potential models. The theory is implemented numerically to a simplified model of the scattering of an Ar atom from a LiF(100) surface.

  18. Scale-adaptive tensor algebra for local many-body methods of electronic structure theory

    SciTech Connect

    Liakh, Dmitry I

    2014-01-01

    While the formalism of multiresolution analysis (MRA), based on wavelets and adaptive integral representations of operators, is actively progressing in electronic structure theory (mostly on the independent-particle level and, recently, second-order perturbation theory), the concepts of multiresolution and adaptivity can also be utilized within the traditional formulation of correlated (many-particle) theory which is based on second quantization and the corresponding (generally nonorthogonal) tensor algebra. In this paper, we present a formalism called scale-adaptive tensor algebra (SATA) which exploits an adaptive representation of tensors of many-body operators via the local adjustment of the basis set quality. Given a series of locally supported fragment bases of a progressively lower quality, we formulate the explicit rules for tensor algebra operations dealing with adaptively resolved tensor operands. The formalism suggested is expected to enhance the applicability and reliability of local correlated many-body methods of electronic structure theory, especially those directly based on atomic orbitals (or any other localized basis functions).

  19. Borel Summability of Perturbative Series in 4D N=2 and 5D N=1 Supersymmetric Theories.

    PubMed

    Honda, Masazumi

    2016-05-27

    We study weak coupling perturbative series in 4D N=2 and 5D N=1 supersymmetric gauge theories with Lagrangians. We prove that the perturbative series of these theories in the zero-instanton sector are Borel summable for various observables. Our result for the 4D N=2 case supports an expectation from a recent proposal on a semiclassical realization of infrared renormalons in QCD-like theories, where the semiclassical solution does not exist in N=2 theories and the perturbative series are unambiguous, namely, Borel summable. We also prove that the perturbative series in an arbitrary number of instanton sectors are Borel summable for a wide class of theories. It turns out that exact results can be obtained by summing over the Borel resummations with every instanton number.

  20. Does the orbit-averaged theory require a scale separation between periodic orbit size and perturbation correlation length?

    SciTech Connect

    Zhang, Wenlu; Lin, Zhihong

    2013-10-15

    Using the canonical perturbation theory, we show that the orbit-averaged theory only requires a time-scale separation between equilibrium and perturbed motions and verifies the widely accepted notion that orbit averaging effects greatly reduce the microturbulent transport of energetic particles in a tokamak. Therefore, a recent claim [Hauff and Jenko, Phys. Rev. Lett. 102, 075004 (2009); Jenko et al., ibid. 107, 239502 (2011)] stating that the orbit-averaged theory requires a scale separation between equilibrium orbit size and perturbation correlation length is erroneous.

  1. Manifestly gauge invariant theory of the nonlinear cosmological perturbations in the leading order of the gradient expansion

    NASA Astrophysics Data System (ADS)

    Hamazaki, Takashi

    2011-07-01

    In the full nonlinear cosmological perturbation theory in the leading order of the gradient expansion, all the types of the gauge invariant perturbation variables are defined. The metric junction conditions across the spacelike transition hypersurface are formulated in a manifestly gauge invariant manner. It is manifestly shown that all the physical laws such as the evolution equations, the constraint equations, and the junction conditions can be written using the gauge invariant variables which we defined only. Based on the existence of the universal adiabatic growing mode in the nonlinear perturbation theory and the ρ philosophy where the physical evolution are described using the energy density ρ as the evolution parameter, we give the definitions of the adiabatic perturbation variable and the entropic perturbation variables in the full nonlinear perturbation theory. In order to give the analytic order estimate of the nonlinear parameter fNL, we present the exponent evaluation method. As the models where fNL changes continuously and becomes large, using the ρ philosophy, we investigate the non-Gaussianity induced by the entropic perturbation of the component which does not govern the cosmic energy density, and we show that in order to obtain the significant non-Gaussianity it is necessary that the scalar field which supports the entropic perturbation is extremely small compared with the scalar field which supports the adiabatic perturbation.

  2. On post-inflation validity of perturbation theory in Horndeski scalar-tensor models

    NASA Astrophysics Data System (ADS)

    Germani, Cristiano; Kudryashova, Nina; Watanabe, Yuki

    2016-08-01

    By using the newtonian gauge, we re-confirm that, as in the minimal case, the re-scaled Mukhanov-Sasaki variable is conserved leading to a constraint equation for the Newtonian potential. However, conversely to the minimal case, in Horndeski theories, the super-horizon Newtonian potential can potentially grow to very large values after inflation exit. If that happens, inflationary predictability is lost during the oscillating period. When this does not happen, the perturbations generated during inflation can be standardly related to the CMB, if the theory chosen is minimal at low energies. As a concrete example, we analytically and numerically discuss the new Higgs inflationary case. There, the Inflaton is the Higgs boson that is non-minimally kinetically coupled to gravity. During the high-energy part of the post-inflationary oscillations, the system is anisotropic and the Newtonian potential is largely amplified. Thanks to the smallness of today's amplitude of curvature perturbations, however, the system stays in the linear regime, so that inflationary predictions are not lost. At low energies, when the system relaxes to the minimal case, the anisotropies disappear and the Newtonian potential converges to a constant value. We show that the constant value to which the Newtonian potential converges is related to the frozen part of curvature perturbations during inflation, precisely like in the minimal case.

  3. Reference interaction site model and optimized perturbation theories of colloidal dumbbells with increasing anisotropy

    SciTech Connect

    Munaò, Gianmarco Costa, Dino; Caccamo, Carlo; Gámez, Francisco; Giacometti, Achille

    2015-06-14

    We investigate thermodynamic properties of anisotropic colloidal dumbbells in the frameworks provided by the Reference Interaction Site Model (RISM) theory and an Optimized Perturbation Theory (OPT), this latter based on a fourth-order high-temperature perturbative expansion of the free energy, recently generalized to molecular fluids. Our model is constituted by two identical tangent hard spheres surrounded by square-well attractions with same widths and progressively different depths. Gas-liquid coexistence curves are obtained by predicting pressures, free energies, and chemical potentials. In comparison with previous simulation results, RISM and OPT agree in reproducing the progressive reduction of the gas-liquid phase separation as the anisotropy of the interaction potential becomes more pronounced; in particular, the RISM theory provides reasonable predictions for all coexistence curves, bar the strong anisotropy regime, whereas OPT performs generally less well. Both theories predict a linear dependence of the critical temperature on the interaction strength, reproducing in this way the mean-field behavior observed in simulations; the critical density—that drastically drops as the anisotropy increases—turns to be less accurate. Our results appear as a robust benchmark for further theoretical studies, in support to the simulation approach, of self-assembly in model colloidal systems.

  4. Sine-Gordon model and the small k+ region of light-cone perturbation theory

    NASA Astrophysics Data System (ADS)

    Griffin, Paul A.

    1992-10-01

    The nonperturbative 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 nonperturbative β2=8π critical point by a light-cone version of Coleman's variational method. Vacuum bubbles, which are k+=0 diagrams in light-cone field theory and are individually finite and nonvanishing for all β, conspire to generate ultraviolet divergences of the light-cone energy density. The k+=0 region of momentum also contributes 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.

  5. Correlators of left charges and weak operators in finite volume chiral perturbation theory

    NASA Astrophysics Data System (ADS)

    Hernández, Pilar; Laine, Mikko

    2003-01-01

    We compute the two-point correlator between left-handed flavour charges, and the three-point correlator between two left-handed charges and one strangeness violating DeltaI = 3/2 weak operator, at next-to-leading order in finite volume SU(3)L × SU(3)R chiral perturbation theory, in the so-called epsilon-regime. Matching these results with the corresponding lattice measurements would in principle allow to extract the pion decay constant F, and the effective chiral theory parameter g27, which determines the Delta I = 3/2 amplitude of the weak decays K to pipi as well as the kaon mixing parameter BK in the chiral limit. We repeat the calculations in the replica formulation of quenched chiral perturbation theory, finding only mild modifications. In particular, a properly chosen ratio of the three-point and two-point functions is shown to be identical in the full and quenched theories at this order.

  6. Convection-pulsation coupling. I. A mixing-length perturbative theory

    NASA Astrophysics Data System (ADS)

    Grigahcène, A.; Dupret, M.-A.; Gabriel, M.; Garrido, R.; Scuflaire, R.

    2005-05-01

    We present in details a time-dependent convection treatment in the frame of the Mixing-Length Theory (MLT). Following the original ideas by Unno (1967, PASJ, 19, 140), this theory has been developed by Gabriel et al. (1974, Bull. Ac. Roy. Belgique, Classe des Sciences, 60, 866) and Gabriel (1996, Bull. Astron. Soc. India, 24, 233). In this paper, we present it in a united form, we detail the basic derivations and approximations and give final improvements. A new perturbation of the energy closure equation is proposed for the first time, making it possible to avoid the occurrence of short wavelength spatial oscillations of the thermal eigenfunctions. This theory accounts for the perturbation of the convective flux, the turbulent Reynolds stress and the turbulent kinetic energy dissipation. It has been numerically implemented in a non-radial non-adiabatic pulsation code and the first results published in a Letter by Dupret et al. (2004a, A&A, 414, L17) indicate that the theory predicts the observed red border of the lower end of the instability strip and the driving mechanism of the recently discovered γ Dor stars.

  7. Systematic treatmeant of displacements, strains, and electric fields in density-functional perturbation theory

    NASA Astrophysics Data System (ADS)

    Wu, Xifan; Vanderbilt, David; Hamann, D. R.

    2004-03-01

    Using the methods of density-functional perturbation theory, it is possible to compute first derivatives of the electronic wavefunctions with respect to atomic-displacement, electric-field, and strain perturbations; and from these, tensors of second energy derivatives including both `diagonal responses' (force-constant, dielectric susceptibility, and elastic tensors) and `off-diagonal' ones (piezoelectric, internal-strain, and Born-charge tensors). For polar insulators, these quantities can couple in complex ways. Here, we describe a systematic approach for computing all of these quantities in a unified fashion, and for combining the information thus obtained to compute such properties as clamped-strain vs. free-stress dielectric tensors, elastic constants under different electrical boundary conditions, and piezoelectric coupling factors. The calculations are implemented in the ABINIT code package, and their application will be illustrated for the cases of ZnO and BaTiO3 in their zero-temperature wurzite and rhombohedral structures, respectively.

  8. Nonequilibrium transport through a Kondo dot in a magnetic field: perturbation theory and poor man's scaling.

    PubMed

    Rosch, A; Paaske, J; Kroha, J; Wölfle, P

    2003-02-21

    We consider electron transport through a quantum dot described by the Kondo model in the regime of large transport voltage V in the presence of a magnetic field B with max((V,B)>T(K). The electric current I and the local magnetization M are found to be universal functions of V/T(K) and B/T(K), where T(K) is the equilibrium Kondo temperature. We present a generalization of the perturbative renormali-zation group to frequency dependent coupling functions, as necessitated by the structure of bare perturbation theory. We calculate I and M within a poor man's scaling approach and find excellent agreement with experiment. PMID:12633260

  9. Diagrammatic perturbation theory - The ground state of the carbon monosulfide molecule

    NASA Technical Reports Server (NTRS)

    Wilson, S.

    1977-01-01

    Diagrammatic many-body perturbation theory is employed in a study of the ground state of the carbon monosulfide molecule for bond lengths close to the equilibrium value. The calculations are complete through third order in the energy within the algebraic approximation. Two different zero-order Hamiltonians are considered, and all two-, three-, and four-body terms are determined for the corresponding perturbation expansions. Many-body effects are found to be very important. Pade approximants to the energy expansion are constructed, and upper bounds evaluated. Almost 53 percent of the estimated correlation energy is recovered. The variation of components of the correlation energy with nuclear separation is investigated. Spectroscopic constants are also calculated.

  10. Characteristics of spectral-hole burning in Tm3+:YAG based on the perturbation theory

    NASA Astrophysics Data System (ADS)

    Zhang, Shi-Yu; Ma, Xiu-Rong; Zhang, Shuang-Gen; Chen-Lei; Wang, Xia-Yang; Mu, Kuan-Lin; Wang, Song

    2014-06-01

    In this paper, the physical mechanism of the interaction between electromagnetic wave and spectral-hole burning crystal material is investigated in detail. In the small signal regime, a perturbation theory model is used to analyze the mechanism of spectral-hole burning. By solving the Liouville equation, three-order perturbation results are obtained. From the theoretic analysis, spectral-hole burning can be interpreted as a photon echo of the zero-order diffraction echo when the first optical pulse and the second optical pulse are overlapped in time. According to the model, the spectral-hole width is dependent on the chirp rate of the reading laser. When the chirp rate is slow with respect to the spectral features of interest, the spectral hole is closely mapped into time domain. For a fast chirp rate, distortions are observed. The results follow Maxwell—Bloch model and they are also in good agreement with the experimental results.

  11. Non-perturbative BRST quantization of Euclidean Yang-Mills theories in Curci-Ferrari gauges

    NASA Astrophysics Data System (ADS)

    Pereira, A. D.; Sobreiro, R. F.; Sorella, S. P.

    2016-10-01

    In this paper we address the issue of the non-perturbative quantization of Euclidean Yang-Mills theories in the Curci-Ferrari gauge. In particular, we construct a refined Gribov-Zwanziger action for this gauge, which takes into account the presence of gauge copies as well as the dynamical formation of dimension-two condensates. This action enjoys a non-perturbative BRST symmetry recently proposed in Capri et al. (Phys. Rev. D 92(4), 045039. doi: 10.1103/PhysRevD.92.045039 arXiv:1506.06995 [hep-th], 2015). Finally, we pay attention to the gluon propagator in different space-time dimensions.

  12. Guidance in Kagome-like photonic crystal fibres II: perturbation theory for a realistic fibre structure.

    PubMed

    Chen, Lei; Bird, David M

    2011-03-28

    A perturbation theory is developed that treats a localised mode embedded within a continuum of states. The method is applied to a model rectangular hollow-core photonic crystal fibre structure, where the basic modes are derived from an ideal, scalar model and the perturbation terms include vector effects and structural difference between the ideal and realistic structures. An expression for the attenuation of the fundamental mode due to interactions with cladding modes is derived, and results are presented for a rectangular photonic crystal fibre structure. Attenuations calculated in this way are in good agreement with numerical simulations. The origin of the guidance in our model structure is explained through this quantitative analysis. Further perspectives are obtained through investigating the influence of fibre parameters on the attenuation.

  13. Analysis of a renormalization group method and normal form theory for perturbed ordinary differential equations

    NASA Astrophysics Data System (ADS)

    DeVille, R. E. Lee; Harkin, Anthony; Holzer, Matt; Josić, Krešimir; Kaper, Tasso J.

    2008-06-01

    For singular perturbation problems, the renormalization group (RG) method of Chen, Goldenfeld, and Oono [Phys. Rev. E. 49 (1994) 4502-4511] has been shown to be an effective general approach for deriving reduced or amplitude equations that govern the long time dynamics of the system. It has been applied to a variety of problems traditionally analyzed using disparate methods, including the method of multiple scales, boundary layer theory, the WKBJ method, the Poincaré-Lindstedt method, the method of averaging, and others. In this article, we show how the RG method may be used to generate normal forms for large classes of ordinary differential equations. First, we apply the RG method to systems with autonomous perturbations, and we show that the reduced or amplitude equations generated by the RG method are equivalent to the classical Poincaré-Birkhoff normal forms for these systems up to and including terms of O(ɛ2), where ɛ is the perturbation parameter. This analysis establishes our approach and generalizes to higher order. Second, we apply the RG method to systems with nonautonomous perturbations, and we show that the reduced or amplitude equations so generated constitute time-asymptotic normal forms, which are based on KBM averages. Moreover, for both classes of problems, we show that the main coordinate changes are equivalent, up to translations between the spaces in which they are defined. In this manner, our results show that the RG method offers a new approach for deriving normal forms for nonautonomous systems, and it offers advantages since one can typically more readily identify resonant terms from naive perturbation expansions than from the nonautonomous vector fields themselves. Finally, we establish how well the solution to the RG equations approximates the solution of the original equations on time scales of O(1/ɛ).

  14. A Computer Code System for the Calculation of Reactivity and Kinetic Parameters by One-Dimensional Neutron Transport Perturbation Theory.

    1985-02-01

    Version 00 TP1 is a transport theory code, developed to determine reactivity effects and kinetic parameters such as effective delayed neutron fractions and mean generation time by applying the usual perturbation formalism for one-dimensional geometry.

  15. A Computer Program for the Calculation of Reactivity and Kinetic Parameters by Two-Dimensional Neutron Transport Perturbation Theory.

    1985-02-01

    Version 00 TP2 is a transport theory code, developed to determine reactivity effects and kinetic parameters such as effective delayed neutron fractions and mean generation time by applying the usual perturbation formalism for two-dimensional geometry.

  16. Dual chain perturbation theory: A new equation of state for polyatomic molecules.

    PubMed

    Marshall, Bennett D

    2016-04-28

    In the development of equations of state for polyatomic molecules, thermodynamic perturbation theory (TPT) is widely used to calculate the change in free energy due to chain formation. TPT is a simplification of a more general and exact multi-density cluster expansion for associating fluids. In TPT, all contributions to the cluster expansion which contain chain-chain interactions are neglected. That is, all inter-chain interactions are treated at the reference fluid level. This allows for the summation of the cluster theory in terms of reference system correlation functions only. The resulting theory has been shown to be accurate and has been widely employed as the basis of many engineering equations of state. While highly successful, TPT has many handicaps which result from the neglect of chain-chain contributions. The subject of this document is to move beyond the limitations of TPT and include chain-chain contributions to the equation of state.

  17. Dual chain perturbation theory: A new equation of state for polyatomic molecules

    NASA Astrophysics Data System (ADS)

    Marshall, Bennett D.

    2016-04-01

    In the development of equations of state for polyatomic molecules, thermodynamic perturbation theory (TPT) is widely used to calculate the change in free energy due to chain formation. TPT is a simplification of a more general and exact multi-density cluster expansion for associating fluids. In TPT, all contributions to the cluster expansion which contain chain-chain interactions are neglected. That is, all inter-chain interactions are treated at the reference fluid level. This allows for the summation of the cluster theory in terms of reference system correlation functions only. The resulting theory has been shown to be accurate and has been widely employed as the basis of many engineering equations of state. While highly successful, TPT has many handicaps which result from the neglect of chain-chain contributions. The subject of this document is to move beyond the limitations of TPT and include chain-chain contributions to the equation of state.

  18. A two-scale approach to electron correlation in multiconfigurational perturbation theory.

    PubMed

    Farahani, Pooria; Roca-Sanjuán, Daniel; Aquilante, Francesco

    2014-08-15

    We present a new approach for the calculation of dynamic electron correlation effects in large molecular systems using multiconfigurational second-order perturbation theory (CASPT2). The method is restricted to cases where partitioning of the molecular system into an active site and an environment is meaningful. Only dynamic correlation effects derived from orbitals extending over the active site are included at the CASPT2 level of theory, whereas the correlation effects of the environment are retrieved at lower computational costs. For sufficiently large systems, the small errors introduced by this approximation are contrasted by the substantial savings in both storage and computational demands compared to the full CASPT2 calculation. Provided that static correlation effects are correctly taken into account for the whole system, the proposed scheme represent a hierarchical approach to the electron correlation problem, where two molecular scales are treated each by means of the most suitable level of theory.

  19. Testing higher-order Lagrangian perturbation theory against numerical simulation. 1: Pancake models

    NASA Technical Reports Server (NTRS)

    Buchert, T.; Melott, A. L.; Weiss, A. G.

    1993-01-01

    We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the

  20. A Sharing Item Response Theory Model for Computerized Adaptive Testing

    ERIC Educational Resources Information Center

    Segall, Daniel O.

    2004-01-01

    A new sharing item response theory (SIRT) model is presented that explicitly models the effects of sharing item content between informants and test takers. This model is used to construct adaptive item selection and scoring rules that provide increased precision and reduced score gains in instances where sharing occurs. The adaptive item selection…

  1. Conformal perturbation theory and higher spin entanglement entropy on the torus

    NASA Astrophysics Data System (ADS)

    Datta, Shouvik; David, Justin R.; Kumar, S. Prem

    2015-04-01

    We study the free fermion theory in 1+1 dimensions deformed by chemical potentials for holomorphic, conserved currents at finite temperature and on a spatial circle. For a spin-three chemical potential μ, the deformation is related at high temperatures to a higher spin black hole in hs[0] theory on AdS3 spacetime. We calculate the order μ 2 corrections to the single interval Rényi and entanglement entropies on the torus using the bosonized formulation. A consistent result, satisfying all checks, emerges upon carefully accounting for both perturbative and winding mode contributions in the bosonized language. The order μ 2 corrections involve integrals that are finite but potentially sensitive to contact term singularities. We propose and apply a prescription for defining such integrals which matches the Hamiltonian picture and passes several non-trivial checks for both thermal corrections and the Rényi entropies at this order. The thermal corrections are given by a weight six quasi-modular form, whilst the Rényi entropies are controlled by quasi-elliptic functions of the interval length with modular weight six. We also point out the well known connection between the perturbative expansion of the partition function in powers of the spin-three chemical potential and the Gross-Taylor genus expansion of large- N Yang-Mills theory on the torus. We note the absence of winding mode contributions in this connection, which suggests qualitatively different entanglement entropies for the two systems.

  2. Pion-nucleon scattering in covariant baryon chiral perturbation theory with explicit Delta resonances

    NASA Astrophysics Data System (ADS)

    Yao, De-Liang; Siemens, D.; Bernard, V.; Epelbaum, E.; Gasparyan, A. M.; Gegelia, J.; Krebs, H.; Meißner, Ulf-G.

    2016-05-01

    We present the results of a third order calculation of the pion-nucleon scattering amplitude in a chiral effective field theory with pions, nucleons and delta resonances as explicit degrees of freedom. We work in a manifestly Lorentz invariant formulation of baryon chiral perturbation theory using dimensional regularization and the extended on-mass-shell renormalization scheme. In the delta resonance sector, the on mass-shell renormalization is realized as a complex-mass scheme. By fitting the low-energy constants of the effective Lagrangian to the S- and P -partial waves a satisfactory description of the phase shifts from the analysis of the Roy-Steiner equations is obtained. We predict the phase shifts for the D and F waves and compare them with the results of the analysis of the George Washington University group. The threshold parameters are calculated both in the delta-less and delta-full cases. Based on the determined low-energy constants, we discuss the pion-nucleon sigma term. Additionally, in order to determine the strangeness content of the nucleon, we calculate the octet baryon masses in the presence of decuplet resonances up to next-to-next-to-leading order in SU(3) baryon chiral perturbation theory. The octet baryon sigma terms are predicted as a byproduct of this calculation.

  3. Potential Energy Surface of the Chromium Dimer Re-re-revisited with Multiconfigurational Perturbation Theory.

    PubMed

    Vancoillie, Steven; Malmqvist, Per Åke; Veryazov, Valera

    2016-04-12

    The chromium dimer has long been a benchmark molecule to evaluate the performance of different computational methods ranging from density functional theory to wave function methods. Among the latter, multiconfigurational perturbation theory was shown to be able to reproduce the potential energy surface of the chromium dimer accurately. However, for modest active space sizes, it was later shown that different definitions of the zeroth-order Hamiltonian have a large impact on the results. In this work, we revisit the system for the third time with multiconfigurational perturbation theory, now in order to increase the active space of the reference wave function. This reduces the impact of the choice of zeroth-order Hamiltonian and improves the shape of the potential energy surface significantly. We conclude by comparing our results of the dissocation energy and vibrational spectrum to those obtained from several highly accurate multiconfigurational methods and experiment. For a meaningful comparison, we used the extrapolation to the complete basis set for all methods involved.

  4. Shielding application of perturbation theory to determine changes in neutron and gamma doses due to changes in shield layers

    NASA Technical Reports Server (NTRS)

    Fieno, D.

    1972-01-01

    Perturbation theory formulas were derived and applied to determine changes in neutron and gamma-ray doses due to changes in various radiation shield layers for fixed sources. For a given source and detector position, the perturbation method enables dose derivatives with respect to density, or equivalently thickness, for every layer to be determined from one forward and one inhomogeneous adjoint calculation. A direct determination without the perturbation approach would require two forward calculations to evaluate the dose derivative due to a change in a single layer. Hence, the perturbation method for obtaining dose derivatives requires fewer computations for design studies of multilayer shields. For an illustrative problem, a comparison was made of the fractional change in the dose per unit change in the thickness of each shield layer in a two-layer spherical configuration as calculated by perturbation theory and by successive direct calculations; excellent agreement was obtained between the two methods.

  5. Perturbation theory for graphene-integrated waveguides: Cubic nonlinearity and third-harmonic generation

    NASA Astrophysics Data System (ADS)

    Gorbach, Andrey V.; Ivanov, Edouard

    2016-07-01

    We present perturbation theory for analysis of generic third-order nonlinear processes in graphene-integrated photonic structures. The optical response of graphene is treated as the nonlinear boundary condition in Maxwell's equations. The derived models are applied for analysis of third-harmonic generation in a graphene-coated dielectric microfiber. An efficiency of up to a few percent is predicted when using subpicosecond pump pulses with energies of the order of 0.1 nJ in a submillimeter-long fiber when operating near the resonance of the graphene nonlinear conductivity ℏ ω =(2 /3 ) EF .

  6. Multireference Møller Plesset perturbation theory using spin-dependent orbital energies

    NASA Astrophysics Data System (ADS)

    Kobayashi, Yuka; Nakano, Haruyuki; Hirao, Kimihiko

    2001-03-01

    The use of spin-dependent orbital energies is proposed in the multireference Møller-Plesset perturbation theory. In this method a single canonical Fock orbital set is used for both alpha and beta electrons, while the orbital energies depend on the spin of the electron that occupies the orbital. The method is tested on the energy splitting between states of different spins in the CH 2, CF 2, CO, O 2, N 2+, and o-benzyne molecules. The results agree well with available experimental data; the deviations are within 4 kcal/mol in all cases considered.

  7. Leading SU(3)-breaking corrections to the baryon magnetic moments in chiral perturbation theory.

    PubMed

    Geng, L S; Camalich, J Martin; Alvarez-Ruso, L; Vacas, M J Vicente

    2008-11-28

    We calculate the baryon magnetic moments using covariant chiral perturbation theory (chiPT) within the extended-on-mass-shell renormalization scheme. By fitting the two available low-energy constants, we improve the Coleman-Glashow description of the data when we include the leading SU(3)-breaking effects coming from the lowest-order loops. This success is in dramatic contrast with previous attempts at the same order using heavy-baryon chiPT and covariant infrared chiPT. We also analyze the source of this improvement with particular attention to the comparison between the covariant results.

  8. Fourier Representation Methods for Møller-Plesset Perturbation Theory in One-Dimensionally Periodic Systems

    NASA Astrophysics Data System (ADS)

    Fripiat, J. G.; Delhalle, J.; Harris, Frank E.

    2007-12-01

    Ab initio studies of one-dimensionally periodic systems are advantageously carried out by methods that employ Fourier representations and the Ewald method for accelerating the lattice sums. This communication desribes the first investigation in which these techniques have been applied at the Mo/ller-Plesset level of perturbation theory, MBPT(2). Second-order corrections to the restricted Hartree-Fock energy and energy bands are reported for H2, Be, and LiH chains, and these results are compared to direct-space extended-system and oligomer computations. The methods described herein exhibit improved convergence relative to the other methods to which they are compared.

