Differential cross sections and spin density matrix elements for the reaction gamma p -> p omega
M. Williams, D. Applegate, M. Bellis, C.A. Meyer
2009-12-01
High-statistics differential cross sections and spin density matrix elements for the reaction gamma p -> p omega have been measured using the CLAS at Jefferson Lab for center-of-mass (CM) energies from threshold up to 2.84 GeV. Results are reported in 112 10-MeV wide CM energy bins, each subdivided into cos(theta_CM) bins of width 0.1. These are the most precise and extensive omega photoproduction measurements to date. A number of prominent structures are clearly present in the data. Many of these have not previously been observed due to limited statistics in earlier measurements.
Energy density functional study of nuclear matrix elements for neutrinoless ββ decay.
Rodríguez, Tomás R; Martínez-Pinedo, Gabriel
2010-12-17
We present an extensive study of nuclear matrix elements (NME) for the neutrinoless double-beta decay of the nuclei 48Ca, 76Ge, 82Se, 96Zr, 100Mo, 116Cd, 124Sn, 128Te, 130Te, 136Xe, and 150Nd based on state-of-the-art energy density functional methods using the Gogny D1S functional. Beyond-mean-field effects are included within the generating coordinate method with particle number and angular momentum projection for both initial and final ground states. We obtain a rather constant value for the NMEs around 4.7 with the exception of 48Ca and 150Nd, where smaller values are found. We analyze the role of deformation and pairing in the evaluation of the NME and present detailed results for the decay of 150Nd.
NASA Astrophysics Data System (ADS)
Oberhofer, Harald; Blumberger, Jochen
2010-12-01
We present a plane wave basis set implementation for the calculation of electronic coupling matrix elements of electron transfer reactions within the framework of constrained density functional theory (CDFT). Following the work of Wu and Van Voorhis [J. Chem. Phys. 125, 164105 (2006)], the diabatic wavefunctions are approximated by the Kohn-Sham determinants obtained from CDFT calculations, and the coupling matrix element calculated by an efficient integration scheme. Our results for intermolecular electron transfer in small systems agree very well with high-level ab initio calculations based on generalized Mulliken-Hush theory, and with previous local basis set CDFT calculations. The effect of thermal fluctuations on the coupling matrix element is demonstrated for intramolecular electron transfer in the tetrathiafulvalene-diquinone (Q-TTF-Q-) anion. Sampling the electronic coupling along density functional based molecular dynamics trajectories, we find that thermal fluctuations, in particular the slow bending motion of the molecule, can lead to changes in the instantaneous electron transfer rate by more than an order of magnitude. The thermal average, ( {< {| {H_ab } |^2 } > } )^{1/2} = 6.7 {mH}, is significantly higher than the value obtained for the minimum energy structure, | {H_ab } | = 3.8 {mH}. While CDFT in combination with generalized gradient approximation (GGA) functionals describes the intermolecular electron transfer in the studied systems well, exact exchange is required for Q-TTF-Q- in order to obtain coupling matrix elements in agreement with experiment (3.9 mH). The implementation presented opens up the possibility to compute electronic coupling matrix elements for extended systems where donor, acceptor, and the environment are treated at the quantum mechanical (QM) level.
Oberhofer, Harald; Blumberger, Jochen
2010-12-28
We present a plane wave basis set implementation for the calculation of electronic coupling matrix elements of electron transfer reactions within the framework of constrained density functional theory (CDFT). Following the work of Wu and Van Voorhis [J. Chem. Phys. 125, 164105 (2006)], the diabatic wavefunctions are approximated by the Kohn-Sham determinants obtained from CDFT calculations, and the coupling matrix element calculated by an efficient integration scheme. Our results for intermolecular electron transfer in small systems agree very well with high-level ab initio calculations based on generalized Mulliken-Hush theory, and with previous local basis set CDFT calculations. The effect of thermal fluctuations on the coupling matrix element is demonstrated for intramolecular electron transfer in the tetrathiafulvalene-diquinone (Q-TTF-Q(-)) anion. Sampling the electronic coupling along density functional based molecular dynamics trajectories, we find that thermal fluctuations, in particular the slow bending motion of the molecule, can lead to changes in the instantaneous electron transfer rate by more than an order of magnitude. The thermal average, (<|H(ab)|(2)>)(1/2)=6.7 mH, is significantly higher than the value obtained for the minimum energy structure, |H(ab)|=3.8 mH. While CDFT in combination with generalized gradient approximation (GGA) functionals describes the intermolecular electron transfer in the studied systems well, exact exchange is required for Q-TTF-Q(-) in order to obtain coupling matrix elements in agreement with experiment (3.9 mH). The implementation presented opens up the possibility to compute electronic coupling matrix elements for extended systems where donor, acceptor, and the environment are treated at the quantum mechanical (QM) level.
Analytical O (αs) corrections to the beam frame double-spin density matrix elements of e+e-→t t ¯
NASA Astrophysics Data System (ADS)
Kaldamäe, L.; Groote, S.; Körner, J. G.
2016-12-01
We provide analytical results for the O (αs) corrections to the double-spin density matrix elements in the reaction e+e-→t t ¯ . These concern the elements l l , l t , l n , t t , t n , and n n of the double-spin density matrix elements where l , t , n stand for longitudinal, transverse and normal orientations with respect to the beam frame spanned by the electron and the top quark momentum.
Density matrix perturbation theory.
Niklasson, Anders M N; Challacombe, Matt
2004-05-14
An orbital-free quantum perturbation theory is proposed. It gives the response of the density matrix upon variation of the Hamiltonian by quadratically convergent recursions based on perturbed projections. The technique allows treatment of embedded quantum subsystems with a computational cost scaling linearly with the size of the perturbed region, O(N(pert.)), and as O(1) with the total system size. The method allows efficient high order perturbation expansions, as demonstrated with an example involving a 10th order expansion. Density matrix analogs of Wigner's 2n+1 rule are also presented.
Differential cross sections and spin density matrix elements for γp → φp from CLAS
NASA Astrophysics Data System (ADS)
Dey, Biplab; Meyer, Curtis A.
2011-10-01
Preliminary differential cross-sections and the ρMM'0 spin density matrix elements (SDME) for the reaction γρ → φp for both charged- (φ → K+K-) and neutral-mode (φ → KL0KS0) topologies obtained from CLAS are presented. Our kinematic coverage is from near production threshold (√s ˜1.97 GeV) to (√s = 2.84 GeV), with a wide coverage in the production angle. As seen in previous LEPS results, the differential cross-sections show a localized "bump" between (√s ˜2 and 2.2 GeV that is not expected from a simple Pomeron exchange picture. Comparisons between the charged- and neutral-mode results and possible effects from the K+Λ(1520) channel are discussed. Our SDME results confirm the well-known deviations from t-channel helicity conservation (TCHC) for Pomeron exchange, but s-channel helicity conservation (SCHC) is also seen to be broken.
First Measurements of the 1̂, 2̂, and 3̂ Spin Density Matrix Elements in γp ->pφ using CLAS at JLab
NASA Astrophysics Data System (ADS)
Vernarsky, Brian
2012-10-01
In an effort towards a ``complete'' experiment for the φ meson, we present studies from two experiments with unpolarized targets, one using a circularly polarized photon beam (g1c) and one using a linearly polarized photon beam (g8b), both carried out using the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Lab. The experiments were analyzed using an extended maximum likelihood fit to the cross section with partial wave amplitudes. New likelihood functions were calculated to account for the polarization of the photon beams. The results of these fits are then used to project out the spin density matrix for the φ. First measurements of the 1̂, 2̂, and 3̂ spin density matrix elements will be presented using this method. As a check, we compare to another method, Schilling's method, which fits the decay angular distribution with a function that uses the spin density matrix elements as parameters.
Semiclassical integrable matrix elements
Morehead, J.J.
1996-03-01
A semiclassical expression for matrix elements of an arbitrary operator with respect to the eigenstates of an integrable Hamiltonian is derived. This is essentially the Heisenberg correspondence principle, and it is shown via the Weyl correspondence that the approximation is valid through the lowest two orders in {h_bar}. The result is used to prove that an asymptotic form of the Clebsch-Gordan coefficients for two large and one small angular momenta is valid through two orders. {copyright} {ital 1996 The American Physical Society.}
Vernarsky, Brian J.
2014-01-01
In an effort towards a ''complete'' experiment for the ω meson, we present studies from an experiment with an unpolarized target and a circularly polarized photon beam (g1c), carried out using the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Lab. The experiment was analyzed using an extended maximum likelihood fit with partial wave amplitudes. New likelihood functions were calculated to account for the polarization of the photon beam. Both circular and linear polarizations are explored. The results of these fits are then used to project out the spin density matrix for the {omega}. First measurements of the {rho}{sup 3} spin density matrix elements will be presented using this method.
Lishev, St.; Yordanov, D. Shivarova, A.