  9. The width of the Roper resonance in baryon chiral perturbation theory

    NASA Astrophysics Data System (ADS)

    Gegelia, Jambul; Meißner, Ulf-G.; Yao, De-Liang

    2016-09-01

    We calculate the width of the Roper resonance at next-to-leading order in a systematic expansion of baryon chiral perturbation theory with pions, nucleons, and the delta and Roper resonances as dynamical degrees of freedom. Three unknown low-energy constants contribute up to the given order. One of them can be fixed by reproducing the empirical value for the width of the Roper decay into a pion and a nucleon. Assuming that the remaining two couplings of the Roper interaction take values equal to those of the nucleon, the result for the width of the Roper decaying into a nucleon and two pions is consistent with the experimental value.

  10. Effective interaction in the Rayleigh–Schrödinger perturbation theory

    SciTech Connect

    Takayanagi, Kazuo

    2014-11-15

    We present a unified description of the effective interaction v in the Rayleigh–Schrödinger perturbation theory. First, we generalize the well-known bracketing expression for the energy shift ΔE in a one-dimensional model space to express the effective interaction v in a multi-dimensional model space. Second, we show that the generalized bracketing representation has a natural graphic expression in terms of folded diagrams. The present work thus gives a unified understanding of the effective interaction (i) in one- and multi-dimensional model spaces and (ii) in algebraic (bracketing) and graphic (folded diagram) representations.

  11. Even- and Odd-Parity Charmed Meson Masses in Heavy Hadron Chiral Perturbation Theory

    SciTech Connect

    Thomas Mehen; Roxanne Springer

    2005-03-01

    We derive mass formulae for the ground state, J{sup P} = 0{sup -} and 1{sup -}, and first excited even-parity, J{sup P} = 0{sup +} and 1{sup +}, charmed mesons including one loop chiral corrections and {Omicron}(1/m{sub c}) counterterms in heavy hadron chiral perturbation theory. We show a variety of fits to the current data. We find that certain parameter relations in the parity doubling model are not renormalized at one loop, providing a natural explanation for the equality of the hyperfine splittings of ground state and excited doublets.

  12. Towards the Right Hamiltonian for Singular Perturbations via Regularization and Extension Theory

    NASA Astrophysics Data System (ADS)

    Neidhardt, Hagen; Zagrebnov, Valentin

    For singular potentials in quantum mechanics it can happen that the Schrödinger operator is not esssentially self-adjoint on a natural domain, i.e., each self-adjoint extension is a candidate for the right physical Hamiltonian. Traditional way to single out this Hamiltonian is the removing cut-offs for regularizing potential. Connecting regularization and extension theory we develop an abstract operator method to treat the problem of the right Hamiltonian. We show that, using the notion of the maximal (with respect to the perturbation) Friedrichs extension of unperturbed operator, one can classify the above problem as wellposed or ill-posed depending on intersection of the quadratic form domain of perturbation and deficiency subspace corresponding to restriction of unperturbed operator to stability domain. If this intersection is trivial, then the right Hamiltonian is unique: it coincides with the form sum of perturbation and the Friedrich extension of the unperturbed operator restricted to the stability domain. Otherwise it is not unique: the family of “right Hamiltonians” can be described in terms of symmetric extensions reducing the ill-posed problem to the well-posed problem.

  13. Locally extracting scalar, vector and tensor modes in cosmological perturbation theory

    NASA Astrophysics Data System (ADS)

    Clarkson, Chris; Osano, Bob

    2011-11-01

    Cosmological perturbation theory relies on the decomposition of perturbations into so-called scalar, vector and tensor modes. This decomposition is non-local and depends on unknowable boundary conditions. The non-locality is particularly important at second and higher order because perturbative modes are sourced by products of lower order modes, which must be integrated over all space in order to isolate each mode. However, given a trace-free rank-2 tensor, a locally defined scalar mode may be trivially derived by taking two divergences, which knocks out the vector and tensor degrees of freedom. A similar local differential operation will return a pure vector mode. This means that scalar and vector degrees of freedom have local descriptions. The corresponding local extraction of the tensor mode is unknown however. We give it here. The operators we define are useful for defining gauge-invariant quantities at second order. We perform much of our analysis using an index-free ‘vector-calculus’ approach which makes manipulating tensor equations considerably simpler.

  14. Emergent “quantum” theory in complex adaptive systems

    NASA Astrophysics Data System (ADS)

    Minic, Djordje; Pajevic, Sinisa

    2016-03-01

    Motivated by the question of stability, in this paper we argue that an effective quantum-like theory can emerge in complex adaptive systems. In the concrete example of stochastic Lotka-Volterra dynamics, the relevant effective “Planck constant” associated with such emergent “quantum” theory has the dimensions of the square of the unit of time. Such an emergent quantum-like theory has inherently nonclassical stability as well as coherent properties that are not, in principle, endangered by thermal fluctuations and therefore might be of crucial importance in complex adaptive systems.

  15. The large coefficient problem; can we make sense out of QCD perturbation theory

    SciTech Connect

    West, G.B.

    1989-01-01

    There is the possibility of an impending crisis looming on the horizon for QCD. The problem is that in many processes, large coefficients arise in the perturbation series expansion leading to serious uncertainties concerning its predictive power. Until recently most of the examples of such a phenomenon occurred in the calculation of decay rates. These were, by and large, either ignored or dismissed using possible scheme-dependence arguments as a way out. However, more recently a calculation of the 3-loop contribution to the total e{sup +}e{sup -} annihilation cross-section was performed which gave an enormous coefficient of the order of 50 times that of the 2-loop term. If correct, this would imply that the 3-loop contribution actually exceeds that of the 2-loop Thus, from a conservative viewpoint, the validity of the perturbation series expansion as an estimate for the total e{sup +}e{sup -} cross-section is called into question. Since this process has played a key role in the development and understanding of QCD and since, in many ways, it is one of the cleanest methods for extracting {alpha}{sub s} the problem can no longer be avoided. Furthermore, there is no reason to doubt that this problem should occur in all physical processes. Coming to grips with it is, of course, not only important for testing QCD but also for extracting fundamental quantities such as {alpha}{sub s}. Clearly one needs to understand the nature and origin of such large coefficients before one can confidently continue to use perturbative estimates. The purpose of this talk is to focus on these problems. I shall first review the experimental situation with some examples illustrating the problem. I shall then discuss various general components and properties of perturbation theory before attempting to give a possible resolution of the problem. 18 refs., 5 figs.

  16. Photoreceptor perturbation around subretinal drusenoid deposits revealed by adaptive optics scanning laser ophthalmoscopy

    PubMed Central

    Zhang, Yuhua; Wang, Xiaolin; Rivero, Ernesto Blanco; Clark, Mark E; Witherspoon, Clark Douglas; Spaide, Richard F; Girkin, Christopher A.; Owsley, Cynthia; Curcio, Christine A.

    2014-01-01

    Purpose To describe the microscopic structure of photoreceptors impacted by subretinal drusenoid deposits, also called pseudodrusen, an extracellular lesion associated with age-related macular degeneration (AMD), using adaptive optics scanning laser ophthalmoscopy (AOSLO). Design Observational case series. Methods Fifty-three patients with AMD and 10 age-similar subjects in normal retinal health were recruited. All subjects underwent color fundus photography, infrared reflectance, red-free reflectance, autofluorescence, and spectral-domain optical coherence tomography (SD-OCT). Subretinal drusenoid deposits were classified with a 3-stage OCT-based grading system. Lesions and surrounding photoreceptors were examined with AOSLO. Results Subretinal drusenoid deposits were found in 26 eyes of 13 patients with AMD and imaged by AOSLO and SD-OCT in 18 eyes (n=342 lesions). SD-OCT showed subretinal drusenoid deposits as highly reflective material accumulated internal to the retinal pigment epithelium. AOSLO revealed that photoreceptor reflectivity was qualitatively reduced by stage 1 subretinal drusenoid deposits and greatly reduced by stage 2. AOSLO presented a distinct structure in stage 3, a hyporeflective annulus consisting of deflected, degenerated or absent photoreceptors. A central core with a reflectivity superficially resembling photoreceptors is formed by the lesion material itself. A hyporeflective gap in the photoreceptor ellipsoid zone on either side of this core shown in SD-OCT corresponded to the hyporeflective annulus seen by AOSLO. Conclusions AOSLO and multimodal imaging of subretinal drusenoid deposits indicate solid, space filling lesions in the subretinal space. Associated retinal reflectivity changes are related to lesion stages and are consistent with perturbations to photoreceptors, as suggested by histology. PMID:24907433

  17. Evidence for Cascades of Perturbation and Adaptation in the Metabolic Genes of Higher Termite Gut Symbionts

    PubMed Central

    Zhang, Xinning; Leadbetter, Jared R.

    2012-01-01

    ABSTRACT Termites and their gut microbes engage in fascinating dietary mutualisms. Less is known about how these complex symbioses have evolved after first emerging in an insect ancestor over 120 million years ago. Here we examined a bacterial gene, formate dehydrogenase (fdhF), that is key to the mutualism in 8 species of “higher” termite (members of the Termitidae, the youngest and most biomass-abundant and species-rich termite family). Patterns of fdhF diversity in the gut communities of higher termites contrasted strongly with patterns in less-derived (more-primitive) insect relatives (wood-feeding “lower” termites and roaches). We observed phylogenetic evidence for (i) the sweeping loss of several clades of fdhF that may reflect extinctions of symbiotic protozoa and, importantly, bacteria dependent on them in the last common ancestor of all higher termites and (ii) a radiation of genes from the (possibly) single allele that survived. Sweeping gene loss also resulted in (iii) the elimination of an entire clade of genes encoding selenium (Se)-independent enzymes from higher termite gut communities, perhaps reflecting behavioral or morphological innovations in higher termites that relaxed preexisting environmental limitations of Se, a dietary trace element. Curiously, several higher termite gut communities may have subsequently reencountered Se limitation, reinventing genes for Se-independent proteins via convergent evolution. Lastly, the presence of a novel fdhF lineage within litter-feeding and subterranean higher (but not other) termites may indicate recent gene “invasion” events. These results imply that cascades of perturbation and adaptation by distinct evolutionary mechanisms have impacted the evolution of complex microbial communities in a highly successful lineage of insects. PMID:22911968

  18. New predictions for generalized spin polarizabilities from heavy baryon chiral perturbation theory

    SciTech Connect

    Chung-Wen Kao; Barbara Pasquini; Marc Vanderhaeghen

    2004-08-01

    We extract the next-to-next-to-leading order results for spin-flip generalized polarizabilities (GPs) of the nucleon from the spin-dependent amplitudes for virtual Compton scattering (VCS) at {Omicron}(p{sup 4}) in heavy baryon chiral perturbation theory. At this order, no unknown low energy constants enter the theory, allowing us to make absolute predictions for all spin-flip GPs. Furthermore, by using constraint equations between the GPs due to nucleon crossing combined with charge conjugation symmetry of the VCS amplitudes, we get a next-to-next-to-next-to-leading order prediction for one of the GPs. We provide estimates for forthcoming double polarization experiments which allow to access these spin-flip GPs of the nucleon.

  19. New predictions for generalized spin polarizabilities from heavy baryon chiral perturbation theory

    SciTech Connect

    Kao, C.-W.; Pasquini, Barbara; Vanderhaeghen, Marc

    2004-12-01

    We extract the next-to-next-to-leading order results for spin-flip generalized polarizabilities (GPs) of the nucleon from the spin-dependent amplitudes for virtual Compton scattering at O(p{sup 4}) in heavy baryon chiral perturbation theory. At this order, no unknown low-energy constants enter the theory, allowing us to make absolute predictions for all spin-flip GPs. Furthermore, by using constraint equations between the GPs due to nucleon crossing combined with charge conjugation symmetry of the virtual Compton scattering amplitudes, we get a next-to-next-to-next-to-leading order prediction for one of the GPs. We provide estimates for forthcoming double-polarization experiments which allow one to access these spin-flip GPs of the nucleon.

  20. Shielded attractive shell model again: resummed thermodynamic perturbation theory for central force potential

    NASA Astrophysics Data System (ADS)

    Reščič, J.; Kalyuzhnyi, Y. V.; Cummings, P. T.

    2016-10-01

    The approach developed earlier to describe the dimerizing shielded attractive shell (SAS) primitive model of chemical association due to Cummings and Stell is generalized and extended to include a description of a polymerizing SAS model. Our extension is based on the combination of the resummed thermodynamic perturbation theory for central force (RTPT-CF) associating potential and self consistent scheme, which takes into account the changes in the system free volume due to association. Theoretical results for thermodynamical properties of the model at different bonding length, density and temperature are compared against newly generated computer simulation results. The theory gives very accurate predictions for the model with bonding length L * from the range 0  <  L *  <  0.6 at all values of the density and temperature studied, including the limit of infinitely large temperature.

  1. Electronic excitations of bulk LiCl from many-body perturbation theory

    SciTech Connect

    Jiang, Yun-Feng; Wang, Neng-Ping; Rohlfing, Michael

    2013-12-07

    We present the quasiparticle band structure and the optical excitation spectrum of bulk LiCl, using many-body perturbation theory. Density-functional theory is used to calculate the ground-state geometry of the system. The quasiparticle band structure is calculated within the GW approximation. Taking the electron-hole interaction into consideration, electron-hole pair states and optical excitations are obtained by solving the Bethe-Salpeter equation for the electron-hole two-particle Green function. The calculated band gap is 9.5 eV, which is in good agreement with the experimental result of 9.4 eV. And the calculated optical absorption spectrum, which contains an exciton peak at 8.8 eV and a resonant-exciton peak at 9.8 eV, is also in good agreement with experimental data.

  2. Application of schwinger perturbation theory in electron diffraction analysis. Part I. Linear XY 2 type molecules

    NASA Astrophysics Data System (ADS)

    Ermakov, K. V.; Butayev, B. S.; Spiridonov, V. P.

    1989-06-01

    The analysis of molecules by electron diffraction in terms of the intramolecular potential function is presented. The method is based on the coordinate distribution function obtained using Schwinger operator perturbation theory wit the effective harmonic oscillator as an initial approximation. The primary advantage of the approach is that it circumvents problems involving resonance denominators. Analytical formulae for the coordinate distribution function are developed for linear XY 2 molecules with due account being taken for vibration-rotation coupling. A test of the performance of the theory devised is given by calculating various moments and comparing the results with those of the variational treatment of Hilderbrandt and Kohl. The scheme of diffraction analysis, which provides suitable facility for incorporating spectroscopic frequences, is proposed and checked by treatment of the intensity data for CO 2.

  3. High-order terms in the renormalized perturbation theory for the Anderson impurity model

    NASA Astrophysics Data System (ADS)

    Pandis, Vassilis; Hewson, Alex C.

    2015-09-01

    We study the renormalized perturbation theory of the single-impurity Anderson model, particularly the high-order terms in the expansion of the self-energy in powers of the renormalized coupling U ˜. Though the presence of counterterms in the renormalized theory may appear to complicate the diagrammatics, we show how these can be seamlessly accommodated by carrying out the calculation order-by-order in terms of skeleton diagrams. We describe how the diagrams pertinent to the renormalized self-energy and four vertex can be automatically generated, translated into integrals, and numerically integrated. To maximize the efficiency of our approach we introduce a generalized k -particle/hole propagator, which is used to analytically simplify the resultant integrals and reduce the dimensionality of the integration. We present results for the self-energy and spectral density to fifth order in U ˜, for various values of the model asymmetry, and compare them to a numerical renormalization group calculation.

  4. The ionization potential of aqueous hydroxide computed using many-body perturbation theory

    SciTech Connect

    Opalka, Daniel Sprik, Michiel; Pham, Tuan Anh; Galli, Giulia

    2014-07-21

    The ionization potentials of electrolyte solutions provide important information about the electronic structure of liquids and solute-solvent interactions. We analyzed the positions of solute and solvent bands of aqueous hydroxide and the influence of the solvent environment on the ionization potential of hydroxide ions. We used the concept of a computational hydrogen electrode to define absolute band positions with respect to vacuum. We found that many-body perturbation theory in the G{sub 0} W{sub 0} approximation substantially improves the relative and absolute positions of the band edges of solute and solvent with respect to those obtained within Density Functional Theory, using semi-local functionals, yielding results in satisfactory agreement with recent experiments.

  5. Matching Pion-Nucleon Roy-Steiner Equations to Chiral Perturbation Theory.

    PubMed

    Hoferichter, Martin; Ruiz de Elvira, Jacobo; Kubis, Bastian; Meissner, Ulf-G

    2015-11-01

    We match the results for the subthreshold parameters of pion-nucleon scattering obtained from a solution of Roy-Steiner equations to chiral perturbation theory up to next-to-next-to-next-to-leading order, to extract the pertinent low-energy constants including a comprehensive analysis of systematic uncertainties and correlations. We study the convergence of the chiral series by investigating the chiral expansion of threshold parameters up to the same order and discuss the role of the Δ(1232) resonance in this context. Results for the low-energy constants are also presented in the counting scheme usually applied in chiral nuclear effective field theory, where they serve as crucial input to determine the long-range part of the nucleon-nucleon potential as well as three-nucleon forces. PMID:26588373

  6. An adaptive computation mesh for the solution of singular perturbation problems

    NASA Technical Reports Server (NTRS)

    Brackbill, J. U.; Saltzman, J.

    1980-01-01

    In singular perturbation problems, control of zone size variation can affect the effort required to obtain accurate, numerical solutions of finite difference equations. The mesh is generated by the solution of potential equations. Numerical results for a singular perturbation problem in two dimensions are presented. The mesh was used in calculations of resistive magnetohydrodynamic flow in two dimensions.

  7. Renormalized second-oder perturbation theory for the electron correlation energy: concepts and benchmarks

    NASA Astrophysics Data System (ADS)

    Rinke, Patrick; Ren, Xinguo; Scheffler, Matthias; Scuseria, Gustavo

    2012-02-01

    We present a renormalized second-oder perturbation theory (R2PT) for the electron correlation energy that combines the random-phase approximation (RPA), second-order screened exchange (SOSEX) [1], and renormalized single excitations (rSE) [2]. These three terms all involve a summation of certain types of diagrams to infinite order, and can be viewed as a ``renormalization" of the direct, the exchange and the single excitation (SE) term of 2nd-order Rayleigh-Schr"ordinger perturbation theory based on an (approximate) Kohn-Sham reference state. A preliminary version of R2PT has been benchmarked for covalently-bonded molecular systems and chemical reaction barrier heights [3] and shows an overall well balanced performance. We have extended this, by including ``off-diagonal'' diagrams into the rSE term and expect this refined version of R2PT to be more generally applicable to electronic systems of different bonding characteristics. Extended benchmarks of van-der-Waals-bonded molecules and crystalline solids will be presented. [1] A. Gr"uneis et al., J. Chem. Phys. 131, 154115 (2009). [2] X. Ren et al., Phys. Rev. Lett. 106, 153003 (2011). [3] J. Paier et al., arXiv:cond-mat/1111.0173.

  8. A study of relative velocity statistics in Lagrangian perturbation theory with PINOCCHIO

    NASA Astrophysics Data System (ADS)

    Heisenberg, Lavinia; Schäfer, Björn Malte; Bartelmann, Matthias

    2011-10-01

    Subject of this paper is a detailed analysis of the PINpointing Orbit-Crossing Collapsed HIerarchical Object (PINOCCHIO) algorithm for studying the relative velocity statistics of merging haloes in Lagrangian perturbation theory. Given a cosmological background model, a power spectrum of fluctuations as well as a Gaussian linear density contrast field δl is generated on a cubic grid, which is then smoothed repeatedly with Gaussian filters. For each Lagrangian particle at position q and each smoothing radius R, the collapse time, the velocities and ellipsoidal truncation are computed using Lagrangian perturbation theory. The collapsed medium is then fragmented into isolated objects by an algorithm designed to mimic the accretion and merger events of hierarchical collapse. Directly after the fragmentation process the mass function, merger histories of haloes and the statistics of the relative velocities at merging are evaluated. We reimplemented the algorithm in C++, recovered the mass function and optimized the construction of halo merging histories. When compared with the output of the Millennium Simulation our results suggest that the PINOCCHIO is well suited for studying relative velocities of merging haloes and is able to reproduce the pairwise velocity distribution.

  9. Third-order many-body perturbation theory calculations for the beryllium and magnesium isoelectronic sequences

    NASA Astrophysics Data System (ADS)

    Ho, H. C.; Johnson, W. R.; Blundell, S. A.; Safronova, M. S.

    2006-08-01

    Third-order relativistic many-body perturbation theory (MBPT) is applied to obtain energies of ions with two valence electrons in the no virtual-pair approximation (NVPA). A total of 302 third-order Goldstone diagrams are organized into 12 one-body and 23 two-body terms. Only third-order two-body terms and diagrams are presented in this paper, owing to the fact that the one-body terms are identical to the previously studied third-order terms in monovalent ions. Dominant classes of diagrams are identified. The model potential is the Dirac-Hartree-Fock potential VN-2 , and B -spline basis functions in a cavity of finite radius are employed in the numerical calculations. The Breit interaction is taken into account through the second order of perturbation theory, and the lowest-order Lamb shift is also evaluated. Sample calculations are performed for berylliumlike ions with Z=4-7 , and for the magnesiumlike ion PIV . The third-order excitation energies are in excellent agreement with measurement with an accuracy at 0.2% level for the cases considered. Comparisons are made with second-order MBPT results, and with other calculations. The third-order energy correction is shown to be significant, improving the previous second-order calculations by an order of magnitude.

  10. Electromagnetic structure of the lowest-lying decuplet resonances in covariant chiral perturbation theory

    SciTech Connect

    Geng, L. S.; Camalich, J. Martin; Vacas, M. J. Vicente

    2009-08-01

    We present a calculation of the leading SU(3)-breaking O(p{sup 3}) corrections to the electromagnetic moments and charge radius of the lowest-lying decuplet resonances in covariant chiral perturbation theory. In particular, the magnetic dipole moment of the members of the decuplet is predicted fixing the only low-energy constant (LEC) present up to this order with the well-measured magnetic dipole moment of the {omega}{sup -}. We predict {mu}{sub {delta}}{sup ++}=6.04(13) and {mu}{sub {delta}}{sup +}=2.84(2), which agree well with the current experimental information. For the electric quadrupole moment and the charge radius, we use state-of-the-art lattice QCD results to determine the corresponding LECs, whereas for the magnetic octupole moment there is no unknown LEC up to the order considered here, and we obtain a pure prediction. We compare our results with those reported in large N{sub c}, lattice QCD, heavy-baryon chiral perturbation theory, and other models.

  11. Non-perturbative calculation of molecular magnetic properties within current-density functional theory

    SciTech Connect

    Tellgren, E. I. Lange, K. K.; Ekström, U.; Helgaker, T.; Teale, A. M.; Furness, J. W.

    2014-01-21

    We present a novel implementation of Kohn–Sham density-functional theory utilizing London atomic orbitals as basis functions. External magnetic fields are treated non-perturbatively, which enable the study of both magnetic response properties and the effects of strong fields, using either standard density functionals or current-density functionals—the implementation is the first fully self-consistent implementation of the latter for molecules. Pilot applications are presented for the finite-field calculation of molecular magnetizabilities, hypermagnetizabilities, and nuclear magnetic resonance shielding constants, focusing on the impact of current-density functionals on the accuracy of the results. Existing current-density functionals based on the gauge-invariant vorticity are tested and found to be sensitive to numerical details of their implementation. Furthermore, when appropriately regularized, the resulting magnetic properties show no improvement over standard density-functional results. An advantage of the present implementation is the ability to apply density-functional theory to molecules in very strong magnetic fields, where the perturbative approach breaks down. Comparison with high accuracy full-configuration-interaction results show that the inadequacies of current-density approximations are exacerbated with increasing magnetic field strength. Standard density-functionals remain well behaved but fail to deliver high accuracy. The need for improved current-dependent density-functionals, and how they may be tested using the presented implementation, is discussed in light of our findings.

  12. Solubilities of Solutes in Ionic Liquids from a SimplePerturbed-Hard-Sphere Theory

    SciTech Connect

    Qin, Yuan; Prausnitz, John M.

    2005-09-20

    In recent years, several publications have provided solubilities of ordinary gases and liquids in ionic liquids. This work reports an initial attempt to correlate the experimental data using a perturbed-hard-sphere theory; the perturbation is based on well-known molecular physics when the solution is considered as a dielectric continuum. For this correlation, the most important input parameters are hard-sphere diameters of the solute and of the cation and anion that constitute the ionic liquid. In addition, the correlation uses the solvent density and the solute's polarizability and dipole and quadrupole moments, if any. Dispersion-energy parameters are obtained from global correlation of solubility data. Results are given for twenty solutes in several ionic liquids at normal temperatures; in addition, some results are given for gases in two molten salts at very high temperatures. Because the theory used here is much simplified, and because experimental uncertainties (especially for gaseous solutes) are often large, the accuracy of the correlation presented here is not high; in general, predicted solubilities (Henry's constants) agree with experiment to within roughly {+-} 70%. As more reliable experimental data become available, modifications in the characterizing parameters are likely to improve accuracy. Nevertheless, even in its present form, the correlation may be useful for solvent screening in engineering design.

  13. van der Waals forces in density functional theory: Perturbational long-range electron-interaction corrections

    SciTech Connect

    Angyan, Janos G.; Gerber, Iann C.; Savin, Andreas; Toulouse, Julien

    2005-07-15

    Long-range exchange and correlation effects, responsible for the failure of currently used approximate density functionals in describing van der Waals forces, are taken into account explicitly after a separation of the electron-electron interaction in the Hamiltonian into short- and long-range components. We propose a 'range-separated hybrid' functional based on a local density approximation for the short-range exchange-correlation energy, combined with a long-range exact exchange energy. Long-range correlation effects are added by a second-order perturbational treatment. The resulting scheme is general and is particularly well adapted to describe van der Waals complexes, such as rare gas dimers.

  14. Expression proteomics identifies biochemical adaptations and defense responses in transgenic plants with perturbed polyamine metabolism.

    PubMed

    Franceschetti, Marina; Perry, Barry; Thompson, Benjamin; Hanfrey, Colin; Michael, Anthony J

    2004-10-22

    Soluble proteins from leaves of transgenic tobacco plants with perturbed polyamine metabolism, caused by S-adenosylmethionine decarboxylase overexpression, were analysed by comparative proteomics. A group of proteins was found to be increasingly repressed, in parallel with the degree of polyamine perturbation, in each of the three independent transgenic lines. These were identified as isoforms of chloroplast ribonucleoproteins, known to be involved in chloroplast mRNA stability, processing and translation. Another group of eight proteins strongly induced in the most metabolically perturbed line was identified as multiple, uncharacterised isoforms of the defense protein PR-1, a known marker for systemic acquired resistance.

  15. An integral-factorized implementation of the driven similarity renormalization group second-order multireference perturbation theory.

    PubMed

    Hannon, Kevin P; Li, Chenyang; Evangelista, Francesco A

    2016-05-28

    We report an efficient implementation of a second-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT2) [C. Li and F. A. Evangelista, J. Chem. Theory Comput. 11, 2097 (2015)]. Our implementation employs factorized two-electron integrals to avoid storage of large four-index intermediates. It also exploits the block structure of the reference density matrices to reduce the computational cost to that of second-order Møller-Plesset perturbation theory. Our new DSRG-MRPT2 implementation is benchmarked on ten naphthyne isomers using basis sets up to quintuple-ζ quality. We find that the singlet-triplet splittings (ΔST) of the naphthyne isomers strongly depend on the equilibrium structures. For a consistent set of geometries, the ΔST values predicted by the DSRG-MRPT2 are in good agreements with those computed by the reduced multireference coupled cluster theory with singles, doubles, and perturbative triples.

  16. Thermodynamic perturbation theory for self-assembling mixtures of divalent single patch colloids.

    PubMed

    Marshall, Bennett D; Chapman, Walter G

    2014-07-28

    In this work we extend Wertheim's thermodynamic perturbation theory (TPT) to binary mixtures (species A and species B) of patchy colloids were each species has a single patch which can bond a maximum of twice (divalent). Colloids are treated as hard spheres with a directional conical association site. We restrict the system such that only patches between unlike species share attractions; meaning there are AB attractions but no AA or BB attractions. The theory is derived in Wertheim's two density formalism for one site associating fluids. Since the patches are doubly bondable, associated chains, of all chain lengths, as well as 4-mer rings consisting of two species A and two species B colloids are accounted for. With the restriction of only AB attractions, triatomic rings of doubly bonded colloids, which dominate in the corresponding pure component case, cannot form. The theory is shown to be in good agreement with Monte Carlo simulation data for the structure and thermodynamics of these patchy colloid mixtures as a function of temperature, density, patch size and composition. It is shown that 4-mer rings dominate at low temperature, inhibiting the polymerization of the mixture into long chains. Mixtures of this type have been recently synthesized by researchers. This work provides the first theory capable of accurately modeling these mixtures.

  17. A hybrid perturbed-chain SAFT density functional theory for representing fluid behavior in nanopores: Mixtures

    NASA Astrophysics Data System (ADS)

    Shen, Gulou; Ji, Xiaoyan; Öberg, Sven; Lu, Xiaohua

    2013-11-01

    The perturbed-chain statistical associating fluid theory (PC-SAFT) density functional theory developed in our previous work was extended to the description of inhomogeneous confined behavior in nanopores for mixtures. In the developed model, the modified fundamental measure theory and the weighted density approximation were used to represent the hard-sphere and dispersion free energy functionals, respectively, and the chain free energy functional from interfacial statistical associating fluid theory was used to account for the chain connectivity. The developed model was verified by comparing the model prediction with molecular simulation results, and the agreement reveals the reliability of the proposed model in representing the confined behaviors of chain mixtures in nanopores. The developed model was further used to predict the adsorption of methane-carbon dioxide mixtures on activated carbons, in which the parameters of methane and carbon dioxide were taken from the bulk PC-SAFT and those for solid surface were determined from the fitting to the pure-gas adsorption isotherms measured experimentally. The comparison of the model prediction with the available experimental data of mixed-gas adsorption isotherms shows that the model can reliably reproduce the confined behaviors of physically existing mixtures in nanopores.

  18. A hybrid perturbed-chain SAFT density functional theory for representing fluid behavior in nanopores

    NASA Astrophysics Data System (ADS)

    Shen, Gulou; Ji, Xiaoyan; Lu, Xiaohua

    2013-06-01

    A hybrid statistical mechanical model, which is fully consistent with the bulk perturbed-chain statistical associating fluid theory (PC-SAFT) in describing properties of fluids, was developed by coupling density functional theory with PC-SAFT for the description of the inhomogeneous behavior of real chain molecules in nanopores. In the developed model, the modified fundamental measure theory was used for the hard sphere contribution; the dispersion free energy functional was represented with weighted density approximation by averaging the density in the range of interaction, and the chain free energy functional from interfacial statistical associating fluid theory was used to account for the chain connectivity. Molecular simulation results of the density profile were compared with model prediction, and the considerable agreement reveals the reliability of the proposed model in representing the confined behaviors of chain molecules in an attractive slit. The developed model was further used to represent the adsorptions of methane and carbon dioxide on activated carbons, in which methane and carbon dioxide were modeled as chain molecules with the parameters taken from the bulk PC-SAFT, while the parameters of solid surface were obtained from the fitting of gas adsorption isotherms measured experimentally. The results show that the model can reliably reproduce the confined behaviors of physically existing substances in nanopores.

  19. Nonlinear adaptive networks: A little theory, a few applications

    SciTech Connect

    Jones, R.D.; Qian, S.; Barnes, C.W.; Bisset, K.R.; Bruce, G.M.; Lee, K.; Lee, L.A.; Mead, W.C.; O'Rourke, M.K.; Thode, L.E. ); Lee, Y.C.; Flake, G.W. Maryland Univ., College Park, MD ); Poli, I.J. Bologna Univ. )

    1990-01-01

    We present the theory of nonlinear adaptive networks and discuss a few applications. In particular, we review the theory of feedforward backpropagation networks. We than present the theory of the Connectionist Normalized Linear Spline network in both its feedforward and iterated modes. Also, we briefly discuss the theory of stochastic cellular automata. We then discuss applications to chaotic time series tidal prediction in Venice Lagoon, sonar transient detection, control of nonlinear processes, balancing a double inverted pendulum and design advice for free electron lasers. 26 refs., 23 figs.

  20. Orbital theory in terms of KS elements with luni-solar perturbations

    NASA Astrophysics Data System (ADS)

    Sellamuthu, Harishkumar; Sharma, Ram

    2016-07-01

    Precise orbit computation of Earth orbiting satellites is essential for efficient mission planning of planetary exploration, navigation and satellite geodesy. The third-body perturbations of the Sun and the Moon predominantly affect the satellite motion in the high altitude and elliptical orbits, where the effect of atmospheric drag is negligible. The physics of the luni-solar gravity effect on Earth satellites have been studied extensively over the years. The combined luni-solar gravitational attraction will induce a cumulative effect on the dynamics of satellite orbits, which mainly oscillates the perigee altitude. Though accurate orbital parameters are computed by numerical integration with respect to complex force models, analytical theories are highly valued for the manifold of solutions restricted to relatively simple force models. During close approach, the classical equations of motion in celestial mechanics are almost singular and they are unstable for long-term orbit propagation. A new singularity-free analytical theory in terms of KS (Kustaanheimo and Stiefel) regular elements with respect to luni-solar perturbation is developed. These equations are regular everywhere and eccentric anomaly is the independent variable. Plataforma Solar de Almería (PSA) algorithm and a Fourier series algorithm are used to compute the accurate positions of the Sun and the Moon, respectively. Numerical studies are carried out for wide range of initial parameters and the analytical solutions are found to be satisfactory when compared with numerically integrated values. The symmetrical nature of the equations allows only two of the nine equations to be solved for computing the state vectors and the time. Only a change in the initial conditions is required to solve the other equations. This theory will find multiple applications including on-board software packages and for mission analysis purposes.

  1. Nonlinear perturbation theory with halo bias and redshift-space distortions via the Lagrangian picture

    NASA Astrophysics Data System (ADS)

    Matsubara, Takahiko

    2008-10-01

    The nonlinear perturbation theory of gravitational instability is extended to include effects of both biasing and redshift-space distortions, which are inevitable in predicting observable quantities in galaxy surveys. Weakly nonlinear effects in galaxy clustering on large scales recently attracted great interest, since the precise determination of scales of baryon acoustic oscillations is crucial to investigate the nature of dark energy by galaxy surveys. We find that a local Lagrangian bias and redshift-space distortions are naturally incorporated in our formalism of perturbation theory with a resummation technique via the Lagrangian picture. Our formalism is applicable to any biasing scheme which is local in Lagrangian space, including the halo bias as a special case. Weakly nonlinear effects on halo clustering in redshift space are analytically given. We assume only a fundamental idea of the halo model: haloes form according to the extended Press-Schechter theory, and the spatial distributions are locally biased in Lagrangian space. There is no need for assuming the spherical collapse model to follow the dynamical evolution, which is additionally assumed in standard halo prescriptions. One-loop corrections to the power spectrum and correlation function of haloes in redshift space are explicitly derived and presented. Instead of relying on expensive numerical simulations, our approach provides an analytic way of investigating the weakly nonlinear effects, simultaneously including the nonlinear biasing and nonlinear redshift-space distortions. Nonlinearity introduces a weak scale dependence in the halo bias. The scale dependence is a smooth function in Fourier space, and the bias does not critically change the feature of baryon acoustic oscillations in the power spectrum. The same feature in the correlation function is less affected by nonlinear effects of biasing.

  2. Three dimensional hydrodynamic calculations with adaptive mesh refinement of the evolution of Rayleigh Taylor and Richtmyer Meshkov instabilities in converging geometry: Multi-mode perturbations

    SciTech Connect

    Klein, R.I. |; Bell, J.; Pember, R.; Kelleher, T.

    1993-04-01

    The authors present results for high resolution hydrodynamic calculations of the growth and development of instabilities in shock driven imploding spherical geometries in both 2D and 3D. They solve the Eulerian equations of hydrodynamics with a high order Godunov approach using local adaptive mesh refinement to study the temporal and spatial development of the turbulent mixing layer resulting from both Richtmyer Meshkov and Rayleigh Taylor instabilities. The use of a high resolution Eulerian discretization with adaptive mesh refinement permits them to study the detailed three-dimensional growth of multi-mode perturbations far into the non-linear regime for converging geometries. They discuss convergence properties of the simulations by calculating global properties of the flow. They discuss the time evolution of the turbulent mixing layer and compare its development to a simple theory for a turbulent mix model in spherical geometry based on Plesset`s equation. Their 3D calculations show that the constant found in the planar incompressible experiments of Read and Young`s may not be universal for converging compressible flow. They show the 3D time trace of transitional onset to a mixing state using the temporal evolution of volume rendered imaging. Their preliminary results suggest that the turbulent mixing layer loses memory of its initial perturbations for classical Richtmyer Meshkov and Rayleigh Taylor instabilities in spherically imploding shells. They discuss the time evolution of mixed volume fraction and the role of vorticity in converging 3D flows in enhancing the growth of a turbulent mixing layer.

  3. Towards a general theory of adaptive walks on rugged landscapes.

    PubMed

    Kauffman, S; Levin, S

    1987-09-01

    Adaptive evolution, to a large extent, is a complex combinatorial optimization process. In this article we take beginning steps towards developing a general theory of adaptive "walks" via fitter variants in such optimization processes. We introduce the basic idea of a space of entities, each a 1-mutant neighbor of many other entities in the space, and the idea of a fitness ascribed to each entity. Adaptive walks proceed from an initial entity, via fitter neighbors, to locally or globally optimal entities that are fitter than their neighbors. We develop a general theory for the number of local optima, lengths of adaptive walks, and the number of alternative local optima accessible from any given initial entity, for the baseline case of an uncorrelated fitness landscape. Most fitness landscapes are correlated, however. Therefore we develop parts of a universal theory of adaptation on correlated landscapes by adaptive processes that have sufficient numbers of mutations per individual to "jump beyond" the correlation lengths in the underlying landscape. In addition, we explore the statistical character of adaptive walks in two independent complex combinatorial optimization problems, that of evolving a specific cell type in model genetic networks, and that of finding good solutions to the traveling salesman problem. Surprisingly, both show similar statistical features, encouraging the hope that a general theory for adaptive walks on correlated and uncorrelated landscapes can be found. In the final section we explore two limits to the efficacy of selection. The first is new, and surprising: for a wide class of systems, as the complexity of the entities under selection increases, the local optima that are attainable fall progressively closer to the mean properties of the underlying space of entities. This may imply that complex biological systems, such as genetic regulatory systems, are "close" to the mean properties of the ensemble of genomic regulatory systems explored

  4. A Investigation of the Hamiltonian Theory of Perturbed and Coupled Gradient-Index Fibers.

    NASA Astrophysics Data System (ADS)

    Saad, Said Muawad Sayed

    The formal analogy between classical mechanics with geometrical optics on the one hand and quantum mechanics with wave optics on the other hand provides an elegant approach to the study of propagation in gradient-index fibers. This analogy is developed in connection with a review of propagation in a single square-law (slab) fiber. The application of the operator formalism is illustrated and quantum coherent-states identified with optical beam-modes. Since a perfect square-law variation of the fiber index is evidently not attainable, it is necessary to discuss propagation in perturbed fibers. Two cases are considered. First, index variations specified by a power series including higher powers than the second are studied employing conventional (time independent) perturbation theory. Second, index variations specified by an exponent which differs from two by a small quantity were studied. A new perturbation approach based on beam-mode propagation is developed for this case. The need to examine propagation in coupled fibers appears in connection with a number of applications: crosstalk, beam-oscillation suppression, and multimode lidar antennas. An approximate coupled-mode technique is applied to this problem. It is known that due to imperfections even initially axial beams launched in gradient index fibers gradually drift into an oscillatory trajectory about the beam axis and that these oscillations, if not positively suppressed would statistically continue to increase. On the strength of very general geometric optical considerations based on Liouville's theorem (mechanics) it was accepted that no passive optical component could function as an oscillation suppressor. Recently it was shown that, by providing a new degree of freedom, a second fiber appropriately coupled to the first could act to suppress beam oscillations with small net loss. This mechanism is examined in detail and several models of coupled slab-fibers are considered. The same configuration of coupled

  5. Enzymatic Kinetic Isotope Effects from Path-Integral Free Energy Perturbation Theory.

    PubMed

    Gao, J

    2016-01-01

    Path-integral free energy perturbation (PI-FEP) theory is presented to directly determine the ratio of quantum mechanical partition functions of different isotopologs in a single simulation. Furthermore, a double averaging strategy is used to carry out the practical simulation, separating the quantum mechanical path integral exactly into two separate calculations, one corresponding to a classical molecular dynamics simulation of the centroid coordinates, and another involving free-particle path-integral sampling over the classical, centroid positions. An integrated centroid path-integral free energy perturbation and umbrella sampling (PI-FEP/UM, or simply, PI-FEP) method along with bisection sampling was summarized, which provides an accurate and fast convergent method for computing kinetic isotope effects for chemical reactions in solution and in enzymes. The PI-FEP method is illustrated by a number of applications, to highlight the computational precision and accuracy, the rule of geometrical mean in kinetic isotope effects, enhanced nuclear quantum effects in enzyme catalysis, and protein dynamics on temperature dependence of kinetic isotope effects.

  6. Hartree-Fock many-body perturbation theory for nuclear ground-states

    NASA Astrophysics Data System (ADS)

    Tichai, Alexander; Langhammer, Joachim; Binder, Sven; Roth, Robert

    2016-05-01

    We investigate the order-by-order convergence behavior of many-body perturbation theory (MBPT) as a simple and efficient tool to approximate the ground-state energy of closed-shell nuclei. To address the convergence properties directly, we explore perturbative corrections up to 30th order and highlight the role of the partitioning for convergence. The use of a simple Hartree-Fock solution for the unperturbed basis leads to a convergent MBPT series for soft interactions, in contrast to the divergent MBPT series obtained with a harmonic oscillator basis. For larger model spaces and heavier nuclei, where a direct high-order MBPT calculation is not feasible, we perform third-order calculations and compare to advanced ab initio coupled-cluster results for the same interactions and model spaces. We demonstrate that third-order MBPT provides ground-state energies for nuclei up into the tin isotopic chain in excellent agreement with the best available coupled-cluster calculations at a fraction of the computational cost.

  7. Heat capacity changes in RNA folding: application of perturbation theory to hammerhead ribozyme cold denaturation

    PubMed Central

    Mikulecky, Peter J.; Feig, Andrew L.

    2004-01-01

    In proteins, empirical correlations have shown that changes in heat capacity (ΔCP) scale linearly with the hydrophobic surface area buried upon folding. The influence of ΔCP on RNA folding has been widely overlooked and is poorly understood. In addition to considerations of solvent reorganization, electrostatic effects might contribute to ΔCPs of folding in polyanionic species such as RNAs. Here, we employ a perturbation method based on electrostatic theory to probe the hot and cold denaturation behavior of the hammerhead ribozyme. This treatment avoids much of the error associated with imposing two-state folding models on non-two-state systems. Ribozyme stability is perturbed across a matrix of solvent conditions by varying the concentration of NaCl and methanol co-solvent. Temperature-dependent unfolding is then monitored by circular dichroism spectroscopy. The resulting array of unfolding transitions can be used to calculate a ΔCP of folding that accurately predicts the observed cold denaturation temperature. We confirm the accuracy of the calculated ΔCP by using isothermal titration calorimetry, and also demonstrate a methanol-dependence of the ΔCP. We weigh the strengths and limitations of this method for determining ΔCP values. Finally, we discuss the data in light of the physical origins of the ΔCPs for RNA folding and consider their impact on biological function. PMID:15282329

  8. Entanglement entropy of excited states in conformal perturbation theory and the Einstein equation

    NASA Astrophysics Data System (ADS)

    Speranza, Antony J.

    2016-04-01

    For a conformal field theory (CFT) deformed by a relevant operator, the entanglement entropy of a ball-shaped region may be computed as a perturbative expansion in the coupling. A similar perturbative expansion exists for excited states near the vacuum. Using these expansions, this work investigates the behavior of excited state entanglement entropies of small, ball-shaped regions. The motivation for these calculations is Jacobson's recent work on the equivalence of the Einstein equation and the hypothesis of maximal vacuum entropy [arXiv:1505.04753], which relies on a conjecture stating that the behavior of these entropies is sufficiently similar to a CFT. In addition to the expected type of terms which scale with the ball radius as R d , the entanglement entropy calculation gives rise to terms scaling as R 2Δ, where Δ is the dimension of the deforming operator. When \\varDelta ≤ d/2 , the latter terms dominate the former, and suggest that a modification to the conjecture is needed.

  9. The application of secular perturbation theory to explain warping in the circumstellar disk of Beta Pictoris

    NASA Astrophysics Data System (ADS)

    Novotny, Steven J.

    This research is a numerical investigation into the dynamical influences of planets on the dust disks surrounding young main sequence stars. Motivating this research effort are the observations of the Beta Pictoris circumstellar disk made by the 17 Department of Astronomy's mid-IR team. These IR images show with unprecedented clarity the features and asymmetries of the inner, ≤100 AU, portion of the Beta Pictoris disk; the most interesting of which is the dramatic warping of the disk's mid-plane. Analyses of prior observations have suggested that the features are attributed to the presence of a planet or a planetary system. Past dynamic analysis has focused primarily on the presence of a single planet and the resulting perturbations on the dust disk through hydrodynamic or N-body analysis. This research will show that the type of features observed in these images, specifically the warping of the disk, can also be explained with a system of two (or more) planets and secular perturbation theory while using more plausible assumptions than did other models.

  10. Enzymatic Kinetic Isotope Effects from Path-Integral Free Energy Perturbation Theory.

    PubMed

    Gao, J

    2016-01-01

    Path-integral free energy perturbation (PI-FEP) theory is presented to directly determine the ratio of quantum mechanical partition functions of different isotopologs in a single simulation. Furthermore, a double averaging strategy is used to carry out the practical simulation, separating the quantum mechanical path integral exactly into two separate calculations, one corresponding to a classical molecular dynamics simulation of the centroid coordinates, and another involving free-particle path-integral sampling over the classical, centroid positions. An integrated centroid path-integral free energy perturbation and umbrella sampling (PI-FEP/UM, or simply, PI-FEP) method along with bisection sampling was summarized, which provides an accurate and fast convergent method for computing kinetic isotope effects for chemical reactions in solution and in enzymes. The PI-FEP method is illustrated by a number of applications, to highlight the computational precision and accuracy, the rule of geometrical mean in kinetic isotope effects, enhanced nuclear quantum effects in enzyme catalysis, and protein dynamics on temperature dependence of kinetic isotope effects. PMID:27498645

  11. Halo/galaxy bispectrum with primordial non-Gaussianity from integrated perturbation theory

    NASA Astrophysics Data System (ADS)

    Yokoyama, Shuichiro; Matsubara, Takahiko; Taruya, Atsushi

    2014-02-01

    We derive a formula for the halo/galaxy bispectrum on the basis of the integrated perturbation theory (iPT). In addition to the gravity-induced non-Gaussianity, we consider the non-Gaussianity of the primordial curvature perturbations and investigate in detail the effect of such primordial non-Gaussianity on the large-scale halo/galaxy bispectrum. In iPT, the effects of primordial non-Gaussianity are wholly encapsulated in the linear (primordial) polyspectra, and we systematically calculate the contributions to the large-scale behaviors arising from the three types of primordial bispectrum (local, equilateral, and orthogonal types), and primordial trispectrum of the local-type non-Gaussianity. We find that the equilateral- and orthogonal-type non-Gaussianities show distinct scale-dependent behaviors which can dominate the gravity-induced non-Gaussianity at very large scales. For the local-type non-Gaussianity, higher-order loop corrections are found to give a significantly large contribution to the halo/galaxy bispectrum of the squeezed shape and eventually dominate over the other contributions on large scales. A diagrammatic approach based on the iPT helps us to systematically investigate an impact of such higher-order contributions to the large-scale halo/galaxy bispectrum.

  12. Entanglement-based perturbation theory for highly anisotropic Bose-Einstein condensates

    SciTech Connect

    Tacla, Alexandre B.; Caves, Carlton M.

    2011-11-15

    We investigate the emergence of three-dimensional behavior in a reduced-dimension Bose-Einstein condensate trapped by a highly anisotropic potential. We handle the problem analytically by performing a perturbative Schmidt decomposition of the condensate wave function between the tightly confined (transverse) direction(s) and the loosely confined (longitudinal) direction(s). The perturbation theory is valid when the nonlinear scattering energy is small compared to the transverse energy scales. Our approach provides a straightforward way, first, to derive corrections to the transverse and longitudinal wave functions of the reduced-dimension approximation and, second, to calculate the amount of entanglement that arises between the transverse and longitudinal spatial directions. Numerical integration of the three-dimensional Gross-Pitaevskii equation for different cigar-shaped potentials and experimentally accessible parameters reveals good agreement with our analytical model even for relatively high nonlinearities. In particular, we show that even for such stronger nonlinearities the entanglement remains remarkably small, which allows the condensate to be well described by a product wave function that corresponds to a single Schmidt term.

  13. The time-resolved photoelectron spectrum of toluene using a perturbation theory approach

    SciTech Connect

    Richings, Gareth W.; Worth, Graham A.

    2014-12-28

    A theoretical study of the intra-molecular vibrational-energy redistribution of toluene using time-resolved photo-electron spectra calculated using nuclear quantum dynamics and a simple, two-mode model is presented. Calculations have been carried out using the multi-configuration time-dependent Hartree method, using three levels of approximation for the calculation of the spectra. The first is a full quantum dynamics simulation with a discretisation of the continuum wavefunction of the ejected electron, whilst the second uses first-order perturbation theory to calculate the wavefunction of the ion. Both methods rely on the explicit inclusion of both the pump and probe laser pulses. The third method includes only the pump pulse and generates the photo-electron spectrum by projection of the pumped wavepacket onto the ion potential energy surface, followed by evaluation of the Fourier transform of the autocorrelation function of the subsequently propagated wavepacket. The calculations performed have been used to study the periodic population flow between the 6a and 10b16b modes in the S{sub 1} excited state, and compared to recent experimental data. We obtain results in excellent agreement with the experiment and note the efficiency of the perturbation method.

  14. Cluster perturbation theory for the self-assembly of associating fluids into complex structures

    NASA Astrophysics Data System (ADS)

    Marshall, Bennett D.

    2014-12-01

    Wertheim's two-density thermodynamic perturbation theory (TPT) has proven to be an indispensable statistical mechanical tool in the description of associating fluids with a single association site. TPT was developed to enforce the monovalence of the hydrogen bond and only recently has been extended to account for divalent association sites. It has been shown through experiment and molecular simulation that certain one-site associating fluids can self-assemble into complex extended supramolecular structures as a result of multiple bonding of association sites. In this paper we reorganize TPT into a form that is more easily applied to complex associated structures. The derived theory is general to all possible self-assemble structures. We obtain the free energy and bonding fractions in a general way in terms of single-cluster partition functions and averages. The new formalism removes any reference to graph theory allowing for the conceptually straightforward application of the two-density formalism to complex self-assembled structures.

  15. Statistical Mechanical Study of Molecular Fluids: Perturbation Theory and Computer Simulation

    NASA Astrophysics Data System (ADS)

    Azadipour, Saeed Rahnama

    1995-01-01

    The first part of our work is based on thermodynamic perturbation theory in which the directional electrostatic forces between molecules contributing to the thermodynamic properties are evaluated through a series expansion about a reference potential model. We use the perturbation scheme introduced by Gubbins and Twu to study thermodynamic behavior of non-ideal fluids and their mixtures. This theory was shown to work very well for small molecules with strong polar and quadpolar forces (2,3). Henderson (4) in his review of equations of state and perterbation theories, describes the inaccuracy of the Carnahan Starling-type expressions for mixture of hard spheres when one of the components in the mixture is very large. Our first concern was to incorporate the intermolecular shape forces which are stronger and shorter ranged in the reference model, and apply a perterbation theory to account for the weaker and longer ranged electro-static forces. The rotational equation of state REOS (5) incorporates a new structural parameter alpha into the compressibility equation through inclusion of rotational motions of molecules in the partition function. In addition, the equation has been correlated to provide quantitative prediction of thermodynamic properties of pure normal paraffins up to n-C_ {20} (5). Using the three parameter REOS model as the reference together with the perturbation scheme of Gubbins and Twu, thermodynamic behavior of some non -ideal mixtures were studied. In this work, we use the 4-parameter BACK (7) as reference equation in the Gubbins -Twu perturbation scheme to predict volumetric behavior of pure polar compounds. The energy parameter epsilon_{x} and size parameter sigma_{x} of the mixture was calculated from the van-der-Waals 1 mixing rules (10). A new mixing rule for alpha _{x} is proposed which is established through an optimization process for all non-polar mixtures studied here. The second part of this work involves molecular simulation studies of

  16. Time-sliced perturbation theory II: baryon acoustic oscillations and infrared resummation

    NASA Astrophysics Data System (ADS)

    Blas, Diego; Garny, Mathias; Ivanov, Mikhail M.; Sibiryakov, Sergey

    2016-07-01

    We use time-sliced perturbation theory (TSPT) to give an accurate description of the infrared non-linear effects affecting the baryonic acoustic oscillations (BAO) present in the distribution of matter at very large scales. In TSPT this can be done via a systematic resummation that has a simple diagrammatic representation and does not involve uncontrollable approximations. We discuss the power counting rules and derive explicit expressions for the resummed matter power spectrum up to next-to leading order and the bispectrum at the leading order. The two-point correlation function agrees well with N-body data at BAO scales. The systematic approach also allows to reliably assess the shift of the baryon acoustic peak due to non-linear effects.

  17. A non-perturbative approach to non-commutative scalar field theory

    NASA Astrophysics Data System (ADS)

    Steinacker, Harold

    2005-03-01

    Non-commutative euclidean scalar field theory is shown to have an eigenvalue sector which is dominated by a well-defined eigenvalue density, and can be described by a matrix model. This is established using regularizations of Bbb R2nθ via fuzzy spaces for the free and weakly coupled case, and extends naturally to the non-perturbative domain. It allows to study the renormalization of the effective potential using matrix model techniques, and is closely related to UV/IR mixing. In particular we find a phase transition for the phi4 model at strong coupling, to a phase which is identified with the striped or matrix phase. The method is expected to be applicable in 4 dimensions, where a critical line is found which terminates at a non-trivial point, with nonzero critical coupling. This provides evidence for a non-trivial fixed-point for the 4-dimensional NC phi4 model.

  18. Nonfactorization of four-quark condensates at low energies within chiral perturbation theory

    SciTech Connect

    Gomez Nicola, A.; Pelaez, J. R.; Ruiz de Elvira, J.

    2010-10-01

    Four-quark correlators and the factorization hypothesis are analyzed in the meson sector within chiral perturbation theory. We define the four-quark condensate as lim{sub x{yields}0}, which is equivalent to other definitions commonly used in the literature. Factorization of the four-quark condensate holds to leading and next to leading order. However, at next to next to leading order, a term with a nontrivial space-time dependence in the four-quark correlator yields a divergent four-quark condensate, whereas the two-quark condensate and the scalar susceptibility are finite. Such a nonfactorization term vanishes only in the chiral limit. We also comment on how factorization still holds in the large N{sub c} limit, provided such a limit is taken before renormalization.

  19. Ab initio downfolding for electron-phonon-coupled systems: Constrained density-functional perturbation theory

    NASA Astrophysics Data System (ADS)

    Nomura, Yusuke; Arita, Ryotaro

    2015-12-01

    We formulate an ab initio downfolding scheme for electron-phonon-coupled systems. In this scheme, we calculate partially renormalized phonon frequencies and electron-phonon coupling, which include the screening effects of high-energy electrons, to construct a realistic Hamiltonian consisting of low-energy electron and phonon degrees of freedom. We show that our scheme can be implemented by slightly modifying the density functional-perturbation theory (DFPT), which is one of the standard methods for calculating phonon properties from first principles. Our scheme, which we call the constrained DFPT, can be applied to various phonon-related problems, such as superconductivity, electron and thermal transport, thermoelectricity, piezoelectricity, dielectricity, and multiferroicity. We believe that the constrained DFPT provides a firm basis for the understanding of the role of phonons in strongly correlated materials. Here, we apply the scheme to fullerene superconductors and discuss how the realistic low-energy Hamiltonian is constructed.

  20. Some useful odds and ends from the n-electron valence state perturbation theory.

    PubMed

    Angeli, Celestino; Cimiraglia, Renzo

    2014-08-21

    The n-electron valence state perturbation theory makes use of zero-order wave functions whose energies are endowed with a direct physical interest, describing various processes occurring in the active space (removal/addition of one or two electrons, electronic excitations). It is shown that the zero-order energies related to the process of removal of an electron from the active space provide a reasonable and cheap approximation to the vertical ionization potentials. The zero-order energies referring to the process of an electronic excitation within the active space can also provide a first approximation to electronic transition energies, provided that a careful choice of the active molecular orbitals is performed. Test calculations have been carried out on the molecules N2 and H2CO.

  1. Taming the Electronic Structure of Diradicals through the Window of Computationally Cost Effective Multireference Perturbation Theory.

    PubMed

    Sinha Ray, Suvonil; Ghosh, Anirban; Chattopadhyay, Sudip; Chaudhuri, Rajat K

    2016-07-28

    Recently a state-specific multireference perturbation theory (SSMRPT) with an improved virtual orbitals complete active space configuration interaction (IVO-CASCI) reference function has been proposed for treating electronic structures of radicals such as methylene, m-benzyne, pyridyne, and pyridynium cation. This new development in MRPT, termed as IVO-SSMRPT, ensures that it is able to describe the structure of radicaloids with reasonable accuracy even with small reference spaces. IVO-SSMRPT is also capable of predicting the correct ordering of the lowest singlet-triplet gaps. Investigation of the first three electronic states of the oxygen molecule has also been used for rating our method. The agreement of our estimates with the available far more expensive benchmark state-of-the-art ab initio calculations is creditable. The IVO-SSMRPT method provides an effective avenue with manageable cost/accuracy ratio for accurately dealing with radicaloid systems possessing varying degrees of quasidegeneracy. PMID:27355260

  2. Stationary waves on nonlinear quantum graphs: General framework and canonical perturbation theory.

    PubMed

    Gnutzmann, Sven; Waltner, Daniel

    2016-03-01

    In this paper we present a general framework for solving the stationary nonlinear Schrödinger equation (NLSE) on a network of one-dimensional wires modeled by a metric graph with suitable matching conditions at the vertices. A formal solution is given that expresses the wave function and its derivative at one end of an edge (wire) nonlinearly in terms of the values at the other end. For the cubic NLSE this nonlinear transfer operation can be expressed explicitly in terms of Jacobi elliptic functions. Its application reduces the problem of solving the corresponding set of coupled ordinary nonlinear differential equations to a finite set of nonlinear algebraic equations. For sufficiently small amplitudes we use canonical perturbation theory, which makes it possible to extract the leading nonlinear corrections over large distances.

  3. Perturbation Theory for Quantum Mechanics in its Hessenberg-Matrix Representation

    NASA Astrophysics Data System (ADS)

    Znojil, Miloslav

    For years, the partial integrability in quantum mechanics [e.g., the exceptional terminating Lanczos solutions or the so called quasi-exactly solvable "next-to-elementary" systems] represented a challenge in perturbation theory. The main difficulty lied in an incompleteness of the available zero-order wavefunctions and in the related impossibility of an easy construction of the necessary zero-order propagators. We describe a solution of this problem, based on an unusual choice of model space. A few examples illustrate the underlying technicalities: Paying detailed attention to the Hessenberg-matrix Hamiltonians, our formalism compensates the incompleteness of integrability by a slightly less elementary (viz., non-diagonal but still triangular) matrix structure of its propagators.

  4. Heavy-baryon chiral perturbation theory approach to thermal neutron capture on {sup 3}He

    SciTech Connect

    Lazauskas, Rimantas; Park, Tae-Sun

    2011-03-15

    The cross section for radiative thermal neutron capture on {sup 3}He ({sup 3}He+n{yields}{sup 4}He+{gamma}; known as the hen reaction) is calculated based on heavy-baryon chiral perturbation theory. The relevant M1 operators are derived up to next-to-next-to-next-to-leading order (N{sup 3}LO). The initial and final nuclear wave functions are obtained from the rigorous Faddeev-Yakubovski equations for five sets of realistic nuclear interactions. Up to N{sup 3}LO, the M1 operators contain two low-energy constants, which appear as the coefficients of nonderivative two-nucleon contact terms. After determining these two constants using the experimental values of the magnetic moments of the triton and {sup 3}He, we carry out a parameter-free calculation of the hen cross section. The results are in good agreement with the data.

  5. Particle-hole configuration interaction and many-body perturbation theory: Application to Hg+

    NASA Astrophysics Data System (ADS)

    Berengut, J. C.

    2016-07-01

    The combination of configuration interaction and many-body perturbation theory methods is extended to nonperturbatively include configurations with electron holes below the designated Fermi level, allowing us to treat systems where holes play an important role. For example, the method can treat valence-hole systems like Ir17 +, particle-hole excitations in noble gases, and difficult transitions such as the 6 s →5 d-16 s2 optical clock transition in Hg+. We take the latter system as our test case for the method and obtain very good accuracy (˜1 %) for the low-lying transition energies. The α dependence of these transitions is calculated and used to reinterpret the existing best laboratory limits on the time dependence of the fine-structure constant.

  6. Proof of a Conjecture for the One-Dimensional Perturbed Gelfand Problem from Combustion Theory

    NASA Astrophysics Data System (ADS)

    Huang, Shao-Yuan; Wang, Shin-Hwa

    2016-11-01

    We study global bifurcation curves and the exact multiplicity of positive solutions for the two-point boundary value problem arising in combustion theory: u^' ' }(x)+λ exp (au/a+u) =0,quad -1 0} is the Frank-Kamenetskii parameter and a > 0 is the activation energy parameter. We prove that there exists a critical bifurcation value a 0 {≈ 4.069} such that, on the {(λ,||u||_{∞})}-plane, the bifurcation curve is S-shaped for {a > a0} and is monotone increasing for {0 < a ≤q a0}. That is, we prove the long-standing conjecture for the one-dimensional perturbed Gelfand problem. We also study, in the {(a,λ, Vert uVert _{∞})}-space, the shape and structure of the bifurcation surface.

  7. Impacts of biasing schemes in the one-loop integrated perturbation theory

    NASA Astrophysics Data System (ADS)

    Matsubara, Takahiko; Desjacques, Vincent

    2016-06-01

    The impact of biasing schemes on the clustering of tracers of the large-scale structure is analytically studied in the weakly nonlinear regime. For this purpose, we use the one-loop approximation of the integrated perturbation theory together with the renormalized bias functions of various, physically motivated Lagrangian bias schemes. These include the halo, peaks, and excursion set peaks model, for which we derive useful formulas for the evaluation of their renormalized bias functions. The shapes of the power spectra and correlation functions are affected by the different bias models at the level of a few percent on weakly nonlinear scales. These effects are studied quantitatively both in real and redshift space. The amplitude of the scale-dependent bias in the presence of primordial non-Gaussianity also depends on the details of the bias models. If left unaccounted for, these theoretical uncertainties could affect the robustness of the cosmological constraints extracted from galaxy clustering data.

  8. On the use of the autonomous Birkhoff equations in Lie series perturbation theory

    NASA Astrophysics Data System (ADS)

    Boronenko, T. S.

    2016-10-01

    In this article, we present the Lie transformation algorithm for autonomous Birkhoff systems. Here, we are referring to Hamiltonian systems that obey a symplectic structure of the general form. The Birkhoff equations are derived from the linear first-order Pfaff-Birkhoff variational principle, which is more general than the Hamilton principle. The use of 1-form in formulating the equations of motion in dynamics makes the Birkhoff method more universal and flexible. Birkhoff's equations have a tensorial character, so their form is independent of the coordinate system used. Two examples of normalization in the restricted three-body problem are given to illustrate the application of the algorithm in perturbation theory. The efficiency of this algorithm for problems of asymptotic integration in dynamics is discussed for the case where there is a need to use non-canonical variables in phase space.

  9. Proof of a Conjecture for the One-Dimensional Perturbed Gelfand Problem from Combustion Theory

    NASA Astrophysics Data System (ADS)

    Huang, Shao-Yuan; Wang, Shin-Hwa

    2016-05-01

    We study global bifurcation curves and the exact multiplicity of positive solutions for the two-point boundary value problem arising in combustion theory: u^' ' (x)+λ exp (au/a+u) =0,quad -1 0} is the Frank-Kamenetskii parameter and a > 0 is the activation energy parameter. We prove that there exists a critical bifurcation value a 0 {≈ 4.069} such that, on the {(λ,||u||_{∞})} -plane, the bifurcation curve is S-shaped for {a > a0} and is monotone increasing for {0 < a ≤q a0} . That is, we prove the long-standing conjecture for the one-dimensional perturbed Gelfand problem. We also study, in the {(a,λ, Vert uVert _{∞})} -space, the shape and structure of the bifurcation surface.

  10. Renormalized second-order perturbation theory for the electron correlation energy: Concept, implementation, and benchmarks

    NASA Astrophysics Data System (ADS)

    Ren, Xinguo; Rinke, Patrick; Scuseria, Gustavo E.; Scheffler, Matthias

    2013-07-01

    We present a renormalized second-order perturbation theory (rPT2), based on a Kohn-Sham (KS) reference state, for the electron correlation energy that includes the random-phase approximation (RPA), second-order screened exchange (SOSEX), and renormalized single excitations (rSE). These three terms all involve a summation of certain types of diagrams to infinite order, and can be viewed as ``renormalization'' of the second-order direct, exchange, and single-excitation (SE) terms of Rayleigh-Schrödinger perturbation theory based on a KS reference. In this work, we establish the concept of rPT2 and present the numerical details of our SOSEX and rSE implementations. A preliminary version of rPT2, in which the renormalized SE (rSE) contribution was treated approximately, has already been benchmarked for molecular atomization energies and chemical reaction barrier heights and shows a well-balanced performance [J. Paier , New J. Phys.1367-263010.1088/1367-2630/14/4/043002 14, 043002 (2012)]. In this work, we present a refined version of rPT2, in which we evaluate the rSE series of diagrams rigorously. We then extend the benchmark studies to noncovalent interactions, including the rare-gas dimers, and the S22 and S66 test sets, as well as the cohesive energy of small copper clusters, and the equilibrium geometry of 10 diatomic molecules. Despite some remaining shortcomings, we conclude that rPT2 gives an overall satisfactory performance across different electronic situations, and is a promising step towards a generally applicable electronic-structure approach.

  11. High-precision extreme-mass-ratio inspirals in black hole perturbation theory and post-Newtonian theory

    NASA Astrophysics Data System (ADS)

    Forseth, Erik Robert

    The recent detection of gravitational wave (GW) signal GW150914 by the Advanced LIGO experiment has inaugurated the long-anticipated era of GW astronomy. This event saw the merger of two black holes, having roughly 36 and 29 solar masses, as well as the ringdown of the resulting 62 solar mass black hole. The energy emitted in gravitational radiation was equivalent to about three solar masses. The detection underscored the importance of theoretical models for not only isolating signal from noise, but especially for the accurate estimation of source parameters. The two-body problem in Einstein's general theory has no exact solution, and so the development of these models is highly nontrivial. We present in this thesis a set of original results on the dynamics of the inspiral for a class of binary systems known as extreme-mass-ratio inspirals (EMRIs), comprised of a small compact object (generically a stellar mass black hole) in orbit about a supermassive black hole. Our work also has potential application to intermediate-mass-ratio inspirals (IMRIs). IMRIs are thought to be a potentially strong source for ground-based GW experiments such as Advanced LIGO/VIRGO. Though not generally a good source for the LIGO network, EMRIs on the other hand are well-suited for detection by proposed space-based detectors, e.g. eLISA. Our work particularly constitutes a program of developing computational tools, methods, and results for eccentric E/IMRIs, which are thought to be astrophysically important but are much more challenging to model theoretically compared with circular orbits. We begin with a brief review of relevant parts of general relativity (GR) theory, followed by overviews of two prevailing approximation formalisms in GR, black hole perturbation (BHP) theory and post-Newtonian (PN) theory. Our first original result is a high-precision computation of the first-order gravitational metric perturbation using a Lorenz gauge frequency domain procedure. Next, we present a fast

  12. Canonical perturbation theory; stability and diffusion in Hamiltonian systems: applications in dynamical astronomy

    NASA Astrophysics Data System (ADS)

    Efthymiopoulos, C.

    We present some basic methods and techniques of canonical perturbation theory, as well as some of its applications in problems of stability and/or dif- fusion in dynamical astronomy. The methods presented are: i) the Birkhoff normal form, ii) the Kolmogorov normal form, iii) the resonant normal form, and iv) the hyperbolic normal form used in the computation of in- variant manifolds of unstable periodic orbits in the chaotic regime. For each method we give concrete examples presented in some detail in order to facilitate study. In particular, we discuss a step by step implementation of a so-called `book-keeping' algorithm by which all quantities (i.e. Hamil- tonian, generating functions etc.) can be split in groups of terms of similar order of smallness. We explain why the book-keeping schemes presently suggested are particularly suitable in computer-algebraic implementations of normal forms. Also, for each method we explain the pattern by which small divisors are accumulated in the series terms at successive normaliza- tion steps, outlining why such accumulation leads to a divergent normal- ization process in the case of the Birkhoff normal form (both non-resonant or resonant), while it leads to a convergent normalization process in the case of the Kolmogorov normal form or the hyperbolic normal form. After these formal aspects, we present applications of canonical perturbation the- ory in concrete Hamiltonian dynamical systems appearing in problems of dynamical astronomy. In particular, we explain how resonant normal form theory is connected to the phenomenon of Arnold diffusion, as well as to estimates of the diffusion rate in the action space in systems of three (or more) degrees of freedom. We discuss how is `book-keeping' implemented in paradigmatic cases, like the treatment of mean motion resonances in so- lar system dynamics, and the study of orbits in axisymmetric galaxies or in barred-spiral rotating galaxies. Finally, we give an example of implemen

  13. Cognitive Adaptation Theory and Breast Cancer Recurrence: Are There Limits?

    ERIC Educational Resources Information Center

    Tomich, Patricia L.; Helgeson, Vicki S.

    2006-01-01

    Relations of the components of cognitive adaptation theory (self-esteem, optimism, control) to quality of life and benefit finding were examined for 70 women (91% Caucasian) diagnosed with Stage I, II, or III breast cancer over 5 years ago. Half of these women experienced a recurrence within the 5 years; the other half remained disease free. Women…

  14. An Adaptation of Constructive Alternativism as Theory for Audience Analysis.

    ERIC Educational Resources Information Center

    Losee, Doug

    An examination of audience analysis factors in representative communication textbooks indicates that current pedagogical applications are broadly categorized into demographic and dispositional properties. The adaptation of constructivist theory to audience analysis can give speech students reasons why the speaker-audience relationship is as it is.…

  15. Perturbation Theory Reloaded : Toward The Precise Modeling Of The Galaxy Power Spectrum In The High-z Galaxy Survey

    NASA Astrophysics Data System (ADS)

    Jeong, Donghui; Komatsu, E.

    2007-12-01

    We shall show that there exist quasi-nonlinear regions in the k-space, where one can actually model the effect of nonlinearities on the galaxy power spectrum by comparing the large number of N-body simulations with the nonlinear perturbation theory. Especially, we shall show that in the high redshift universe, the nonlinear matter evolution, and nonlinear halo bias are now perfectly modeled within a suffcient range in k-space, by the perturbation theory. And the nonlinear redshift space distortion is also well understood, except for the highly nonlinear Finger of God effect. D. J. acknowledges support from the Texas Advanced Research Program.

  16. Non-perturbative effects in quantum field theory: QCD, supersymmetric QCD and axions

    NASA Astrophysics Data System (ADS)

    Wu, Weitao

    In the study of non-perturbative effects in four dimenstional non-Abelian gauge theories, instantons have played an important conceptual role. However, their role in the quantitative understanding these theories has remained obscure. In the first part of this thesis, we revisit the question of whether or not one can perform reliable semiclassical QCD computation at zero temperature. We study correlation functions with no perturbative contributions, and organize the problem by means of the operator product expansion, establishing a precise criterion for the validity of semiclassical calculation. For N f > Nc, a systematic computation is possible; for Nf < Nc, it is not. Nf = Nc is a borderline case. As an application, we describe a test of QCD lattice gauge theory computations in the chiral limit. Supersymmetry has provided a tool with which to obtain a range of exact results in field theory and string theory. Arguably the first inkling that one could obtain such results was the work of Novikov, Shifman, Vainshtein, and Zakharov (NSVZ). They argued for two exact results in gauge theories using instanton computation. First, that one could compute certain correlation functions exactly at weak coupling, and extend the results to strong coupling; second, that one could obtain exact expressions for beta-functions. However, each of these results raised questions. As methods exploiting systematic weak coupling expansions and holomorphy were developed, it became clear that the strong coupling instanton computation was incorrect. This in turn called the exact beta-function into question. In the second part of this thesis, we will provide resolutions to both of these questions. First, we explain why the instanton computation in the pure supersymmetric gauge theory is not reliable, even at short distances. The semiclassical expansion about the instanton is purely formal; if infrared divergences appear, they spoil arguments based on holomorphy. For the question of the NSVZbeta

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

    PubMed

    Hoffmann, Mark R; Helgaker, Trygve

    2015-03-01

    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.

  18. Semiclassical Transition-State Theory Based on Fourth-Order Vibrational Perturbation Theory: The Symmetrical Eckart Barrier.

    PubMed

    Stanton, John F

    2016-07-21

    Semiclassical transition-state theory based on fourth-order vibrational perturbation theory (VPT4-SCTST) is applied to compute the barrier transmission coefficient for the symmetric Eckart potential. For a barrier parametrized to mimic the H2 + H exchange reaction, the results obtained are in excellent agreement with exact quantum calculations over a range of energy that extends down to roughly 1% of the barrier height, V0, where tunneling is negligible. The VPT2-SCTST treatment, which is commonly used in chemical kinetics studies, also performs quite well but already shows an error of a few percent at ca. 0.8 V0 where tunneling is still important. This suggests that VPT4-SCTST could offer an improvement over VPT2-SCTST in applications studies. However, the computational effort for VPT4-SCTST treatments of molecules is excessive, and any improvement gained is unlikely to warrant the increased effort. Nevertheless, the treatment of the symmetric Eckart barrier problem here suggests a simple modification of the usual VPT2-SCTST protocol that warrants further investigation. PMID:27358083

  19. Poisson-Based Inference for Perturbation Models in Adaptive Spelling Training

    ERIC Educational Resources Information Center

    Baschera, Gian-Marco; Gross, Markus

    2010-01-01

    We present an inference algorithm for perturbation models based on Poisson regression. The algorithm is designed to handle unclassified input with multiple errors described by independent mal-rules. This knowledge representation provides an intelligent tutoring system with local and global information about a student, such as error classification…

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

    NASA Astrophysics Data System (ADS)

    Assawaroongruengchot, Monchai

    Perturbation theory is a technique used for the estimation of changes in performance functionals, such as linear reaction rate ratio and eigenvalue affected by small variations in reactor core compositions. Here the algorithm of perturbation theory is developed for the multigroup integral neutron transport problems in 2D fuel assemblies with isotropic scattering. The integral transport equation is used in the perturbative formulation because it represents the interconnecting neutronic systems of the lattice assemblies via the tracking lines. When the integral neutron transport equation is used in the formulation, one needs to solve the resulting integral transport equations for the flux importance and generalized flux importance functions. The relationship between the generalized flux importance and generalized source importance functions is defined in order to transform the generalized flux importance transport equations into the integro-differential equations for the generalized adjoints. Next we develop the adjoint and generalized adjoint transport solution algorithms based on the method of cyclic characteristics (MOCC) in DRAGON code. In the MOCC method, the adjoint characteristics equations associated with a cyclic tracking line are formulated in such a way that a closed form for the adjoint angular function can be obtained. The MOCC method then requires only one cycle of scanning over the cyclic tracking lines in each spatial iteration. We also show that the source importance function by CP method is mathematically equivalent to the adjoint function by MOCC method. In order to speed up the MOCC solution algorithm, a group-reduction and group-splitting techniques based on the structure of the adjoint scattering matrix are implemented. A combined forward flux/adjoint function iteration scheme, based on the group-splitting technique and the common use of a large number of variables storing tracking-line data and exponential values, is proposed to reduce the

  1. Molecular-orbital-free algorithm for excited states in time-dependent perturbation theory.

    PubMed

    Lucero, Melissa J; Niklasson, Anders M N; Tretiak, Sergei; Challacombe, Matt

    2008-08-14

    A nonlinear conjugate gradient optimization scheme is used to obtain excitation energies within the random phase approximation (RPA). The solutions to the RPA eigenvalue equation are located through a variational characterization using a modified Thouless functional, which is based upon an asymmetric Rayleigh quotient, in an orthogonalized atomic orbital representation. In this way, the computational bottleneck of calculating molecular orbitals is avoided. The variational space is reduced to the physically-relevant transitions by projections. The feasibility of an RPA implementation scaling linearly with system size N is investigated by monitoring convergence behavior with respect to the quality of initial guess and sensitivity to noise under thresholding, both for well- and ill-conditioned problems. The molecular-orbital-free algorithm is found to be robust and computationally efficient, providing a first step toward large-scale, reduced complexity calculations of time-dependent optical properties and linear response. The algorithm is extensible to other forms of time-dependent perturbation theory including, but not limited to, time-dependent density functional theory. PMID:18715058

  2. Third-order thermodynamic perturbation theory for effective potentials that model complex fluids

    NASA Astrophysics Data System (ADS)

    Zhou, Shiqi; Solana, J. R.

    2008-08-01

    We have performed Monte Carlo simulations to obtain the thermodynamic properties of fluids with two kinds of hard-core plus attractive-tail or oscillatory potentials. One of them is the square-well potential with small well width. The other is a model potential with oscillatory and decaying tail. Both model potentials are suitable for modeling the effective potential arising in complex fluids and fluid mixtures with extremely-large-size asymmetry, as is the case of the solvent-induced depletion interactions in colloidal dispersions. For the former potential, the compressibility factor, the excess energy, the constant-volume excess heat capacity, and the chemical potential have been obtained. For the second model potential only the first two of these quantities have been obtained. The simulations cover the whole density range for the fluid phase and several temperatures. These simulation data have been used to test the performance of a third-order thermodynamic perturbation theory (TPT) recently developed by one of us [S. Zhou, Phys. Rev. E 74, 031119 (2006)] as compared with the well-known second-order TPT based on the macroscopic compressibility approximation due to Barker and Henderson. It is found that the first of these theories provides much better accuracy than the second one for all thermodynamic properties analyzed for the two effective potential models.

  3. Nuclear Energy Gradients for Internally Contracted Complete Active Space Second-Order Perturbation Theory: Multistate Extensions.

    PubMed

    Vlaisavljevich, Bess; Shiozaki, Toru

    2016-08-01

    We report the development of the theory and computer program for analytical nuclear energy gradients for (extended) multistate complete active space perturbation theory (CASPT2) with full internal contraction. The vertical shifts are also considered in this work. This is an extension of the fully internally contracted CASPT2 nuclear gradient program recently developed for a state-specific variant by us [MacLeod and Shiozaki, J. Chem. Phys. 2015, 142, 051103]; in this extension, the so-called λ equation is solved to account for the variation of the multistate CASPT2 energies with respect to the change in the amplitudes obtained in the preceding state-specific CASPT2 calculations, and the Z vector equations are modified accordingly. The program is parallelized using the MPI3 remote memory access protocol that allows us to perform efficient one-sided communication. The optimized geometries of the ground and excited states of a copper corrole and benzophenone are presented as numerical examples. The code is publicly available under the GNU General Public License.

  4. MOLGW 1: Many-body perturbation theory software for atoms, molecules, and clusters

    NASA Astrophysics Data System (ADS)

    Bruneval, Fabien; Rangel, Tonatiuh; Hamed, Samia M.; Shao, Meiyue; Yang, Chao; Neaton, Jeffrey B.

    2016-11-01

    We summarize the MOLGW code that implements density-functional theory and many-body perturbation theory in a Gaussian basis set. The code is dedicated to the calculation of the many-body self-energy within the GW approximation and the solution of the Bethe-Salpeter equation. These two types of calculations allow the user to evaluate physical quantities that can be compared to spectroscopic experiments. Quasiparticle energies, obtained through the calculation of the GW self-energy, can be compared to photoemission or transport experiments, and neutral excitation energies and oscillator strengths, obtained via solution of the Bethe-Salpeter equation, are measurable by optical absorption. The implementation choices outlined here have aimed at the accuracy and robustness of calculated quantities with respect to measurements. Furthermore, the algorithms implemented in MOLGW allow users to consider molecules or clusters containing up to 100 atoms with rather accurate basis sets, and to choose whether or not to apply the resolution-of-the-identity approximation. Finally, we demonstrate the parallelization efficacy of the MOLGW code over several hundreds of processors.

  5. Conformers of CL-20 explosive and ab initio refinement using perturbation theory: implications to detonation mechanisms.

    PubMed

    Molt, Robert W; Bartlett, Rodney J; Watson, Thomas; Bazanté, Alexandre P

    2012-12-13

    We have identified the major conformers of CL-20 explosive, otherwise known as 2,4,6,8,10,12-hexanitrohexaazaisowurtzitane, more formally known as 2,4,6,8,10,12-hexanitrohexaazatetracyclo[5.5.0.0]-dodecane, via Monte Carlo search in conformational space through molecular mechanics and subsequent quantum mechanical refinement using perturbation theory. Our search produced enough conformers to account for all of the various forms of CL-20 found in crystals. This suggests that our methodology will be useful in studying the conformational landscape of other nitramines. The energy levels of the conformers found are all within 0.25 eV of one another based on MBPT(2)/6-311G(d,p); consequently, without further refinement from a method such as coupled cluster theory, all conformers may reasonably be populated at STP in the gas phase. We also report the harmonic vibrational frequencies of conformers, including the implications on the mechanism of detonation. In particular, we establish that the weakest N-N nitramine of CL-20 is the cyclohexane equatorial nitramine. This preliminary mapping of the conformers of CL-20 makes it possible to study the mechanism of detonation of this explosive rigorously in future work.

  6. The Kaon B-parameter in mixed action chiral perturbation theory

    SciTech Connect

    Aubin, C.; Laiho, Jack; Van de Water, Ruth S.; /Fermilab

    2006-09-01

    We calculate the kaon B-parameter, B{sub K}, in chiral perturbation theory for a partially quenched, mixed action theory with Ginsparg-Wilson valence quarks and staggered sea quarks. We find that the resulting expression is similar to that in the continuum, and in fact has only two additional unknown parameters. At one-loop order, taste-symmetry violations in the staggered sea sector only contribute to flavor-disconnected diagrams by generating an {Omicron}(a{sup 2}) shift to the masses of taste-singlet sea-sea mesons. Lattice discretization errors also give rise to an analytic term which shifts the tree-level value of B{sub K} by an amount of {Omicron}(a{sup 2}). This term, however, is not strictly due to taste-breaking, and is therefore also present in the expression for B{sub K} for pure G-W lattice fermions. We also present a numerical study of the mixed B{sub K} expression in order to demonstrate that both discretization errors and finite volume effects are small and under control on the MILC improved staggered lattices.

  7. Conformers of CL-20 explosive and ab initio refinement using perturbation theory: implications to detonation mechanisms.

    PubMed

    Molt, Robert W; Bartlett, Rodney J; Watson, Thomas; Bazanté, Alexandre P

    2012-12-13

    We have identified the major conformers of CL-20 explosive, otherwise known as 2,4,6,8,10,12-hexanitrohexaazaisowurtzitane, more formally known as 2,4,6,8,10,12-hexanitrohexaazatetracyclo[5.5.0.0]-dodecane, via Monte Carlo search in conformational space through molecular mechanics and subsequent quantum mechanical refinement using perturbation theory. Our search produced enough conformers to account for all of the various forms of CL-20 found in crystals. This suggests that our methodology will be useful in studying the conformational landscape of other nitramines. The energy levels of the conformers found are all within 0.25 eV of one another based on MBPT(2)/6-311G(d,p); consequently, without further refinement from a method such as coupled cluster theory, all conformers may reasonably be populated at STP in the gas phase. We also report the harmonic vibrational frequencies of conformers, including the implications on the mechanism of detonation. In particular, we establish that the weakest N-N nitramine of CL-20 is the cyclohexane equatorial nitramine. This preliminary mapping of the conformers of CL-20 makes it possible to study the mechanism of detonation of this explosive rigorously in future work. PMID:23136867

  8. Peculiar velocities in redshift space: formalism, N-body simulations and perturbation theory

    SciTech Connect

    Okumura, Teppei; Seljak, Uroš; Vlah, Zvonimir; Desjacques, Vincent E-mail: useljak@berkeley.edu E-mail: Vincent.Desjacques@unige.ch

    2014-05-01

    Direct measurements of peculiar velocities of galaxies and clusters of galaxies can in principle provide explicit information on the three dimensional mass distribution, but this information is modulated by the fact that velocity field is sampled at galaxy positions, and is thus probing galaxy momentum. We derive expressions for the cross power spectrum between the density and momentum field and the auto spectrum of the momentum field in redshift space, by extending the distribution function method to these statistics. The resulting momentum cross and auto power spectra in redshift space are expressed as infinite sums over velocity moment correlators in real space, as is the case for the density power spectrum in redshift space. We compute each correlator using Eulerian perturbation theory (PT) and halo biasing model and compare the resulting redshift-space velocity statistics to those measured from N-body simulations for both dark matter and halos. We find that in redshift space linear theory predictions for the density-momentum cross power spectrum as well as for the momentum auto spectrum fail to predict the N-body results at very large scales. On the other hand, our nonlinear PT prediction for these velocity statistics, together with real-space power spectrum for dark matter from simulations, improves the accuracy for both dark matter and halos. We also present the same analysis in configuration space, computing the redshift-space pairwise mean infall velocities and velocity correlation function and compare to nonlinear PT.

  9. Mass spectra of heavy-light mesons in heavy hadron chiral perturbation theory

    NASA Astrophysics Data System (ADS)

    Alhakami, Mohammad H.

    2016-05-01

    We study the masses of the low-lying charm and bottom mesons within the framework of heavy hadron chiral perturbation theory (HHChPT). We work to third order in the chiral expansion, where meson loops contribute. In contrast to previous approaches, we use physical meson masses in evaluating these loops. This ensures that their imaginary parts are consistent with the observed widths of the D mesons. The lowest odd- and even-parity, strange and nonstrange charm mesons provide enough constraints to determine only certain linear combinations of the low-energy constants in the effective Lagrangian. We comment on how lattice QCD could provide further information to disentangle these constants. Then, we use the results from the charm sector to predict the spectrum of odd and even parity of the bottom mesons. The predicted masses from our theory are in good agreement with experimentally measured masses for the case of the odd-parity sector. For the even-parity sector, the B -meson states have not yet been observed; thus, our results provide useful information for experimentalists investigating such states. The near degeneracy of nonstrange and strange scalar B mesons is confirmed in our predictions using HHChPT. We show why previous approaches of using HHChPT in studying the mass degeneracy in the scalar states of charm and bottom meson sectors gave unsatisfactory results.

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

    SciTech Connect

    Vlah, Zvonimir; Seljak, Uroš; Okumura, Teppei; Desjacques, Vincent E-mail: seljak@physik.uzh.ch E-mail: Vincent.Desjacques@unige.ch

    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.

  11. Nuclear Energy Gradients for Internally Contracted Complete Active Space Second-Order Perturbation Theory: Multistate Extensions.

    PubMed

    Vlaisavljevich, Bess; Shiozaki, Toru

    2016-08-01

    We report the development of the theory and computer program for analytical nuclear energy gradients for (extended) multistate complete active space perturbation theory (CASPT2) with full internal contraction. The vertical shifts are also considered in this work. This is an extension of the fully internally contracted CASPT2 nuclear gradient program recently developed for a state-specific variant by us [MacLeod and Shiozaki, J. Chem. Phys. 2015, 142, 051103]; in this extension, the so-called λ equation is solved to account for the variation of the multistate CASPT2 energies with respect to the change in the amplitudes obtained in the preceding state-specific CASPT2 calculations, and the Z vector equations are modified accordingly. The program is parallelized using the MPI3 remote memory access protocol that allows us to perform efficient one-sided communication. The optimized geometries of the ground and excited states of a copper corrole and benzophenone are presented as numerical examples. The code is publicly available under the GNU General Public License. PMID:27388038

  12. Benchmark of a modified iterated perturbation theory approach on the fcc lattice at strong coupling

    NASA Astrophysics Data System (ADS)

    Arsenault, Louis-François; Sémon, Patrick; Tremblay, A.-M. S.

    2012-08-01

    The dynamical mean-field theory approach to the Hubbard model requires a method to solve the problem of a quantum impurity in a bath of noninteracting electrons. Iterated perturbation theory (IPT) has proven its effectiveness as a solver in many cases of interest. Based on general principles and on comparisons with an essentially exact continuous-time quantum Monte Carlo (CTQMC) solver, here we show that the standard implementation of IPT fails away from half-filling when the interaction strength is much larger than the bandwidth. We propose a slight modification to the IPT algorithm that replaces one of the equations by the requirement that double occupancy calculated with IPT gives the correct value. We call this method IPT-D. We recover the Fermi liquid ground state away from half-filling. The Fermi liquid parameters, density of states, chemical potential, energy, and specific heat on the fcc lattice are calculated with both IPT-D and CTQMC as benchmark examples. We also calculated the resistivity and the optical conductivity within IPT-D. Particle-hole asymmetry persists even at coupling twice the bandwidth. A generalization to the multiorbital case is suggested. Several algorithms that speed up the calculations are described in appendixes.

  13. Elastic pion-nucleon scattering in chiral perturbation theory: A fresh look

    NASA Astrophysics Data System (ADS)

    Siemens, D.; Bernard, V.; Epelbaum, E.; Gasparyan, A.; Krebs, H.; Meißner, Ulf-G.

    2016-07-01

    Elastic pion-nucleon scattering is analyzed in the framework of chiral perturbation theory up to fourth order within the heavy-baryon expansion and a covariant approach based on an extended on-mass-shell renormalization scheme. We discuss in detail the renormalization of the various low-energy constants and provide explicit expressions for the relevant β functions and the finite subtractions of the power-counting breaking terms within the covariant formulation. To estimate the theoretical uncertainty from the truncation of the chiral expansion, we employ an approach which has been successfully applied in the most recent analysis of the nuclear forces. This allows us to reliably extract the relevant low-energy constants from the available scattering data at low energy. The obtained results provide clear evidence that the breakdown scale of the chiral expansion for this reaction is related to the Δ resonance. The explicit inclusion of the leading contributions of the Δ isobar is demonstrated to substantially increase the range of applicability of the effective field theory. The resulting predictions for the phase shifts are in an excellent agreement with the predictions from the recent Roy-Steiner-equation analysis of pion-nucleon scattering.

  14. Electron correlation and dimerization in trans-polyacetylene: Many-body perturbation theory versus density-functional methods

    NASA Astrophysics Data System (ADS)

    Suhai, Sándor

    1995-06-01

    Structural and energetic aspects of the Peierls-type lattice dimerization were investigated in infinite, one-dimensional, periodic trans-polyacetylene (t-PA) using many-body perturbation theory (MBPT) and density-functional theory (DFT). Cohesive properties and dimerization parameters were obtained first for the classical Coulomb potential in the Hartree approximation and then by gradually turning on exchange and correlation potentials. Besides the nonlocal Hartree-Fock exchange, several other exchange functionals were used incorporating gradient corrections as well. For MBPT, electron correlation was included up to the fourth order of the Mo/ller-Plesset scheme and the behavior of lattice sums for different PT terms was analyzed in detail. The electrostatic part of the infinite lattice sums was computed by the multipole expansion technique. In solving the polymer Kohn-Sham equations, the performance of several different correlation potentials was studied again including different gradient corrections. Atomic basis sets of systematically increasing size, in the range of double-zeta to triple-zeta (TZ) up to TZ (3df,3p2d), were used in all calculations to construct the symmetry-adapted (Bloch-type) polymer wave functions, to fully optimize the structures, and to extrapolate different physical quantities to the limit of a hypothetical infinite basis set. Comparison of the different DFT results with MBPT and with experiments demonstrated the importance of gradient terms both for exchange and correlation. On the other hand, the best DFT functional, using a medium-size atomic basis set, excellently reproduced the cohesive and dimerization energies obtained for infinite t-PA at the MP4/TZ(3d2f,3p2d) level and provided dimerization parameters close to experiment. The experimentally observed lattice spacing of 2.46+/-0.01 Å will be correctly predicted both at the MBPT and DFT levels with 2.48 and 2.44 Å, respectively.

  15. Perturbation theory of relativistic corrections. 2. Analysis and classification of known and other possible methods

    NASA Astrophysics Data System (ADS)

    Kutzelnigg, W.

    1990-03-01

    Methods for perturbation theory of relativistic corrections for an electron in a Coulomb field are divided into three categories: (1) in terms of 4-component spinors; (2) in terms of the ‘large components’ of the Dirac spinor; (3) involving a Foldy-Wouthuysen type transformation, where one attempts to obtain a two-component spinor different from the ‘large component’. In methods of category 1 (the ‘direct perturbation theory’ of paper I of this series, the related approaches by Rutkowski as well as by Gesteszy, Grosse, and Thaller and a somewhat different one by Moore) the wave function, the energy and the Hamiltonian are analytic in c -2. No divergent terms arise. In methods of category 2 (that of the elemination of the small component as well as a similarity transformation in intermediate normalization) wave function and energy are still analytic in c -2, but the effective Hamiltonian no longer is. Regularized results can be obtained by controlled cancellation of divergent terms. In category 3 both the effective Hamiltonian and the wave function are highly singular and non-analytic in c -1. A controlled cancellation of divergent terms is at least very difficult. These pathologic feature survive in the non-relativistic limit and have hence little to do with relativistic effects. They are related to the fact that for r → 0 the sign of the quantum number κ rather than that of the energy determines which component of the Dirac spinor is large and which is small. In the limit r → 0 and c → ∞ the Foldy-Wouthuysen wave function of a 2 p 1/2 state is a 1 p wave function. Hierarchies of transformations of the Dirac equation and its non-relativistic limit are presented and discussed. Finally the problem of the regularization of effective Hamiltonians on 2-component level ‘for electrons only’ is addressed.

  16. Distribution function approach to redshift space distortions. Part IV: perturbation theory applied to dark matter

    SciTech Connect

    Vlah, Zvonimir; Seljak, Uroš; Baldauf, Tobias; McDonald, Patrick; Okumura, Teppei E-mail: seljak@physik.uzh.ch E-mail: teppei@ewha.ac.kr

    2012-11-01

    We develop a perturbative approach to redshift space distortions (RSD) using the phase space distribution function approach and apply it to the dark matter redshift space power spectrum and its moments. RSD can be written as a sum over density weighted velocity moments correlators, with the lowest order being density, momentum density and stress energy density. We use standard and extended perturbation theory (PT) to determine their auto and cross correlators, comparing them to N-body simulations. We show which of the terms can be modeled well with the standard PT and which need additional terms that include higher order corrections which cannot be modeled in PT. Most of these additional terms are related to the small scale velocity dispersion effects, the so called finger of god (FoG) effects, which affect some, but not all, of the terms in this expansion, and which can be approximately modeled using a simple physically motivated ansatz such as the halo model. We point out that there are several velocity dispersions that enter into the detailed RSD analysis with very different amplitudes, which can be approximately predicted by the halo model. In contrast to previous models our approach systematically includes all of the terms at a given order in PT and provides a physical interpretation for the small scale dispersion values. We investigate RSD power spectrum as a function of μ, the cosine of the angle between the Fourier mode and line of sight, focusing on the lowest order powers of μ and multipole moments which dominate the observable RSD power spectrum. Overall we find considerable success in modeling many, but not all, of the terms in this expansion. This is similar to the situation in real space, but predicting power spectrum in redshift space is more difficult because of the explicit influence of small scale dispersion type effects in RSD, which extend to very large scales.

  17. Analytical Methods and Perturbation Theory for the Elliptic Restricted Three-Body Problem of Astrodynamics

    NASA Astrophysics Data System (ADS)

    Duffy, Brenton

    The distinguishing characteristic of the elliptic restricted three-body problem from that of the circular case is a pulsating potential field resulting in non-autonomous and non-integrable spacecraft dynamics, which are difficult to model using classical methods of analysis. The purpose of this study is to harness modern methods of analytical perturbation theory to normalize the system dynamics about the circular restricted three-body problem and about one of the triangular Lagrange points. The normalization is achieved through a canonical transformation of the system Hamiltonian function based on the Lie transform method introduced by Hori and Deprit in the 1960s. The classic method derives a near-identity transformation of a Hamiltonian function expanded about a single parameter such that the transformed system possesses ideal properties of integrability. One of the major contributions of this study is to extend the normalization method to two-parameter expansions and to non-autonomous Hamiltonian systems. The two-parameter extension is used to normalize the system dynamics of the elliptic restricted three-body problem such that the stability of the triangular Lagrange points may be determined using the Kolmogorov-Arnold-Moser theorem. Further dynamical analysis is performed in the transformed phase space in terms of local integrals of motion akin to Jacobi's integral of the circular restricted three-body problem. The local phase space around the Lagrange point is foliated by invariant tori that effectively separate the planar dynamics into qualitative regions of motion. Additional analysis is presented for the incorporation of control into the normalization routine with the goal of eliminating the non-circular secular perturbations. The control method is validated on a test case and applied to the elliptic restricted three-body problem for the purposes of stabilizing the motion around the triangular Lagrange points.

  18. Development and Application of Single-Referenced Perturbation and Coupled-Cluster Theories for Excited Electronic States

    NASA Technical Reports Server (NTRS)

    Lee, Timothy J.; Langhoff, Stephen R. (Technical Monitor)

    1997-01-01

    Recent work on the development of single-reference perturbation theories for the study of excited electronic states will be discussed. The utility of these methods will be demonstrated by comparison to linear-response coupled-cluster excitation energies. Results for some halogen molecules of interest in stratospheric chemistry will be presented.

  19. A Computer Program for the Reactivity and Kinetic Parameters for Two-Dimensional Triangular Geometry by Transport Perturbation Theory.

    1990-04-25

    Version 00 TPTRIA calculates reactivity, effective delayed neutron fractions and mean generation time for two-dimensional triangular geometry on the basis of neutron transport perturbation theory. DIAMANT2 (also designated as CCC-414), is a multigroup two-dimensional discrete ordinates transport code system for triangular and hexagonal geometry which calculates direct and adjoint angular fluxes.

  20. Generalization of iterative perturbation theory and coherent potential approximation (ITP+CPA) to double exchange model with orbital degeneracy

    NASA Astrophysics Data System (ADS)

    Liu, Zi-Xin; Wen, Sheng-Hui; Li, Ming

    2008-06-01

    A combination of the iterative perturbation theory (ITP) of the dynamical mean field theory (DMFT) and coherent-potential approximation (CPA) is generalized to the double exchange model with orbital degeneracy. The Hubbard interaction and the off-diagonal components for the hopping matrix tmnij(m ≠ n) are considered in our calculation of spectrum and optical conductivity. The numerical results show that the effects of the non-diagonal hopping matrix elements are important.

  1. Galaxy power spectrum in redshift space: Combining perturbation theory with the halo model

    SciTech Connect

    Okumura, Teppei; Hand, Nick; Seljak, Uros; Vlah, Zvonimir; Desjacques, Vincent

    2015-11-19

    Theoretical modeling of the redshift-space power spectrum of galaxies is crucially important to correctly extract cosmological information from galaxy redshift surveys. The task is complicated by the nonlinear biasing and redshift space distortion (RSD) effects, which change with halo mass, and by the wide distribution of halo masses and their occupations by galaxies. One of the main modeling challenges is the existence of satellite galaxies that have both radial distribution inside the halos and large virial velocities inside halos, a phenomenon known as the Finger-of-God (FoG) effect. We present a model for the redshift-space power spectrum of galaxies in which we decompose a given galaxy sample into central and satellite galaxies and relate different contributions to the power spectrum to 1-halo and 2-halo terms in a halo model. Our primary goal is to ensure that any parameters that we introduce have physically meaningful values, and are not just fitting parameters. For the lowest order 2-halo terms we use the previously developed RSD modeling of halos in the context of distribution function and perturbation theory approach. This term needs to be multiplied by the effect of radial distances and velocities of satellites inside the halo. To this one needs to add the 1-halo terms, which are nonperturbative. We show that the real space 1-halo terms can be modeled as almost constant, with the finite extent of the satellites inside the halo inducing a small k2R2 term over the range of scales of interest, where R is related to the size of the halo given by its halo mass. Furthermore, we adopt a similar model for FoG in redshift space, ensuring that FoG velocity dispersion is related to the halo mass. For FoG k2 type expansions do not work over the range of scales of interest and FoG resummation must be used instead. We test several simple damping functions to model the velocity dispersion FoG effect. Applying the formalism to mock

  2. Galaxy power spectrum in redshift space: Combining perturbation theory with the halo model

    DOE PAGES

    Okumura, Teppei; Hand, Nick; Seljak, Uros; Vlah, Zvonimir; Desjacques, Vincent

    2015-11-19

    Theoretical modeling of the redshift-space power spectrum of galaxies is crucially important to correctly extract cosmological information from galaxy redshift surveys. The task is complicated by the nonlinear biasing and redshift space distortion (RSD) effects, which change with halo mass, and by the wide distribution of halo masses and their occupations by galaxies. One of the main modeling challenges is the existence of satellite galaxies that have both radial distribution inside the halos and large virial velocities inside halos, a phenomenon known as the Finger-of-God (FoG) effect. We present a model for the redshift-space power spectrum of galaxies in whichmore » we decompose a given galaxy sample into central and satellite galaxies and relate different contributions to the power spectrum to 1-halo and 2-halo terms in a halo model. Our primary goal is to ensure that any parameters that we introduce have physically meaningful values, and are not just fitting parameters. For the lowest order 2-halo terms we use the previously developed RSD modeling of halos in the context of distribution function and perturbation theory approach. This term needs to be multiplied by the effect of radial distances and velocities of satellites inside the halo. To this one needs to add the 1-halo terms, which are nonperturbative. We show that the real space 1-halo terms can be modeled as almost constant, with the finite extent of the satellites inside the halo inducing a small k2R2 term over the range of scales of interest, where R is related to the size of the halo given by its halo mass. Furthermore, we adopt a similar model for FoG in redshift space, ensuring that FoG velocity dispersion is related to the halo mass. For FoG k2 type expansions do not work over the range of scales of interest and FoG resummation must be used instead. We test several simple damping functions to model the velocity dispersion FoG effect. Applying the formalism to mock galaxies modeled after the

  3. FAPT: A Mathematica package for calculations in QCD Fractional Analytic Perturbation Theory

    NASA Astrophysics Data System (ADS)

    Bakulev, Alexander P.; Khandramai, Vyacheslav L.

    2013-01-01

    We provide here all the procedures in Mathematica which are needed for the computation of the analytic images of the strong coupling constant powers in Minkowski (A(s;nf) and Aνglob(s)) and Euclidean (A(Q2;nf) and Aνglob(Q2)) domains at arbitrary energy scales (s and Q2, correspondingly) for both schemes — with fixed number of active flavours nf=3,4,5,6 and the global one with taking into account all heavy-quark thresholds. These singularity-free couplings are inevitable elements of Analytic Perturbation Theory (APT) in QCD, proposed in [10,69,70], and its generalization — Fractional APT, suggested in [42,46,43], needed to apply the APT imperative for renormalization-group improved hadronic observables. Program summaryProgram title: FAPT Catalogue identifier: AENJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENJ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1985 No. of bytes in distributed program, including test data, etc.: 1895776 Distribution format: tar.gz Programming language: Mathematica. Computer: Any work-station or PC where Mathematica is running. Operating system: Windows XP, Mathematica (versions 5 and 7). Classification: 11.5. Nature of problem: The values of analytic images A(Q2) and A(s) of the QCD running coupling powers αsν(Q2) in Euclidean and Minkowski regions, correspondingly, are determined through the spectral representation in the QCD Analytic Perturbation Theory (APT). In the program FAPT we collect all relevant formulas and various procedures which allow for a convenient evaluation of A(Q2) and A(s) using numerical integrations of the relevant spectral densities. Solution method: FAPT uses Mathematica functions to calculate different spectral densities and then performs numerical integration of these spectral integrals

  4. Galaxy power spectrum in redshift space: Combining perturbation theory with the halo model

    NASA Astrophysics Data System (ADS)

    Okumura, Teppei; Hand, Nick; Seljak, Uroš; Vlah, Zvonimir; Desjacques, Vincent

    2015-11-01

    Theoretical modeling of the redshift-space power spectrum of galaxies is crucially important to correctly extract cosmological information from galaxy redshift surveys. The task is complicated by the nonlinear biasing and redshift space distortion (RSD) effects, which change with halo mass, and by the wide distribution of halo masses and their occupations by galaxies. One of the main modeling challenges is the existence of satellite galaxies that have both radial distribution inside the halos and large virial velocities inside halos, a phenomenon known as the Finger-of-God (FoG) effect. We present a model for the redshift-space power spectrum of galaxies in which we decompose a given galaxy sample into central and satellite galaxies and relate different contributions to the power spectrum to 1-halo and 2-halo terms in a halo model. Our primary goal is to ensure that any parameters that we introduce have physically meaningful values, and are not just fitting parameters. For the lowest order 2-halo terms we use the previously developed RSD modeling of halos in the context of distribution function and perturbation theory approach. This term needs to be multiplied by the effect of radial distances and velocities of satellites inside the halo. To this one needs to add the 1-halo terms, which are nonperturbative. We show that the real space 1-halo terms can be modeled as almost constant, with the finite extent of the satellites inside the halo inducing a small k2R2 term over the range of scales of interest, where R is related to the size of the halo given by its halo mass. We adopt a similar model for FoG in redshift space, ensuring that FoG velocity dispersion is related to the halo mass. For FoG k2 type expansions do not work over the range of scales of interest and FoG resummation must be used instead. We test several simple damping functions to model the velocity dispersion FoG effect. Applying the formalism to mock galaxies modeled after the "CMASS" sample of the

  5. Internal models in sensorimotor integration: perspectives from adaptive control theory.

    PubMed

    Tin, Chung; Poon, Chi-Sang

    2005-09-01

    Internal models and adaptive controls are empirical and mathematical paradigms that have evolved separately to describe learning control processes in brain systems and engineering systems, respectively. This paper presents a comprehensive appraisal of the correlation between these paradigms with a view to forging a unified theoretical framework that may benefit both disciplines. It is suggested that the classic equilibrium-point theory of impedance control of arm movement is analogous to continuous gain-scheduling or high-gain adaptive control within or across movement trials, respectively, and that the recently proposed inverse internal model is akin to adaptive sliding control originally for robotic manipulator applications. Modular internal models' architecture for multiple motor tasks is a form of multi-model adaptive control. Stochastic methods, such as generalized predictive control, reinforcement learning, Bayesian learning and Hebbian feedback covariance learning, are reviewed and their possible relevance to motor control is discussed. Possible applicability of a Luenberger observer and an extended Kalman filter to state estimation problems-such as sensorimotor prediction or the resolution of vestibular sensory ambiguity-is also discussed. The important role played by vestibular system identification in postural control suggests an indirect adaptive control scheme whereby system states or parameters are explicitly estimated prior to the implementation of control. This interdisciplinary framework should facilitate the experimental elucidation of the mechanisms of internal models in sensorimotor systems and the reverse engineering of such neural mechanisms into novel brain-inspired adaptive control paradigms in future.

  6. Liquid theory with high accuracy and broad applicability: Coupling parameter series expansion and non hard sphere perturbation strategy

    NASA Astrophysics Data System (ADS)

    Zhou, Shiqi

    2011-12-01

    Thermodynamic and structural properties of liquids are of fundamental interest in physics, chemistry, and biology, and perturbation approach has been fundamental to liquid theoretical approaches since the dawn of modern statistical mechanics and remains so to this day. Although thermodynamic perturbation theory (TPT) is widely used in the chemical physics community, one of the most popular versions of the TPT, i.e. Zwanzig (Zwanzig, R. W. J. Chem. Phys. 1954, 22, 1420-1426) 1st-order high temperature series expansion (HTSE) TPT and its 2nd-order counterpart under a macroscopic compressibility approximation of Barker-Henderson (Barker, J. A.; Henderson, D. J. Chem. Phys. 1967, 47, 2856-2861), have some serious shortcomings: (i) the nth-order term of the HTSE is involved with reference fluid distribution functions of order up to 2n, and the higher-order terms hence progressively become more complicated and numerically inaccessible; (ii) the performance of the HTSE rapidly deteriorates and the calculated results become even qualitatively incorrect as the temperature of interest decreases. This account deals with the developments that we have made over the last five years or so to advance a coupling parameter series expansion (CPSE) and a non hard sphere (HS) perturbation strategy that has scored some of its greatest successes in overcoming the above-mentioned difficulties. In this account (i) we expatiate on implementation details of our schemes: how input information indispensable to high-order truncation of the CPSE in both the HS and non HS perturbation schemes is calculated by an Ornstein-Zernike integral equation theory; how high-order thermodynamic quantities, such as critical parameters and excess constant volume heat capacity, are extracted from the resulting excess Helmholtz free energy with irregular and inevitable numerical errors; how to select reference potential in the non HS perturbation scheme. (ii) We give a quantitative analysis on why convergence

  7. A proposed adaptive step size perturbation and observation maximum power point tracking algorithm based on photovoltaic system modeling

    NASA Astrophysics Data System (ADS)

    Huang, Yu

    Solar energy becomes one of the major alternative renewable energy options for its huge abundance and accessibility. Due to the intermittent nature, the high demand of Maximum Power Point Tracking (MPPT) techniques exists when a Photovoltaic (PV) system is used to extract energy from the sunlight. This thesis proposed an advanced Perturbation and Observation (P&O) algorithm aiming for relatively practical circumstances. Firstly, a practical PV system model is studied with determining the series and shunt resistances which are neglected in some research. Moreover, in this proposed algorithm, the duty ratio of a boost DC-DC converter is the object of the perturbation deploying input impedance conversion to achieve working voltage adjustment. Based on the control strategy, the adaptive duty ratio step size P&O algorithm is proposed with major modifications made for sharp insolation change as well as low insolation scenarios. Matlab/Simulink simulation for PV model, boost converter control strategy and various MPPT process is conducted step by step. The proposed adaptive P&O algorithm is validated by the simulation results and detail analysis of sharp insolation changes, low insolation condition and continuous insolation variation.

  8. A Closed-loop Brain Computer Interface to a Virtual Reality Avatar: Gait Adaptation to Visual Kinematic Perturbations

    PubMed Central

    Luu, Trieu Phat; He, Yongtian; Brown, Samuel; Nakagome, Sho; Contreras-Vidal, Jose L.

    2016-01-01

    The control of human bipedal locomotion is of great interest to the field of lower-body brain computer interfaces (BCIs) for rehabilitation of gait. While the feasibility of a closed-loop BCI system for the control of a lower body exoskeleton has been recently shown, multi-day closed-loop neural decoding of human gait in a virtual reality (BCI-VR) environment has yet to be demonstrated. In this study, we propose a real-time closed-loop BCI that decodes lower limb joint angles from scalp electroencephalography (EEG) during treadmill walking to control the walking movements of a virtual avatar. Moreover, virtual kinematic perturbations resulting in asymmetric walking gait patterns of the avatar were also introduced to investigate gait adaptation using the closed-loop BCI-VR system over a period of eight days. Our results demonstrate the feasibility of using a closed-loop BCI to learn to control a walking avatar under normal and altered visuomotor perturbations, which involved cortical adaptations. These findings have implications for the development of BCI-VR systems for gait rehabilitation after stroke and for understanding cortical plasticity induced by a closed-loop BCI system. PMID:27713915

  9. exciting: a full-potential all-electron package implementing density-functional theory and many-body perturbation theory

    NASA Astrophysics Data System (ADS)

    Gulans, Andris; Kontur, Stefan; Meisenbichler, Christian; Nabok, Dmitrii; Pavone, Pasquale; Rigamonti, Santiago; Sagmeister, Stephan; Werner, Ute; Draxl, Claudia

    2014-09-01

    Linearized augmented planewave methods are known as the most precise numerical schemes for solving the Kohn-Sham equations of density-functional theory (DFT). In this review, we describe how this method is realized in the all-electron full-potential computer package, exciting. We emphasize the variety of different related basis sets, subsumed as (linearized) augmented planewave plus local orbital methods, discussing their pros and cons and we show that extremely high accuracy (microhartrees) can be achieved if the basis is chosen carefully. As the name of the code suggests, exciting is not restricted to ground-state calculations, but has a major focus on excited-state properties. It includes time-dependent DFT in the linear-response regime with various static and dynamical exchange-correlation kernels. These are preferably used to compute optical and electron-loss spectra for metals, molecules and semiconductors with weak electron-hole interactions. exciting makes use of many-body perturbation theory for charged and neutral excitations. To obtain the quasi-particle band structure, the GW approach is implemented in the single-shot approximation, known as G0W0. Optical absorption spectra for valence and core excitations are handled by the solution of the Bethe-Salpeter equation, which allows for the description of strongly bound excitons. Besides these aspects concerning methodology, we demonstrate the broad range of possible applications by prototypical examples, comprising elastic properties, phonons, thermal-expansion coefficients, dielectric tensors and loss functions, magneto-optical Kerr effect, core-level spectra and more.

  10. Exciting: a full-potential all-electron package implementing density-functional theory and many-body perturbation theory.

    PubMed

    Gulans, Andris; Kontur, Stefan; Meisenbichler, Christian; Nabok, Dmitrii; Pavone, Pasquale; Rigamonti, Santiago; Sagmeister, Stephan; Werner, Ute; Draxl, Claudia

    2014-09-10

    Linearized augmented planewave methods are known as the most precise numerical schemes for solving the Kohn-Sham equations of density-functional theory (DFT). In this review, we describe how this method is realized in the all-electron full-potential computer package, exciting. We emphasize the variety of different related basis sets, subsumed as (linearized) augmented planewave plus local orbital methods, discussing their pros and cons and we show that extremely high accuracy (microhartrees) can be achieved if the basis is chosen carefully. As the name of the code suggests, exciting is not restricted to ground-state calculations, but has a major focus on excited-state properties. It includes time-dependent DFT in the linear-response regime with various static and dynamical exchange-correlation kernels. These are preferably used to compute optical and electron-loss spectra for metals, molecules and semiconductors with weak electron-hole interactions. exciting makes use of many-body perturbation theory for charged and neutral excitations. To obtain the quasi-particle band structure, the GW approach is implemented in the single-shot approximation, known as G(0)W(0). Optical absorption spectra for valence and core excitations are handled by the solution of the Bethe-Salpeter equation, which allows for the description of strongly bound excitons. Besides these aspects concerning methodology, we demonstrate the broad range of possible applications by prototypical examples, comprising elastic properties, phonons, thermal-expansion coefficients, dielectric tensors and loss functions, magneto-optical Kerr effect, core-level spectra and more. PMID:25135665

  11. Molecular g-tensors from analytical response theory and quasi-degenerate perturbation theory in the framework of complete active space self-consistent field method

    NASA Astrophysics Data System (ADS)

    Nguyen Lan, Tran; Chalupský, Jakub; Yanai, Takeshi

    2015-07-01

    The molecular g-tensor is an important spectroscopic parameter provided by electron para magnetic resonance (EPR) measurement and often needs to be interpreted using computational methods. Here, we present two new implementations based on the first-order and second-order perturbation theories to calculate the g-tensors within the complete-active space self-consistent field (CASSCF) wave function model. In the first-order method, the quasi-degenerate perturbation theory (QDPT) is employed for constructing relativistic CASSCF states perturbed with the spin-orbit coupling operator, which is described effectively in one-electron form with the flexible nuclear screening spin-orbit approximation introduced recently by us. The second-order method is a newly reported approach built upon the linear response theory which accounts for the perturbation with respect to external magnetic field. It is implemented with the coupled-perturbed CASSCF (CP-CASSCF) approach, which provides an equivalent of untruncated sum-over-states expansion. The comparison of the performances between the first-order and second-order methods is shown for various molecules containing light to heavy elements, highlighting their relative strength and weakness. The formulations of QDPT and CP-CASSCF approaches as well as the derivation of the second-order Douglas-Kroll-Hess picture change of Zeeman operators are given in detail.

  12. Accuracy of second order perturbation theory in the polaron and variational polaron frames

    NASA Astrophysics Data System (ADS)

    Lee, Chee Kong; Moix, Jeremy; Cao, Jianshu

    2012-05-01

    In the study of open quantum systems, the polaron transformation has recently attracted a renewed interest as it offers the possibility to explore the strong system-bath coupling regime. Despite this interest, a clear and unambiguous analysis of the regimes of validity of the polaron transformation is still lacking. Here we provide such a benchmark, comparing second order perturbation theory results in the original untransformed frame, the polaron frame, and the variational extension with numerically exact path integral calculations of the equilibrium reduced density matrix. Equilibrium quantities allow a direct comparison of the three methods without invoking any further approximations as is usually required in deriving master equations. It is found that the second order results in the original frame are accurate for weak system-bath coupling; the results deteriorate when the bath cut-off frequency decreases. The full polaron results are accurate for the entire range of coupling for a fast bath but only in the strong coupling regime for a slow bath. The variational method is capable of interpolating between these two methods and is valid over a much broader range of parameters.

  13. Perturbation theory for non-spherical fluids based on discretization of the interactions

    NASA Astrophysics Data System (ADS)

    Gámez, Francisco; Benavides, Ana Laura

    2013-03-01

    An extension of the discrete perturbation theory [A. L. Benavides and A. Gil-Villegas, Mol. Phys. 97(12), 1225 (1999), 10.1080/00268979909482924] accounting for non-spherical interactions is presented. An analytical expression for the Helmholtz free energy for an equivalent discrete potential is given as a function of density, temperature, and intermolecular parameters with implicit shape dependence. The presented procedure is suitable for the description of the thermodynamics of general intermolecular potential models of arbitrary shape. The overlap and dispersion forces are represented by a discrete potential formed by a sequence of square-well and square-shoulders potentials of shape-dependent widths. By varying the intermolecular parameters through their geometrical dependence, some illustrative cases of square-well spherocylinders and Kihara fluids are considered, and their vapor-liquid phase diagrams are tested against available simulation data. It is found that this theoretical approach is able to reproduce qualitatively and quantitatively well the Monte Carlo data for the selected potentials, except near the critical region.

  14. Baryon acoustic oscillations in 2D: Modeling redshift-space power spectrum from perturbation theory

    NASA Astrophysics Data System (ADS)

    Taruya, Atsushi; Nishimichi, Takahiro; Saito, Shun

    2010-09-01

    We present an improved prescription for the matter power spectrum in redshift space taking proper account of both nonlinear gravitational clustering and redshift distortion, which are of particular importance for accurately modeling baryon acoustic oscillations (BAOs). Contrary to the models of redshift distortion phenomenologically introduced but frequently used in the literature, the new model includes the corrections arising from the nonlinear coupling between the density and velocity fields associated with two competitive effects of redshift distortion, i.e., Kaiser and Finger-of-God effects. Based on the improved treatment of perturbation theory for gravitational clustering, we compare our model predictions with the monopole and quadrupole power spectra of N-body simulations, and an excellent agreement is achieved over the scales of BAOs. Potential impacts on constraining dark energy and modified gravity from the redshift-space power spectrum are also investigated based on the Fisher-matrix formalism, particularly focusing on the measurements of the Hubble parameter, angular diameter distance, and growth rate for structure formation. We find that the existing phenomenological models of redshift distortion produce a systematic error on measurements of the angular diameter distance and Hubble parameter by 1%-2% , and the growth-rate parameter by ˜5%, which would become non-negligible for future galaxy surveys. Correctly modeling redshift distortion is thus essential, and the new prescription for the redshift-space power spectrum including the nonlinear corrections can be used as an accurate theoretical template for anisotropic BAOs.

  15. Analytical energy gradients for second-order multireference perturbation theory using density fitting.

    PubMed

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

    2013-03-14

    We present algorithms for computing analytical energy gradients for multi-configuration self-consistent field methods and partially internally contracted complete active space second-order perturbation theory (CASPT2) using density fitting (DF). Our implementation is applicable to both single-state and multi-state CASPT2 analytical gradients. The accuracy of the new methods is demonstrated for structures and excitation energies of valence and Rydberg states of pyrrole, as well as for structures and adiabatic singlet-triplet energy splittings for the hydro-, the O,O(')-formato-, and the N,N(')-diiminato-copper-dioxygen complexes. It is shown that the effects of density fitting on optimized structures and relative energies are negligible. For cases in which the total cost is dominated by the integral evaluations and transformations, the DF-CASPT2 gradient calculations are found to be faster than the corresponding conventional calculations by typically a factor of three to five using triple-ζ basis sets, and by about a factor of ten using quadruple-ζ basis sets.

  16. Mechanical properties of zirconium alloys and zirconium hydrides predicted from density functional perturbation theory

    DOE PAGES

    Weck, Philippe F.; Kim, Eunja; Tikare, Veena; Mitchell, John A.

    2015-10-13

    Here, the elastic properties and mechanical stability of zirconium alloys and zirconium hydrides have been investigated within the framework of density functional perturbation theory. Results show that the lowest-energy cubic Pn-3m with combining macron]m polymorph of δ-ZrH1.5 does not satisfy all the Born requirements for mechanical stability, unlike its nearly degenerate tetragonal P42/mcm polymorph. Elastic moduli predicted with the Voigt–Reuss–Hill approximations suggest that mechanical stability of α-Zr, Zr-alloy and Zr-hydride polycrystalline aggregates is limited by the shear modulus. According to both Pugh's and Poisson's ratios, α-Zr, Zr-alloy and Zr-hydride polycrystalline aggregates can be considered ductile. The Debye temperatures predicted formore » γ-ZrH, δ-ZrH1.5 and ε-ZrH2 are θD = 299.7, 415.6 and 356.9 K, respectively, while θD = 273.6, 284.2, 264.1 and 257.1 K for the α-Zr, Zry-4, ZIRLO and M5 matrices, i.e. suggesting that Zry-4 possesses the highest micro-hardness among Zr matrices.« less

  17. Baryon mass splittings and strong CP violation in SU(3) chiral perturbation theory

    DOE PAGES

    de Vries, Jordy; Mereghetti, Emanuele; Walker-Loud, Andre

    2015-10-08

    Here, we study SU(3) flavor-breaking corrections to the relation between the octet baryon masses and the nucleon-meson CP-violating interactions induced by the QCD θ¯ term. We work within the framework of SU(3) chiral perturbation theory and work through next-to-next-to-leading order in the SU(3) chiral expansion, which is O(m2q). At lowest order, the CP-odd couplings induced by the QCD θ¯ term are determined by mass splittings of the baryon octet, the classic result of Crewther et al. [Phys. Lett. B 88, 123 (1979)]. We show that for each isospin-invariant CP-violating nucleon-meson interaction there exists one relation that is respected by loopmore » corrections up to the order we work, while other leading-order relations are violated. With these relations we extract a precise value of the pion-nucleon coupling g¯0 by using recent lattice QCD evaluations of the proton-neutron mass splitting. In addition, we derive semiprecise values for CP-violating coupling constants between heavier mesons and nucleons with ~30% uncertainty and discuss their phenomenological impact on electric dipole moments of nucleons and nuclei.« less

  18. Muon capture by a proton in heavy baryon chiral perturbation theory

    SciTech Connect

    Fearing, H.W.; Lewis, R.; Mobed, N.; Scherer, S.

    1997-08-01

    The matrix element for muon capture by a proton is calculated to O(p{sup 3}) within heavy baryon chiral perturbation theory using the new O(p{sup 3}) Lagrangian of Ecker and Moj{hacek z}i{hacek s}. External nucleon fields are renormalized using the appropriate definition of the wave function renormalization factor Z{sub N}. Our expression for Z{sub N} differs somewhat from that found in the existing literature, but is the one which is consistent with the Lagrangian we use and the one which ensures, within our approach, the nonrenormalization of the vector coupling as required by the conserved vector current. Expressions for the standard muon capture form factors are derived and compared to experimental data and we determine three of the coefficients of the Ecker-Moj{hacek z}i{hacek s} Lagrangian, namely, b{sub 7}, b{sub 19}, and b{sub 23}. {copyright} {ital 1997} {ital The American Physical Society}

  19. Off-shell electromagnetic form factors of pions and kaons in chiral perturbation theory

    SciTech Connect

    Rudy, T.E.; Fearing, H.W.; Scherer, S. )

    1994-07-01

    The off-shell electromagnetic vertex of a (pseudo)scalar particle contains, in general, two form factors [ital F] and [ital G] which depend, in addition to the squared momentum transfer, on the invariant masses associated with the initial and final legs of the vertex. Chiral perturbation theory to one loop is used to calculate the off-shell form factors of pions and kaons. The formalism of Gasser and Leutwyler, which was previously used to calculate the on-shell limit of the form factor [ital F], is extended to accommodate the most general form for off-shell Green's functions in the pseudoscalar meson sector. We find that chiral symmetry predicts that the form factors [ital F] of the charged pions and kaons go off-shell in the same way, i.e., the off-shell slope at the real photon point is given by the same new phenomenological constant [beta][sub 1]. Furthermore, it is shown that at order [ital p][sup 4] the form factor [ital F] of the [ital K][sup 0] does not show any off-shell dependence. The form factors [ital G] are all related to the form factors [ital F] in the correct fashion as required by the Ward-Takahashi identity. Numerical results for different off-shell kinematics are presented.

  20. Field transformations and the classical equation of motion in chiral perturbation theory

    SciTech Connect

    Scherer, S.; Fearing, H.W.

    1995-12-01

    The construction of effective Lagrangians commonly involves the application of the ``classical equation of motion`` to eliminate redundant structures and thus generate the minimal number of independent terms. We investigate this procedure in the framework of chiral perturbation theory with particular emphasis on the new features which appear at {ital O}({ital p}{sup 6}). The use of the ``classical equation of motion`` is interpreted in terms of field transformations. Such an interpretation is crucial if one wants to bring a given Lagrangian into a canonical form with a minimal number of terms. We emphasize that the application of field transformations leads to a modification of the coefficients of higher-order terms as well as eliminating structures, or what is equivalent, expressing certain structures in terms of already known different structures. This will become relevant once one considers the problem of expressing in canonical form a model effective interaction containing terms beyond next-to-leading order, i.e., beyond {ital O}({ital p}{sup 4}). In such circumstances the naive application of the clasical equation of motion to simply drop terms, as is commonly done at lowest order, leads to subtle errors, which we discuss.

  1. Baryon acoustic oscillations in 2D: Modeling redshift-space power spectrum from perturbation theory

    SciTech Connect

    Taruya, Atsushi; Nishimichi, Takahiro; Saito, Shun

    2010-09-15

    We present an improved prescription for the matter power spectrum in redshift space taking proper account of both nonlinear gravitational clustering and redshift distortion, which are of particular importance for accurately modeling baryon acoustic oscillations (BAOs). Contrary to the models of redshift distortion phenomenologically introduced but frequently used in the literature, the new model includes the corrections arising from the nonlinear coupling between the density and velocity fields associated with two competitive effects of redshift distortion, i.e., Kaiser and Finger-of-God effects. Based on the improved treatment of perturbation theory for gravitational clustering, we compare our model predictions with the monopole and quadrupole power spectra of N-body simulations, and an excellent agreement is achieved over the scales of BAOs. Potential impacts on constraining dark energy and modified gravity from the redshift-space power spectrum are also investigated based on the Fisher-matrix formalism, particularly focusing on the measurements of the Hubble parameter, angular diameter distance, and growth rate for structure formation. We find that the existing phenomenological models of redshift distortion produce a systematic error on measurements of the angular diameter distance and Hubble parameter by 1%-2%, and the growth-rate parameter by {approx}5%, which would become non-negligible for future galaxy surveys. Correctly modeling redshift distortion is thus essential, and the new prescription for the redshift-space power spectrum including the nonlinear corrections can be used as an accurate theoretical template for anisotropic BAOs.

  2. Linear perturbation theory of reionization in position space: Cosmological radiative transfer along the light cone

    NASA Astrophysics Data System (ADS)

    Mao, Yi; D'Aloisio, Anson; Wandelt, Benjamin D.; Zhang, Jun; Shapiro, Paul R.

    2015-04-01

    The linear perturbation theory of inhomogeneous reionization (LPTR) has been developed as an analytical tool for predicting the global ionized fraction and large-scale power spectrum of ionized density fluctuations during reionization. In the original formulation of the LPTR, the ionization balance and radiative transfer equations are linearized and solved in Fourier space. However, the LPTR's approximation to the full solution of the radiative transfer equation is not straightforward to interpret, since the latter is most intuitively conceptualized in position space. To bridge the gap between the LPTR and the language of numerical radiative transfer, we present a new, equivalent, position-space formulation of the LPTR that clarifies the approximations it makes and facilitates its interpretation. We offer a comparison between the LPTR and the excursion-set model of reionization (ESMR), and demonstrate the built-in capability of the LPTR to explore a wide range of reionization scenarios, and to go beyond the ESMR in exploring scenarios involving X-rays.

  3. Development of Generalized Perturbation Theory Capability within the SCALE Code Package

    SciTech Connect

    Jessee, Matthew Anderson; Williams, Mark L; DeHart, Mark D

    2009-01-01

    Computational capability has been developed to calculate sensitivity coefficients of generalized responses with respect to cross-section data in the SCALE code system. The focus of this paper is the implementation of generalized perturbation theory (GPT) for one-dimensional and two-dimensional deterministic neutron transport calculations. GPT is briefly summarized for computing sensitivity coefficients for reaction rate ratio responses within the existing framework of the TSUNAMI sensitivity and uncertainty (S/U) analysis code package in SCALE. GPT provides the capability to analyze generalized responses related to reactor analysis, such as homogenized cross-sections, relative powers, and conversion ratios, as well as measured experimental parameters such as 28 (epithermal/thermal 238U capture rates) in thermal benchmarks and fission ratios such as 239Pu(n,f)/235U(n,f) in fast benchmarks. The S/U analysis of these experimental integral responses can be used to augment the existing TSUNAMI S/U analysis capabilities for system similarity assessment and data adjustment. S/U analysis is provided for boiling water reactor pin cell as part of the Organization for Economic Cooperation and Development Uncertainty Analysis in Modeling benchmark.

  4. Mechanical properties of zirconium alloys and zirconium hydrides predicted from density functional perturbation theory

    SciTech Connect

    Weck, Philippe F.; Kim, Eunja; Tikare, Veena; Mitchell, John A.

    2015-10-13

    Here, the elastic properties and mechanical stability of zirconium alloys and zirconium hydrides have been investigated within the framework of density functional perturbation theory. Results show that the lowest-energy cubic Pn-3m with combining macron]m polymorph of δ-ZrH1.5 does not satisfy all the Born requirements for mechanical stability, unlike its nearly degenerate tetragonal P42/mcm polymorph. Elastic moduli predicted with the Voigt–Reuss–Hill approximations suggest that mechanical stability of α-Zr, Zr-alloy and Zr-hydride polycrystalline aggregates is limited by the shear modulus. According to both Pugh's and Poisson's ratios, α-Zr, Zr-alloy and Zr-hydride polycrystalline aggregates can be considered ductile. The Debye temperatures predicted for γ-ZrH, δ-ZrH1.5 and ε-ZrH2 are θD = 299.7, 415.6 and 356.9 K, respectively, while θD = 273.6, 284.2, 264.1 and 257.1 K for the α-Zr, Zry-4, ZIRLO and M5 matrices, i.e. suggesting that Zry-4 possesses the highest micro-hardness among Zr matrices.

  5. A Generalized Iterative Perturbation Theory for Multi-Orbital Lattice Model

    NASA Astrophysics Data System (ADS)

    Dasari, Nagamalleswararao; Vidhyadhiraja, N. S.; Chen, Kuang-Shing; Feng, Sheng; Moreno, Juana; Jarrell, Mark

    2013-03-01

    An efficient and accurate quantum impurity solver is needed for solving multi-orbital models by the dynamical mean field approximation. Impurity solvers such as quantum Monte Carlo(QMC) and exact diagonalization(ED) suffer from some limitations even though they are numerically exact, while the approximate method iterative perturbation theory(IPT) is free from these limitations. An IPT algorithm for non-degenerate multi-orbital lattice models is not available. Here we developed a generalized IPT for multi-orbital lattice model, we denote it as M-IPT. It can be applied for degenerate multi- orbital and single-orbital lattice models. As a first test we benchmarked the M-IPT results in the single-band Hubbard model case with the weak-coupling continuous-time Monte Carlo(W-CTQMC) results. We got good agreement between two methods. We are currently benchmarking the M-IPT results for the non-degenerate multi-orbital Hubbard model with the W-CTQMC results.

  6. Baryon mass splittings and strong CP violation in SU(3) chiral perturbation theory

    DOE PAGES

    de Vries, Jordy; Mereghetti, Emanuele; Walker-Loud, Andre P.

    2015-10-08

    We study SU(3) flavor breaking corrections to the relation between the octet baryon masses and the nucleon-meson CP-violating interactions induced by the QCD theta term. We also work within the framework of SU(3) chiral perturbation theory and work through next-to-next-to-leading order in the SU(3) chiral expansion, which is O(m2q). At lowest order, the CP-odd couplings induced by the QCD θ- term are determined by mass splittings of the baryon octet, the classic result of Crewther et al. We show that for each isospin-invariant CP-violating nucleon-meson interaction there exists one relation which is respected by loop corrections up to the ordermore » we work, while other leading-order relations are violated. With these relations we extract a precise value of the pion-nucleon coupling g-0 by using recent lattice QCD evaluations of the proton-neutron mass splitting. Additionally, we derive semi-precise values for CP-violating coupling constants between heavier mesons and nucleons and discuss their phenomenological impact on electric dipole moments of nucleons and nuclei.« less

  7. Partially resummed perturbation theory for multiple Andreev reflections in a short three-terminal Josephson junction

    NASA Astrophysics Data System (ADS)

    Mélin, Régis; Feinberg, Denis; Douçot, Benoît

    2016-03-01

    In a transparent three-terminal Josephson junction, modeling nonequilibrium transport is numerically challenging, owing to the interplay between multiple Andreev reflection (MAR) thresholds and multipair resonances in the pair current. An approximate method, coined as "partially resummed perturbation theory in the number of nonlocal Green's functions", is presented that can be operational on a standard computer and demonstrates compatibility with results existing in the literature. In a linear structure made of two neighboring interfaces (with intermediate transparency) connected by a central superconductor, tunneling through each of the interfaces separately is taken into account to all orders. On the contrary, nonlocal processes connecting the two interfaces are accounted for at the lowest relevant order. This yields logarithmically divergent contributions at the gap edges, which are sufficient as a semi-quantitative description. The method is able to describe the current in the full two-dimensional voltage range, including commensurate as well as incommensurate values. The results found for the multipair (for instance quartet) current-phase characteristics as well as the MAR thresholds are compatible with previous results. At intermediate transparency, the multipair critical current is much larger than the background MAR current, which supports an experimental observation of the quartet and multipair resonances. The paper provides a proof of principle for addressing in the future the interplay between quasiparticles and multipairs in four-terminal structures.

  8. Testing higher-order Lagrangian perturbation theory against numerical simulations. 2: Hierarchical models

    NASA Technical Reports Server (NTRS)

    Melott, A. L.; Buchert, T.; Weib, A. G.

    1995-01-01

    We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of scales. The Lagrangian theory of gravitational instability of Friedmann-Lemaitre cosmogonies is compared with numerical simulations. We study the dynamics of hierarchical models as a second step. In the first step we analyzed the performance of the Lagrangian schemes for pancake models, the difference being that in the latter models the initial power spectrum is truncated. This work probed the quasi-linear and weakly non-linear regimes. We here explore whether the results found for pancake models carry over to hierarchical models which are evolved deeply into the non-linear regime. We smooth the initial data by using a variety of filter types and filter scales in order to determine the optimal performance of the analytical models, as has been done for the 'Zel'dovich-approximation' - hereafter TZA - in previous work. We find that for spectra with negative power-index the second-order scheme performs considerably better than TZA in terms of statistics which probe the dynamics, and slightly better in terms of low-order statistics like the power-spectrum. However, in contrast to the results found for pancake models, where the higher-order schemes get worse than TZA at late non-linear stages and on small scales, we here find that the second-order model is as robust as TZA, retaining the improvement at later stages and on smaller scales. In view of these results we expect that the second-order truncated Lagrangian model is especially useful for the modelling of standard dark matter models such as Hot-, Cold-, and Mixed-Dark-Matter.

  9. Locally adapted fish populations maintain small-scale genetic differentiation despite perturbation by a catastrophic flood event

    PubMed Central

    2010-01-01

    Background Local adaptation to divergent environmental conditions can promote population genetic differentiation even in the absence of geographic barriers and hence, lead to speciation. Perturbations by catastrophic events, however, can distort such parapatric ecological speciation processes. Here, we asked whether an exceptionally strong flood led to homogenization of gene pools among locally adapted populations of the Atlantic molly (Poecilia mexicana, Poeciliidae) in the Cueva del Azufre system in southern Mexico, where two strong environmental selection factors (darkness within caves and/or presence of toxic H2S in sulfidic springs) drive the diversification of P. mexicana. Nine nuclear microsatellites as well as heritable female life history traits (both as a proxy for quantitative genetics and for trait divergence) were used as markers to compare genetic differentiation, genetic diversity, and especially population mixing (immigration and emigration) before and after the flood. Results Habitat type (i.e., non-sulfidic surface, sulfidic surface, or sulfidic cave), but not geographic distance was the major predictor of genetic differentiation. Before and after the flood, each habitat type harbored a genetically distinct population. Only a weak signal of individual dislocation among ecologically divergent habitat types was uncovered (with the exception of slightly increased dislocation from the Cueva del Azufre into the sulfidic creek, El Azufre). By contrast, several lines of evidence are indicative of increased flood-induced dislocation within the same habitat type, e.g., between different cave chambers of the Cueva del Azufre. Conclusions The virtual absence of individual dislocation among ecologically different habitat types indicates strong natural selection against migrants. Thus, our current study exemplifies that ecological speciation in this and other systems, in which extreme environmental factors drive speciation, may be little affected by temporary

  10. A synthesis theory for self-oscillating adaptive systems /SOAS/

    NASA Technical Reports Server (NTRS)

    Horowitz, I.; Smay, J.; Shapiro, A.

    1974-01-01

    A quantitative synthesis theory is presented for the Self-Oscillating Adaptive System (SOAS), whose nonlinear element has a static, odd character with hard saturation. The synthesis theory is based upon the quasilinear properties of the SOAS to forced inputs, which permits the extension of quantitative linear feedback theory to the SOAS. A reasonable definition of optimum design is shown to be the minimization of the limit cycle frequency. The great advantages of the SOAS is its zero sensitivity to pure gain changes. However, quasilinearity and control of the limit cycle amplitude at the system output, impose additional constraints which partially or completely cancel this advantage, depending on the numerical values of the design parameters. By means of narrow-band filtering, an additional factor is introduced which permits trade-off between filter complexity and limit cycle frequency minimization.

  11. Prospects of using the second-order perturbation theory of the MP2 type in the theory of electron scattering by polyatomic molecules

    SciTech Connect

    Čársky, Petr

    2015-01-22

    So far the second-order perturbation theory has been only applied to the hydrogen molecule. No application was attempted for another molecule, probably because of technical difficulties of such calculations. The purpose of this contribution is to show that the calculations of this type are now feasible on larger polyatomic molecules even on commonly used computers.

  12. Impact of Parkinson's Disease and Dopaminergic Medication on Adaptation to Explicit and Implicit Visuomotor Perturbations

    ERIC Educational Resources Information Center

    Mongeon, David; Blanchet, Pierre; Messier, Julie

    2013-01-01

    The capacity to learn new visuomotor associations is fundamental to adaptive motor behavior. Evidence suggests visuomotor learning deficits in Parkinson's disease (PD). However, the exact nature of these deficits and the ability of dopamine medication to improve them are under-explored. Previous studies suggested that learning driven by large and…

  13. Size consistent formulations of the perturb-then-diagonalize Møller-Plesset perturbation theory correction to non-orthogonal configuration interaction

    NASA Astrophysics Data System (ADS)

    Yost, Shane R.; Head-Gordon, Martin

    2016-08-01

    In this paper we introduce two size consistent forms of the non-orthogonal configuration interaction with second-order Møller-Plesset perturbation theory method, NOCI-MP2. We show that the original NOCI-MP2 formulation [S. R. Yost, T. Kowalczyk, and T. VanVoorh, J. Chem. Phys. 193, 174104 (2013)], which is a perturb-then-diagonalize multi-reference method, is not size consistent. We also show that this causes significant errors in large systems like the linear acenes. By contrast, the size consistent versions of the method give satisfactory results for singlet and triplet excited states when compared to other multi-reference methods that include dynamic correlation. For NOCI-MP2 however, the number of required determinants to yield similar levels of accuracy is significantly smaller. These results show the promise of the NOCI-MP2 method, though work still needs to be done in creating a more consistent black-box approach to computing the determinants that comprise the many-electron NOCI basis.

  14. Size consistent formulations of the perturb-then-diagonalize Møller-Plesset perturbation theory correction to non-orthogonal configuration interaction.

    PubMed

    Yost, Shane R; Head-Gordon, Martin

    2016-08-01

    In this paper we introduce two size consistent forms of the non-orthogonal configuration interaction with second-order Møller-Plesset perturbation theory method, NOCI-MP2. We show that the original NOCI-MP2 formulation [S. R. Yost, T. Kowalczyk, and T. VanVoorh, J. Chem. Phys. 193, 174104 (2013)], which is a perturb-then-diagonalize multi-reference method, is not size consistent. We also show that this causes significant errors in large systems like the linear acenes. By contrast, the size consistent versions of the method give satisfactory results for singlet and triplet excited states when compared to other multi-reference methods that include dynamic correlation. For NOCI-MP2 however, the number of required determinants to yield similar levels of accuracy is significantly smaller. These results show the promise of the NOCI-MP2 method, though work still needs to be done in creating a more consistent black-box approach to computing the determinants that comprise the many-electron NOCI basis. PMID:27497537

  15. Twisted mass chiral perturbation theory at next-to-leading order

    NASA Astrophysics Data System (ADS)

    Sharpe, Stephen R.; Wu, Jackson M.

    2005-04-01

    We study the properties of pions in twisted mass lattice QCD (with two degenerate flavors) using chiral perturbation theory (χPT). We work to next-to-leading order (NLO) in a power-counting scheme in which mq˜aΛ2QCD, with mq the physical quark mass and a the lattice spacing. We argue that automatic O(a) improvement of physical quantities at maximal twist, which has been demonstrated in general if mq≫aΛ2QCD, holds even if mq˜aΛ2QCD, as long as one uses an appropriate nonperturbative definition of the twist angle, with the caveat that we have shown this only through NLO in our chiral expansion. We demonstrate this with explicit calculations, for arbitrary twist angle, of all pionic quantities that involve no more than a single pion in the initial and final states: masses, decay constants, form factors, and condensates, as well as the differences between alternate definitions of twist angle. We also calculate the axial and pseudoscalar form factors of the pion, quantities which violate flavor and parity, and which vanish in the continuum limit. These are of interest because they are not automatically O(a) improved at maximal twist. They allow a determination of the unknown low-energy constants introduced by discretization errors, and provide tests of the accuracy of χPT at NLO. We extend our results into the regime where mq˜a2Λ3QCD, and argue in favor of a recent proposal that automatic O(a) improvement at maximal twist remains valid in this regime.

  16. Convergence behavior of multireference perturbation theory: Forced degeneracy and optimization partitioning applied to the beryllium atom

    NASA Astrophysics Data System (ADS)

    Finley, James P.; Chaudhuri, Rajat K.; Freed, Karl F.

    1996-07-01

    High-order multireference perturbation theory is applied to the 1S states of the beryllium atom using a reference (model) space composed of the \\|1s22s2> and the \\|1s22p2> configuration-state functions (CSF's), a system that is known to yield divergent expansions using Mo/ller-Plesset and Epstein-Nesbet partitioning methods. Computations of the eigenvalues are made through 40th order using forced degeneracy (FD) partitioning and the recently introduced optimization (OPT) partitioning. The former forces the 2s and 2p orbitals to be degenerate in zeroth order, while the latter chooses optimal zeroth-order energies of the (few) most important states. Our methodology employs simple models for understanding and suggesting remedies for unsuitable choices of reference spaces and partitioning methods. By examining a two-state model composed of only the \\|1s22p2> and \\|1s22s3s> states of the beryllium atom, it is demonstrated that the full computation with 1323 CSF's can converge only if the zeroth-order energy of the \\|1s22s3s> Rydberg state from the orthogonal space lies below the zeroth-order energy of the \\|1s22p2> CSF from the reference space. Thus convergence in this case requires a zeroth-order spectral overlap between the orthogonal and reference spaces. The FD partitioning is not capable of generating this type of spectral overlap and thus yields a divergent expansion. However, the expansion is actually asymptotically convergent, with divergent behavior not displayed until the 11th order because the \\|1s22s3s> Rydberg state is only weakly coupled with the \\|1s22p2> CSF and because these states are energetically well separated in zeroth order. The OPT partitioning chooses the correct zeroth-order energy ordering and thus yields a convergent expansion that is also very accurate in low orders compared to the exact solution within the basis.

  17. Symmetry Beyond Perturbation Theory: Floppy Molecules and Rotation-Vibration States

    NASA Astrophysics Data System (ADS)

    Schmiedt, Hanno; Schlemmer, Stephan; Jensen, Per

    2015-06-01

    In the customary approach to the theoretical description of the nuclear motion in molecules, the molecule is seen as a near-static structure rotating in space. Vibrational motion causing small structural deformations induces a perturbative treatment of the rotation-vibration interaction, which fails in fluxional molecules, where all vibrational motions are large compared to the linear extension of the molecule. An example is protonated methane (CH_5^+). For this molecule, customary theory fails to simulate reliably even the low-energy spectrum. Within the traditional view of rotation and vibration being near-separable, rotational and vibrational wavefunctions can be symmetry classified separately in the molecular symmetry (MS) group. In the present contribution we discuss a fundamental group theoretical approach to the problem of determining the symmetries of molecular rotation-vibration states. We will show that all MS groups discussed so far are subgroups of the special orthogonal group in three dimensions SO(3) This leads to a group theoretical foundation of the technique of equivalent rotations. The MS group of protonated methane (G240) represents, to the best of our knowledge, the first example of an MS group which is not a subgroup of SO(3) (nor of O(3) nor of SU(2)). Because of this, a separate symmetry classification of vibrational and rotational wavefunctions becomes impossible in this MS group, consistent with the fact that a decoupling of vibrational and rotational motion is impossible. We want to discuss the consequences of this. In conclusion, we show that the prototypical floppy molecule CH_5^+ represents a new class of molecules, where usual group theoretical methods for determining selection rules and spectral assignments fail so that new methods have to be developed. P. Kumar and D. Marx, Physical Chemistry Chemical Physics 8, 573 (2006) Z. Jin, B. J. Braams, and J. M. Bowman, The Journal of Physical Chemistry A 110, 1569 (2006) A. S. Petit, J. E

  18. Nuclear structure with accurate chiral perturbation theory nucleon-nucleon potential: Application to 6Li and 10B

    SciTech Connect

    Navratil, P; Caurier, E

    2003-10-14

    The authors calculate properties of A = 6 system using the accurate charge-dependent nucleon-nucleon (NN) potential at fourth order of chiral perturbation theory. By application of the ab initio no-core shell model (NCSM) and a variational calculation in the harmonic oscillator basis with basis size up to 16 {h_bar}{Omega} they obtain the {sup 6}Li binding energy of 28.5(5) MeV and a converged excitation spectrum. Also, they calculate properties of {sup 10}B using the same NN potential in a basis space of up to 8 {h_bar}{Omega}. The results are consistent with results obtained by standard accurate NN potentials and demonstrate a deficiency of Hamiltonians consisting of only two-body terms. At this order of chiral perturbation theory three-body terms appear. It is expected that inclusion of such terms in the Hamiltonian will improve agreement with experiment.

  19. Current distribution in a three-dimensional IC analyzed by a perturbation method. Part 1: A simple steady state theory

    NASA Technical Reports Server (NTRS)

    Edmonds, Larry D.

    1987-01-01

    The steady state current distribution in a three dimensional integrated circuit is presented. A device physics approach, based on a perturbation method rather than an equivalent lumped circuit approach, is used. The perturbation method allows the various currents to be expressed in terms of elementary solutions which are solutions to very simple boundary value problems. A Simple Steady State Theory is the subtitle because the most obvious limitation of the present version of the analysis is that all depletion region boundary surfaces are treated as equipotential surfaces. This may be an adequate approximation in some applications but it is an obvious weakness in the theory when applied to latched states. Examples that illustrate the use of these analytical methods are not given because they will be presented in detail in the future.

  20. Chiral Perturbation Theory, the 1/N_c expansion and Regge behavior determine the structure of the lightest scalar meson

    SciTech Connect

    Pelaez, J. R.; Michael R. Pennington; de Elvira, J. Ruiz; Wilson, D. J.

    2011-11-01

    The leading 1/N{sub c} behavior of Unitarized Chiral Perturbation Theory distinguishes the nature of the {rho} and the {sigma}. At one loop order the {rho} is a {bar q}q meson, while the {sigma} is not. However, semi-local duality between resonances and Regge behaviour cannot be satisfied for larger N{sub c}, if such a distinction holds. While the {sigma} at N{sub c}= 3 is inevitably dominated by its di-pion component, Unitarised Chiral Perturbation Theory beyond one loop order reveals that as N{sub c} increases above 6-8, the {sigma} has a sub-dominant {bar q}q fraction up at 1.2 GeV. Remarkably this ensures semi-local duality is fulfilled for the range of N{sub c} {approx}< 15-30, where the unitarization procedure adopted applies.

  1. Decay {omega}{sup -}{yields}{xi}{sup -}{pi}{sup +}{pi}{sup -} in chiral perturbation theory

    SciTech Connect

    Antipin, Oleg; Tandean, Jusak; Valencia, G.

    2007-11-01

    We study the decay {omega}{sup -}{yields}{xi}{sup -}{pi}{sup +}{pi}{sup -} in heavy-baryon chiral perturbation theory. At leading order, the decay is completely dominated by the {xi}*{sup 0}(1530) intermediate state, and the predicted rate and {xi}{sup -}{pi}{sup +}-mass distribution are in conflict with currently available data. It is possible to resolve this conflict by considering additional contributions at next-to-leading order.

  2. Multireference M[oslash]ller Plesset perturbation theory with non-canonical and non-orthogonal orbitals

    NASA Astrophysics Data System (ADS)

    Finley, James P.; Hirao, Kimihiko

    2000-09-01

    Using non-orthogonal secondary orbitals and non-canonical (localized) inactive and active orbitals, a second-order multireference perturbation theory is formulated, based on a complete active space self-consistent field (CASSCF) wavefunction. The equations of interest are derived from the first-order Bloch equation by using an approach based on a bi-orthogonal basis and operators expressed in second-quantization.

  3. The correlation function for density perturbations in an expanding universe. II - Nonlinear theory

    NASA Technical Reports Server (NTRS)

    Mcclelland, J.; Silk, J.

    1977-01-01

    A formalism is developed to find the two-point and higher-order correlation functions for a given distribution of sizes and shapes of perturbations which are randomly placed in three-dimensional space. The perturbations are described by two parameters such as central density and size, and the two-point correlation function is explicitly related to the luminosity function of groups and clusters of galaxies

  4. Covariant loop quantum gravity, low-energy perturbation theory, and Einstein gravity with high-curvature UV corrections

    NASA Astrophysics Data System (ADS)

    Han, Muxin

    2014-06-01

    A low-energy perturbation theory is developed from the nonperturbative framework of covariant loop quantum gravity (LQG) by employing the background-field method. The resulting perturbation theory is a two-parameter expansion in the semiclassical and low-energy regime. The two expansion parameters are the large spin and small curvature. The leading-order effective action coincides with the Regge action, which well approximates the Einstein-Hilbert action in the regime. The subleading corrections organized by the two expansion parameters give the modifications of the Regge action in the quantum and high-energy regime from LQG. The perturbation theory developed here shows for the first time that covariant LQG produces the high-curvature corrections to Einstein-Regge gravity. This result means that LQG is not a naive quantization of Einstein gravity; rather, it provides the UV modification. The result of the paper may be viewed as the first step toward understanding the UV completeness of LQG.

  5. Direct adaptive performance optimization of subsonic transports: A periodic perturbation technique

    NASA Technical Reports Server (NTRS)

    Espana, Martin D.; Gilyard, Glenn

    1995-01-01

    Aircraft performance can be optimized at the flight condition by using available redundancy among actuators. Effective use of this potential allows improved performance beyond limits imposed by design compromises. Optimization based on nominal models does not result in the best performance of the actual aircraft at the actual flight condition. An adaptive algorithm for optimizing performance parameters, such as speed or fuel flow, in flight based exclusively on flight data is proposed. The algorithm is inherently insensitive to model inaccuracies and measurement noise and biases and can optimize several decision variables at the same time. An adaptive constraint controller integrated into the algorithm regulates the optimization constraints, such as altitude or speed, without requiring and prior knowledge of the autopilot design. The algorithm has a modular structure which allows easy incorporation (or removal) of optimization constraints or decision variables to the optimization problem. An important part of the contribution is the development of analytical tools enabling convergence analysis of the algorithm and the establishment of simple design rules. The fuel-flow minimization and velocity maximization modes of the algorithm are demonstrated on the NASA Dryden B-720 nonlinear flight simulator for the single- and multi-effector optimization cases.

  6. The interface between air and water: a perturbation source eliciting adaptive behaviour in ciliates.

    PubMed

    Ricci, N; Erra, F; Russo, A; Banchetti, R

    1992-01-01

    Interference with the water-air interface, both direct (by contact with a flat, rigid surface) and indirect (by inducing a meniscus) caused the ciliated protozoa we investigated to actively collect in the water column or on the substrate directly under the area of altered surface tension. A crowding effect is observed in this "rest area" reaching plateau values within one hour after onset of the experiment. The simple experimental procedures described here induced analogous behaviour in both Paramecium caudatum (a swimmer) and Oxytricha bifaria (a crawler). The ciliates seem in this reaction to be seeking a refuge from vibrations transmitted by the free interface. Our discovery is discussed in its implications for the adaptive biology and ecology of these micro-organisms.

  7. Adaptation to Coriolis force perturbation of movement trajectory; role of proprioceptive and cutaneous somatosensory feedback.

    PubMed

    Lackner, James R; DiZio, Paul

    2002-01-01

    Subjects exposed to constant velocity rotation in a large fully-enclosed room that rotates initially make large reaching errors in pointing to targets. The paths and endpoints of their reaches are deviated in the direction of the transient lateral Coriolis forces generated by the forward velocity of their reaches. With additional reaches, subjects soon reach in straighter paths and become more accurate at landing on target even in the absence of visual feedback about their movements. Two factors contribute to this adaptation: first, muscle spindle and golgi tendon organ feedback interpreted in relation to efferent commands provide information about movement trajectory, and second, somatosensory stimulation of the fingertip at the completion of a reach provides information about the location of the fingertip relative to the torso.

  8. Adaptation to Coriolis force perturbation of movement trajectory; role of proprioceptive and cutaneous somatosensory feedback

    NASA Technical Reports Server (NTRS)

    Lackner, James R.; DiZio, Paul

    2002-01-01

    Subjects exposed to constant velocity rotation in a large fully-enclosed room that rotates initially make large reaching errors in pointing to targets. The paths and endpoints of their reaches are deviated in the direction of the transient lateral Coriolis forces generated by the forward velocity of their reaches. With additional reaches, subjects soon reach in straighter paths and become more accurate at landing on target even in the absence of visual feedback about their movements. Two factors contribute to this adaptation: first, muscle spindle and golgi tendon organ feedback interpreted in relation to efferent commands provide information about movement trajectory, and second, somatosensory stimulation of the fingertip at the completion of a reach provides information about the location of the fingertip relative to the torso.

  9. Adaptation to Coriolis perturbations of voluntary body sway transfers to preprogrammed fall-recovery behavior.

    PubMed

    Bakshi, Avijit; Ventura, Joel; DiZio, Paul; Lackner, James R

    2014-03-01

    In a rotating environment, goal-oriented voluntary movements are initially disrupted in trajectory and endpoint, due to movement-contingent Coriolis forces, but accuracy is regained with additional movements. We studied whether adaptation acquired in a voluntary, goal-oriented postural swaying task performed during constant-velocity counterclockwise rotation (10 RPM) carries over to recovery from falling induced using a hold and release (H&R) paradigm. In H&R, standing subjects actively resist a force applied to their chest, which when suddenly released results in a forward fall and activation of an automatic postural correction. We tested H&R postural recovery in subjects (n = 11) before and after they made voluntary fore-aft swaying movements during 20 trials of 25 s each, in a counterclockwise rotating room. Their voluntary sway about their ankles generated Coriolis forces that initially induced clockwise deviations of the intended body sway paths, but fore-aft sway was gradually restored over successive per-rotation trials, and a counterclockwise aftereffect occurred during postrotation attempts to sway fore-aft. In H&R trials, we examined the initial 10- to 150-ms periods of movement after release from the hold force, when voluntary corrections of movement path are not possible. Prerotation subjects fell directly forward, whereas postrotation their forward motion was deviated significantly counterclockwise. The postrotation deviations were in a direction consistent with an aftereffect reflecting persistence of a compensation acquired per-rotation for voluntary swaying movements. These findings show that control and adaptation mechanisms adjusting voluntary postural sway to the demands of a new force environment also influence the automatic recovery of posture.

  10. Adaptive dynamic programming as a theory of sensorimotor control.

    PubMed

    Jiang, Yu; Jiang, Zhong-Ping

    2014-08-01

    Many characteristics of sensorimotor control can be explained by models based on optimization and optimal control theories. However, most of the previous models assume that the central nervous system has access to the precise knowledge of the sensorimotor system and its interacting environment. This viewpoint is difficult to be justified theoretically and has not been convincingly validated by experiments. To address this problem, this paper presents a new computational mechanism for sensorimotor control from a perspective of adaptive dynamic programming (ADP), which shares some features of reinforcement learning. The ADP-based model for sensorimotor control suggests that a command signal for the human movement is derived directly from the real-time sensory data, without the need to identify the system dynamics. An iterative learning scheme based on the proposed ADP theory is developed, along with rigorous convergence analysis. Interestingly, the computational model as advocated here is able to reproduce the motor learning behavior observed in experiments where a divergent force field or velocity-dependent force field was present. In addition, this modeling strategy provides a clear way to perform stability analysis of the overall system. Hence, we conjecture that human sensorimotor systems use an ADP-type mechanism to control movements and to achieve successful adaptation to uncertainties present in the environment.

  11. Adaptive dynamic programming as a theory of sensorimotor control.

    PubMed

    Jiang, Yu; Jiang, Zhong-Ping

    2014-08-01

    Many characteristics of sensorimotor control can be explained by models based on optimization and optimal control theories. However, most of the previous models assume that the central nervous system has access to the precise knowledge of the sensorimotor system and its interacting environment. This viewpoint is difficult to be justified theoretically and has not been convincingly validated by experiments. To address this problem, this paper presents a new computational mechanism for sensorimotor control from a perspective of adaptive dynamic programming (ADP), which shares some features of reinforcement learning. The ADP-based model for sensorimotor control suggests that a command signal for the human movement is derived directly from the real-time sensory data, without the need to identify the system dynamics. An iterative learning scheme based on the proposed ADP theory is developed, along with rigorous convergence analysis. Interestingly, the computational model as advocated here is able to reproduce the motor learning behavior observed in experiments where a divergent force field or velocity-dependent force field was present. In addition, this modeling strategy provides a clear way to perform stability analysis of the overall system. Hence, we conjecture that human sensorimotor systems use an ADP-type mechanism to control movements and to achieve successful adaptation to uncertainties present in the environment. PMID:24962078

  12. Intermittent adaptation. A theory of drug tolerance, dependence and addiction.

    PubMed

    Peper, A

    2009-05-01

    A mathematical model of drug tolerance and its underlying theory is presented. The model is essentially more complex than the generally used model of homeostasis, which is demonstrated to fail in describing tolerance development to repeated drug administrations. The model assumes the development of tolerance to a repeatedly administered drug to be the result of a regulated adaptive process. The oral detection and analysis of endogenous substances is proposed to be the primary stimulus for the mechanism of drug tolerance. Anticipation and environmental cues are in the model considered secondary stimuli, becoming primary only in dependence and addiction or when the drug administration bypasses the natural--oral--route, as is the case when drugs are administered intravenously. The model considers adaptation to the effect of a drug and adaptation to the interval between drug taking autonomous tolerance processes. Simulations with the mathematical model demonstrate the model's behaviour to be consistent with important characteristics of the development of tolerance to repeatedly administered drugs: the gradual decrease in drug effect when tolerance develops, the high sensitivity to small changes in drug dose, the rebound phenomenon and the large reactions following withdrawal in dependence. Simulations of different ways withdrawal can be accomplished, demonstrates the practical applicability of the model.

  13. Study of the phase structure of Abelian field theories through non-lattice, non-perturbative calculations

    SciTech Connect

    Karanikas, A.I.; Ktorides, C.N.; Mavromatos, N.E.

    1986-12-01

    A recently proposed approach to gauge field theories, by which one formulates them non-locally and subsequently approaches locality arbitrarily close, is applied to U(1) gauge theories. We test the possibility that the aformentioned methodology might introduce a measure in the functional integral which supports non-perturbative calculations in the continuum. In particular, we are able to carry relevant calculations pertaining to the expectation value of the Wilson's loop operator in 3+1, 2+1 and 1+1 dimensions. The results are similar to ones obtained through the lattice regularization of R(1) gauge theory, with the important difference that in our case they refer to continuum U(1) gauge theory, as a function of the bare coupling constant. We further solidify the validity of our approach by conducting a calculation referring to the 2-dimensional scalar Heisenberg model, remaining always in the continuum. copyright 1986 Academic Press, Inc.

  14. The correlation function for density perturbations in an expanding universe. I - Linear theory

    NASA Technical Reports Server (NTRS)

    Mcclelland, J.; Silk, J.

    1977-01-01

    The evolution of the two-point correlation function for adiabatic density perturbations in the early universe is studied. Analytical solutions are obtained for the evolution of linearized spherically symmetric adiabatic density perturbations and the two-point correlation function for these perturbations in the radiation-dominated portion of the early universe. The results are then extended to the regime after decoupling. It is found that: (1) adiabatic spherically symmetric perturbations comparable in scale with the maximum Jeans length would survive the radiation-dominated regime; (2) irregular fluctuations are smoothed out up to the scale of the maximum Jeans length in the radiation era, but regular fluctuations might survive on smaller scales; (3) in general, the only surviving structures for irregularly shaped adiabatic density perturbations of arbitrary but finite scale in the radiation regime are the size of or larger than the maximum Jeans length in that regime; (4) infinite plane waves with a wavelength smaller than the maximum Jeans length but larger than the critical dissipative damping scale could survive the radiation regime; and (5) black holes would also survive the radiation regime and might accrete sufficient mass after decoupling to nucleate the formation of galaxies.

  15. Dynamics of weakly inhomogeneous oscillator populations: perturbation theory on top of Watanabe-Strogatz integrability

    NASA Astrophysics Data System (ADS)

    Vlasov, Vladimir; Rosenblum, Michael; Pikovsky, Arkady

    2016-08-01

    As has been shown by Watanabe and Strogatz (WS) (1993 Phys. Rev. Lett. 70 2391), a population of identical phase oscillators, sine-coupled to a common field, is a partially integrable system: for any ensemble size its dynamics reduce to equations for three collective variables. Here we develop a perturbation approach for weakly nonidentical ensembles. We calculate corrections to the WS dynamics for two types of perturbations: those due to a distribution of natural frequencies and of forcing terms, and those due to small white noise. We demonstrate that in both cases, the complex mean field for which the dynamical equations are written is close to the Kuramoto order parameter, up to the leading order in the perturbation. This supports the validity of the dynamical reduction suggested by Ott and Antonsen (2008 Chaos 18 037113) for weakly inhomogeneous populations.

  16. Dynamics of weakly inhomogeneous oscillator populations: perturbation theory on top of Watanabe–Strogatz integrability

    NASA Astrophysics Data System (ADS)

    Vlasov, Vladimir; Rosenblum, Michael; Pikovsky, Arkady

    2016-08-01

    As has been shown by Watanabe and Strogatz (WS) (1993 Phys. Rev. Lett. 70 2391), a population of identical phase oscillators, sine-coupled to a common field, is a partially integrable system: for any ensemble size its dynamics reduce to equations for three collective variables. Here we develop a perturbation approach for weakly nonidentical ensembles. We calculate corrections to the WS dynamics for two types of perturbations: those due to a distribution of natural frequencies and of forcing terms, and those due to small white noise. We demonstrate that in both cases, the complex mean field for which the dynamical equations are written is close to the Kuramoto order parameter, up to the leading order in the perturbation. This supports the validity of the dynamical reduction suggested by Ott and Antonsen (2008 Chaos 18 037113) for weakly inhomogeneous populations.

  17. A UNIFIED THEORY FOR THE EFFECTS OF STELLAR PERTURBATIONS AND GALACTIC TIDES ON OORT CLOUD COMETS

    SciTech Connect

    Collins, Benjamin F.; Sari, Re'em

    2010-11-15

    We examine the effects of passing field stars on the angular momentum of a nearly radial orbit of an Oort cloud comet bound to the Sun. We derive the probability density function of the change in angular momentum from one stellar encounter, assuming a uniform and isotropic field of perturbers. We show that the total angular momentum follows a Levy flight, and determine its distribution function. If there is an asymmetry in the directional distribution of perturber velocities, the marginal probability distribution of each component of the angular momentum vector can be different. The constant torque attributed to Galactic tides arises from a non-cancellation of perturbations with an impact parameter of order the semimajor axis of the comet. When the close encounters are rare, the angular momentum is best modeled by the stochastic growth of stellar encounters. If trajectories passing between the comet and the Sun occur frequently, the angular momentum exhibits the coherent growth attributed to the Galactic tides.

  18. A view on coupled cluster perturbation theory using a bivariational Lagrangian formulation.

    PubMed

    Kristensen, Kasper; Eriksen, Janus J; Matthews, Devin A; Olsen, Jeppe; Jørgensen, Poul

    2016-02-14

    We consider two distinct coupled cluster (CC) perturbation series that both expand the difference between the energies of the CCSD (CC with single and double excitations) and CCSDT (CC with single, double, and triple excitations) models in orders of the Møller-Plesset fluctuation potential. We initially introduce the E-CCSD(T-n) series, in which the CCSD amplitude equations are satisfied at the expansion point, and compare it to the recently developed CCSD(T-n) series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)], in which not only the CCSD amplitude, but also the CCSD multiplier equations are satisfied at the expansion point. The computational scaling is similar for the two series, and both are term-wise size extensive with a formal convergence towards the CCSDT target energy. However, the two series are different, and the CCSD(T-n) series is found to exhibit a more rapid convergence up through the series, which we trace back to the fact that more information at the expansion point is utilized than for the E-CCSD(T-n) series. The present analysis can be generalized to any perturbation expansion representing the difference between a parent CC model and a higher-level target CC model. In general, we demonstrate that, whenever the parent parameters depend upon the perturbation operator, a perturbation expansion of the CC energy (where only parent amplitudes are used) differs from a perturbation expansion of the CC Lagrangian (where both parent amplitudes and parent multipliers are used). For the latter case, the bivariational Lagrangian formulation becomes more than a convenient mathematical tool, since it facilitates a different and faster convergent perturbation series than the simpler energy-based expansion.

  19. Generating the curvature perturbation at the end of inflation in string theory.

    PubMed

    Lyth, David H; Riotto, Antonio

    2006-09-22

    In brane inflationary scenarios, the cosmological perturbations are supposed to originate from the vacuum fluctuations of the inflaton field corresponding to the position of the brane. We show that a significant, and possibly dominant, contribution to the curvature perturbation is generated at the end of inflation through the vacuum fluctuations of fields, other than the inflaton, which are light during the inflationary trajectory and become heavy at the brane-antibrane annihilation. These fields appear generically in string compactifications where the background geometry has exact or approximate isometries and parametrize the internal angular directions of the brane.

  20. Generating the curvature perturbation at the end of inflation in string theory.

    PubMed

    Lyth, David H; Riotto, Antonio

    2006-09-22

    In brane inflationary scenarios, the cosmological perturbations are supposed to originate from the vacuum fluctuations of the inflaton field corresponding to the position of the brane. We show that a significant, and possibly dominant, contribution to the curvature perturbation is generated at the end of inflation through the vacuum fluctuations of fields, other than the inflaton, which are light during the inflationary trajectory and become heavy at the brane-antibrane annihilation. These fields appear generically in string compactifications where the background geometry has exact or approximate isometries and parametrize the internal angular directions of the brane. PMID:17025948

  1. A coarse grained perturbation theory for the Large Scale Structure, with cosmology and time independence in the UV

    SciTech Connect

    Manzotti, Alessandro; Peloso, Marco; Pietroni, Massimo; Viel, Matteo; Villaescusa-Navarro, Francisco E-mail: peloso@physics.umn.edu E-mail: viel@oats.inaf.it

    2014-09-01

    Standard cosmological perturbation theory (SPT) for the Large Scale Structure (LSS) of the Universe fails at small scales (UV) due to strong nonlinearities and to multistreaming effects. In ref. [1] a new framework was proposed in which the large scales (IR) are treated perturbatively while the information on the UV, mainly small scale velocity dispersion, is obtained by nonlinear methods like N-body simulations. Here we develop this approach, showing that it is possible to reproduce the fully nonlinear power spectrum (PS) by combining a simple (and fast) 1-loop computation for the IR scales and the measurement of a single, dominant, correlator from N-body simulations for the UV ones. We measure this correlator for a suite of seven different cosmologies, and we show that its inclusion in our perturbation scheme reproduces the fully non-linear PS with percent level accuracy, for wave numbers up to k∼ 0.4 h Mpc{sup -1} down to 0z=. We then show that, once this correlator has been measured in a given cosmology, there is no need to run a new simulation for a different cosmology in the suite. Indeed, by rescaling this correlator by a proper function computable in SPT, the reconstruction procedure works also for the other cosmologies and for all redshifts, with comparable accuracy. Finally, we clarify the relation of this approach to the Effective Field Theory methods recently proposed in the LSS context.

  2. The bond-breaking and bond-making puzzle: many-body perturbation versus density-functional theory

    NASA Astrophysics Data System (ADS)

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

    2013-03-01

    Diatomic molecules at dissociation provide a prototypical situation in which the ground-state cannot be described by a single Slater determinant. For the paradigmatic case of H2-dissociation we compare state-of-the-art many-body perturbation theory in the GW approximation and density-functional theory (DFT) in the exact-exchange plus random-phase approximation for the correlation energy (RPA). Results from the recently developed renormalized second-order perturbation theory (rPT2) are also reported. For an unbiased comparison and to prevent spurious starting point effects both RPA and GW are iterated to full self-consistency (i.e. sc-RPA and sc- GW). Both include topologically identical diagrams for the exchange and correlation energy but are evaluated with a non-interacting Kohn-Sham and an interacting GW Green function, respectively. This has profound consequences for the kinetic and the correlation energy. GW and rPT2 are both accurate at equilibrium, but fail at dissociation, in contrast to sc-RPA. This failure demonstrates the need of including higher order correlation diagrams in sc- GW . Our results indicate that RPA-based DFT is a strong contender for a universally applicable electronic-structure theory. F. Caruso et al. arxiv.org/abs/1210.8300.

  3. Future planning and evaluation for automated adaptive minehunting: a roadmap for mine countermeasures theory modernization

    NASA Astrophysics Data System (ADS)

    Garcia, Gregory A.; Wettergren, Thomas A.

    2012-06-01

    This paper presents a discussion of U.S. naval mine countermeasures (MCM) theory modernization in light of advances in the areas of autonomy, tactics, and sensor processing. The unifying theme spanning these research areas concerns the capability for in situ adaptation of processing algorithms, plans, and vehicle behaviors enabled through run-time situation assessment and performance estimation. Independently, each of these technology developments impact the MCM Measures of Effectiveness1 [MOE(s)] of time and risk by improving one or more associated Measures of Performance2 [MOP(s)]; the contribution of this paper is to outline an integrated strategy for realizing the cumulative benefits of these technology enablers to the United States Navy's minehunting capability. An introduction to the MCM problem is provided to frame the importance of the foundational research and the ramifications of the proposed strategy on the MIW community. We then include an overview of current and future adaptive capability research in the aforementioned areas, highlighting a departure from the existing rigid assumption-based approaches while identifying anticipated technology acceptance issues. Consequently, the paper describes an incremental strategy for transitioning from the current minehunting paradigm where tactical decision aids rely on a priori intelligence and there is little to no in situ adaptation or feedback to a future vision where unmanned systems3, equipped with a representation of the commander's intent, are afforded the authority and ability to adapt to environmental perturbations with minimal human-in-the-loop supervision. The discussion concludes with an articulation of the science and technology issues which the MCM research community must continue to address.

  4. The General Necessary Condition for the Validity of Dirac's Transition Perturbation Theory

    NASA Technical Reports Server (NTRS)

    Quang, Nguyen Vinh

    1996-01-01

    For the first time, from the natural requirements for the successive approximation the general necessary condition of validity of the Dirac's method is explicitly established. It is proved that the conception of 'the transition probability per unit time' is not valid. The 'super-platinium rules' for calculating the transition probability are derived for the arbitrarily strong time-independent perturbation case.

  5. Theory of cosmological perturbations formulated in terms of a complete set of basic gauge-invariant quantities

    NASA Astrophysics Data System (ADS)

    Banach, Zbigniew; Piekarski, Sławomir

    1996-03-01

    An annoying paradox which has plagued the “naive” description of density perturbations in homogeneous and isotropic cosmological models has been the gauge-dependent character of this description. The corollary of this observation is that only gauge-invariant quantities have any inherent physical meaning. Thus the present paper develops, from a new geometric point of view, a totally gauge-invariant formulation of perturbation theory applicable to the case of a general perfect fluid with two essential thermodynamic variables. Precisely speaking, the main purpose here is the systematic construction of a complete set of basic gauge-invariant variables. This set consists of 17 linearly independent, not identically vanishing quantities. It turns out that these quantities can be used to divide the infinitesimal perturbations into equivalence classes: two perturbations P and P' are said to be equivalent if their difference is equal to the Lie derivative of the background solution of Einstein's propagation equations with respect to an arbitrary vector field on the space-time manifold. In fact, the gauge-invariant perturbations, whose mathematical definition is best understood by introducing the elements of a certain quotient space, are uniquely determined from the basic variables. An additional welcome feature is that any gauge-invariant quantity can be constructed directly from the basic variables through purely algebraic and differential operations. In a companion paper, these results are used to derive the full, gauge-invariant system of equations governing the evolution of basic variables. In this sense, then, the present analysis is complete.

  6. Transients from initial conditions based on Lagrangian perturbation theory in N-body simulations II: the effect of the transverse mode

    SciTech Connect

    Tatekawa, Takayuki

    2014-04-01

    We study the initial conditions for cosmological N-body simulations for precision cosmology. In general, Zel'dovich approximation has been applied for the initial conditions of N-body simulations for a long time. These initial conditions provide incorrect higher-order growth. These error caused by setting up the initial conditions by perturbation theory is called transients. We investigated the impact of transient on non-Gaussianity of density field by performing cosmological N-body simulations with initial conditions based on first-, second-, and third-order Lagrangian perturbation theory in previous paper. In this paper, we evaluates the effect of the transverse mode in the third-order Lagrangian perturbation theory for several statistical quantities such as power spectrum and non-Gaussianty. Then we clarified that the effect of the transverse mode in the third-order Lagrangian perturbation theory is quite small.

  7. Complex adaptive systems and game theory: An unlikely union

    USGS Publications Warehouse

    Hadzikadic, M.; Carmichael, T.; Curtin, C.

    2010-01-01

    A Complex Adaptive System is a collection of autonomous, heterogeneous agents, whose behavior is defined with a limited number of rules. A Game Theory is a mathematical construct that assumes a small number of rational players who have a limited number of actions or strategies available to them. The CAS method has the potential to alleviate some of the shortcomings of GT. On the other hand, CAS researchers are always looking for a realistic way to define interactions among agents. GT offers an attractive option for defining the rules of such interactions in a way that is both potentially consistent with observed real-world behavior and subject to mathematical interpretation. This article reports on the results of an effort to build a CAS system that utilizes GT for determining the actions of individual agents. ?? 2009 Wiley Periodicals, Inc. Complexity, 16,24-42, 2010.

  8. Feynman perturbation expansion for the price of coupon bond options and swaptions in quantum finance. I. Theory.

    PubMed

    Baaquie, Belal E

    2007-01-01

    European options on coupon bonds are studied in a quantum field theory model of forward interest rates. Swaptions are briefly reviewed. An approximation scheme for the coupon bond option price is developed based on the fact that the volatility of the forward interest rates is a small quantity. The field theory for the forward interest rates is Gaussian, but when the payoff function for the coupon bond option is included it makes the field theory nonlocal and nonlinear. A perturbation expansion using Feynman diagrams gives a closed form approximation for the price of coupon bond option. A special case of the approximate bond option is shown to yield the industry standard one-factor HJM formula with exponential volatility.

  9. Adaptive aging in the context of evolutionary theory.

    PubMed

    Mitteldorf, J J

    2012-07-01

    Compelling evidence for an adaptive origin of aging has clashed with traditional evolutionary theory based on exclusively individual selection. The consensus view has been to try to understand aging in the context of a narrow, restrictive evolutionary paradigm, called the Modern Synthesis, or neo-Darwinism. But neo-Darwinism has shown itself to be inadequate in other ways, failing to account for stable ecosystems, for the evolution of sex and the maintenance of diversity and the architecture of the genome, which appears to be optimized for evolvability. Thus aging is not the only reason to consider overhauling the standard theoretical framework. Selection for stable ecosystems is rapid and efficient, and so it is the easiest modification of the neo-Darwinian paradigm to understand and to model. Aging may be understood in this context. More profound and more mysterious are the ways in which the process of evolution itself has been transformed in a bootstrapping process of selection for evolvability. Evolving organisms have learned to channel their variation in ways that are likely to enhance their long-term prospects. This is an expanded notion of fitness. Only in this context can the full spectrum of sophisticated adaptations be understood, including aging, sex, diversity, ecological interdependence, and the structure of the genome.

  10. Perturbation Theory with Convergent Series for Large Values of Coupling Constant:. a Calculation of β-FUNCTION in φ4 Model

    NASA Astrophysics Data System (ADS)

    Belokurov, V. V.; Shavgulidze, E. T.; Solov'yov, Yu. P.; Yudin, I. L.

    2001-04-01

    A new perturbation theory with convergent series is used to calculate quantities given by a finite number of terms of the traditional perturbation theory. As examples of such a problem, the zero-dimensional analog of a functional integral and β-function in gφ4 model in four-dimensional space-time are considered. The results obtained demonstrate high accuracy of the calculation in a wide region of coupling constant values.

  11. Relativistic Many-body Moller-Plesset Perturbation Theory Calculations of the Energy Levels and Transition Probabilities in Na- to P-like Xe Ions

    SciTech Connect

    Vilkas, M J; Ishikawa, Y; Trabert, E

    2007-03-27

    Relativistic multireference many-body perturbation theory calculations have been performed on Xe{sup 43+}-Xe{sup 39+} ions, resulting in energy levels, electric dipole transition probabilities, and level lifetimes. The second-order many-body perturbation theory calculation of energy levels included mass shifts, frequency-dependent Breit correction and Lamb shifts. The calculated transition energies and E1 transition rates are used to present synthetic spectra in the extreme ultraviolet range for some of the Xe ions.

  12. Resummation for Nonequilibrium Perturbation Theory and Application to Open Quantum Lattices

    NASA Astrophysics Data System (ADS)

    Li, Andy C. Y.; Petruccione, F.; Koch, Jens

    2016-04-01

    Lattice models of fermions, bosons, and spins have long served to elucidate the essential physics of quantum phase transitions in a variety of systems. Generalizing such models to incorporate driving and dissipation has opened new vistas to investigate nonequilibrium phenomena and dissipative phase transitions in interacting many-body systems. We present a framework for the treatment of such open quantum lattices based on a resummation scheme for the Lindblad perturbation series. Employing a convenient diagrammatic representation, we utilize this method to obtain relevant observables for the open Jaynes-Cummings lattice, a model of special interest for open-system quantum simulation. We demonstrate that the resummation framework allows us to reliably predict observables for both finite and infinite Jaynes-Cummings lattices with different lattice geometries. The resummation of the Lindblad perturbation series can thus serve as a valuable tool in validating open quantum simulators, such as circuit-QED lattices, currently being investigated experimentally.

  13. Theory of minimum spanning trees. II. Exact graphical methods and perturbation expansion at the percolation threshold

    SciTech Connect

    Jackson, T. S.; Read, N.

    2010-02-15

    Continuing the program begun by the authors in a previous paper, we develop an exact low-density expansion for the random minimum spanning tree (MST) on a finite graph and use it to develop a continuum perturbation expansion for the MST on critical percolation clusters in space dimension d. The perturbation expansion is proved to be renormalizable in d=6 dimensions. We consider the fractal dimension D{sub p} of paths on the latter MST; our previous results lead us to predict that D{sub p}=2 for d>d{sub c}=6. Using a renormalization-group approach, we confirm the result for d>6 and calculate D{sub p} to first order in epsilon=6-d for d<6 using the connection with critical percolation, with the result D{sub p}=2-epsilon/7+O(epsilon{sup 2}).

  14. Perturbation theory for an Anderson quantum dot asymmetrically attached to two superconducting leads

    NASA Astrophysics Data System (ADS)

    Žonda, M.; Pokorný, V.; Janiš, V.; Novotný, T.

    2016-01-01

    Self-consistent perturbation expansion up to the second order in the interaction strength is used to study a single-level quantum dot with local Coulomb repulsion attached asymmetrically to two generally different superconducting leads. At zero temperature and a wide range of other parameters, the spin-symmetric version of the expansion yields excellent results for the position of the 0 -π impurity quantum phase transition boundary and Josephson current together with the energy of Andreev bound states in the 0 phase as confirmed by numerical calculations using the numerical renormalization group method. We analytically prove that the method is charge conserving as well as thermodynamically consistent. Explicit formulas for the position of the 0 -π phase boundary are presented for the Hartree-Fock approximation as well as for its variant called generalized atomic limit. It is shown that the generalized atomic limit can be used as a quick estimate for the position of the phase boundary at half-filling in a broad range of parameters. We apply our second-order perturbation method to the interpretation of the existing experimental data on the phase boundary with very satisfactory outcome, suggesting that the so-far employed heavy numerical tools such as numerical renormalization group and/or quantum Monte Carlo are not necessary in a class of generic situations and can be safely replaced by a perturbative approach.

  15. Quantum network theory of computing with respect to entangled flux qubits and external perturbation

    NASA Astrophysics Data System (ADS)

    Cain, C. A.; Wu, C. H.

    2013-04-01

    In this work, we attempt to show the differences between traditional qubit-based spintronic methodology for quantum computation and the possible ballistic quantum network implementations. Flux qubits can be considered topologically similar to the persistent currents possessed as the angular momentum in Aharonov-Bohm loops, which can be coupled and thus entangled together. Since entanglement is guaranteed for coupled quantum networks, starting from a point-contacted situation, we first investigate how varying the degree of entanglement strength can affect the superposition of the four possible states for two isolated flux qubits being brought together. In general, the superposition is destroyed once the degree of entanglement is altered from the point-contact situation. However, we show that for a specific network with maximum entanglement, a Bell state situation can be produced. We then examine the effects of varying the external perturbation strength on the readout capability in quantum networks by changing the coupling strength through the cross-sectional area ratio. From the analysis of our results, we are persuaded to believe that two universally accepted components for quantum computing are not valid in the quantum network approach: the need of a weak perturbation for measurement of computational results and the requirement of fixed entanglement among qubits. We show there is an interplay between the strength of the entanglement and that of the external perturbation for high-fidelity classical readouts.

  16. Generalized Vibrational Perturbation Theory for Rotovibrational Energies of Linear, Symmetric and Asymmetric Tops: Theory, Approximations, and Automated Approaches to Deal with Medium-to-Large Molecular Systems

    PubMed Central

    Piccardo, Matteo; Bloino, Julien; Barone, Vincenzo

    2015-01-01

    Models going beyond the rigid-rotor and the harmonic oscillator levels are mandatory for providing accurate theoretical predictions for several spectroscopic properties. Different strategies have been devised for this purpose. Among them, the treatment by perturbation theory of the molecular Hamiltonian after its expansion in power series of products of vibrational and rotational operators, also referred to as vibrational perturbation theory (VPT), is particularly appealing for its computational efficiency to treat medium-to-large systems. Moreover, generalized (GVPT) strategies combining the use of perturbative and variational formalisms can be adopted to further improve the accuracy of the results, with the first approach used for weakly coupled terms, and the second one to handle tightly coupled ones. In this context, the GVPT formulation for asymmetric, symmetric, and linear tops is revisited and fully generalized to both minima and first-order saddle points of the molecular potential energy surface. The computational strategies and approximations that can be adopted in dealing with GVPT computations are pointed out, with a particular attention devoted to the treatment of symmetry and degeneracies. A number of tests and applications are discussed, to show the possibilities of the developments, as regards both the variety of treatable systems and eligible methods. © 2015 Wiley Periodicals, Inc. PMID:26345131

  17. Study of equilibrium geometries of diradicaloid systems via state specific multireference Møller-Plesset perturbation theory (SS-MRMPPT)

    NASA Astrophysics Data System (ADS)

    Chattopadhyay, Sudip; Mahapatra, Uttam Sinha; Chaudhuri, Rajat K.

    2010-03-01

    The numerical gradient scheme for rigorously size-extensive spin-free state-specific multireference Møller-Plesset perturbation theory based on Rayleigh-Schrödinger expansion (termed as SS-MRMPPT) has been employed for calculating equilibrium geometrical parameters of diradical systems such as singlet CH 2, m-benzyne and 2,6-pyridyne. These systems possess quasi-degeneracy of varying degrees. A close and quantitative agreement of results obtained by low cost SS-MRMPPT method with the results of highly sophisticated ab initio methods is an encouraging reflection of the ability of the present method in studying geometrical parameters of states plagued by electronic degeneracy.

  18. On equivalence of high temperature series expansion and coupling parameter series expansion in thermodynamic perturbation theory of fluids

    SciTech Connect

    Sai Venkata Ramana, A.

    2014-04-21

    The coupling parameter series expansion and the high temperature series expansion in the thermodynamic perturbation theory of fluids are shown to be equivalent if the interaction potential is pairwise additive. As a consequence, for the class of fluids with the potential having a hardcore repulsion, if the hard-sphere fluid is chosen as reference system, the terms of coupling parameter series expansion for radial distribution function, direct correlation function, and Helmholtz free energy follow a scaling law with temperature. The scaling law is confirmed by application to square-well fluids.

  19. Renormalization of the low-energy constants of chiral perturbation theory from loops with dynamical vector mesons

    NASA Astrophysics Data System (ADS)

    Terschlüsen, Carla; Leupold, Stefan

    2016-07-01

    Starting from a relativistic Lagrangian for pseudoscalar Goldstone bosons and vector mesons in the antisymmetric tensor representation, a one-loop calculation is performed to pin down the divergent structures that appear for the effective low-energy action at chiral orders Q2 and Q4 . The corresponding renormalization-scale dependencies of all low-energy constants up to chiral order Q4 are determined. Calculations are carried out for both the pseudoscalar octet and the pseudoscalar nonet, the latter in the framework of chiral perturbation theory in the limit of a large number of colors.

  20. Development and Standardization of the Diagnostic Adaptive Behavior Scale: Application of Item Response Theory to the Assessment of Adaptive Behavior

    ERIC Educational Resources Information Center

    Tassé, Marc J.; Schalock, Robert L.; Thissen, David; Balboni, Giulia; Bersani, Henry, Jr.; Borthwick-Duffy, Sharon A.; Spreat, Scott; Widaman, Keith F.; Zhang, Dalun; Navas, Patricia

    2016-01-01

    The Diagnostic Adaptive Behavior Scale (DABS) was developed using item response theory (IRT) methods and was constructed to provide the most precise and valid adaptive behavior information at or near the cutoff point of making a decision regarding a diagnosis of intellectual disability. The DABS initial item pool consisted of 260 items. Using IRT…