2015-04-08
Concepts for the extraction of volume-produced negative hydrogen ions from a rf matrix source (a matrix of small-radius discharges with a planar-coil inductive driving) are presented and discussed based on experimental results for the current densities of the extracted ions and the co-extracted electrons. The experiment has been carried out in a single discharge of the source: a rf discharge with a radius of 2.25 cm inductively driven by a 3.5-turn planar coil. The length of the discharge tube, the area of the reference electrode inserted in the discharge volume, the discharge modes, the magnetic filter and its position along the discharge length, the position of the permanent magnets for the separation of the co-extracted electrons from the extracted ions in the extraction device and the bias applied to its first electrode are considered as factors influencing the extracted currents of negative ions.
Chen, Zhenhua; Chen, Xun; Wu, Wei
2013-04-28
In this series, the n-body reduced density matrix (n-RDM) approach for nonorthogonal orbitals and their applications to ab initio valence bond (VB) methods are presented. As the first paper of this series, Hamiltonian matrix elements between internally contracted VB wave functions are explicitly provided by means of nonorthogonal orbital based RDM approach. To this end, a more generalized Wick's theorem, called enhanced Wick's theorem, is presented both in arithmetical and in graphical forms, by which the deduction of expressions for the matrix elements between internally contracted VB wave functions is dramatically simplified, and the matrix elements are finally expressed in terms of tensor contractions of electronic integrals and n-RDMs of the reference VB self-consistent field wave function. A string-based algorithm is developed for the purpose of evaluating n-RDMs in an efficient way. Using the techniques presented in this paper, one is able to develop new methods and efficient algorithms for nonorthogonal orbital based many-electron theory much easier than by use of the first quantized formulism.
Relativistic Dipole Matrix Element Zeros
NASA Astrophysics Data System (ADS)
Lajohn, L. A.; Pratt, R. H.
2002-05-01
There is a special class of relativistic high energy dipole matrix element zeros (RZ), whose positions with respect to photon energy ω , only depend on the bound state l quantum number according to ω^0=mc^2/(l_b+1) (independent of primary quantum number n, nuclear charge Z, central potential V and dipole retardation). These RZ only occur in (n,l_b,j_b)arrow (ɛ , l_b+1,j_b) transitions such as ns_1/2arrow ɛ p_1/2; np_3/2arrow ɛ d_3/2: nd_5/2arrow ɛ f_5/2 etc. The nonrelativistic limit of these matrix elements can be established explicitly in the Coulomb case. Within the general matrix element formalism (such as that in [1]); when |κ | is substituted for γ in analytic expressions for matrix elements, the zeros remain, but ω^0 now becomes dependent on n and Z. When the reduction to nonrelativistic form is completed by application of the low energy approximation ω mc^2 mc^2, the zeros disappear. This nonzero behavior was noted in nonrelativistic dipole Coulomb matrix elements by Fano and Cooper [2] and later proven by Oh and Pratt[3]. (J. H. Scofield, Phys. Rev. A 40), 3054 (1989 (U. Fano and J. W. Cooper, Rev. Mod. Phys. 40), 441 (1968). (D. Oh and R. H. Pratt, Phys. Rev. A 34), 2486 (1986); 37, 1524 (1988); 45, 1583 (1992).
NASA Astrophysics Data System (ADS)
Williams, Mike
This work presents measurements of differential cross sections, dsigma/dcos qwCM , and spin density matrix elements, r0MM' , for the reaction gammap → po in the energy range 1.72 GeV< s <2.84 GeV. The data were collected at Jefferson Lab, using the CLAS detector, as part of the g11a run period in 2004. Our r0MM' measurements vastly increase the precision of the world's data and extend the large angle measurements by over 400 MeV in s . Our data confirms that for s < 2.1 GeV, the forward angle (small |t|) production amplitude is dominated by t-channel pi0 exchange. At higher energies, existing non-resonant models do a poor job of describing our data. In particular, u-channel models fail to reproduce our highest energy backwards r0MM' measurements. A mass-independent partial wave analysis has also been performed. Near threshold, the dominant resonance contributions extracted are the **** F15 (1680) and *** D 13(1700). Together with the t-channel pi0 exchange, these three waves provide a remarkably good description of our differential cross section and spin density matrix element measurements for s < 2 GeV. Strong, but not conclusive, evidence for the **** G17(2190) has also been extracted. Improved non-resonant models may be necessary to irrefutably show whether this state contributes to o photoproduction. Evidence for missing resonances is suggestive, but inconclusive without theoretical input.
Vibrational Density Matrix Renormalization Group.
Baiardi, Alberto; Stein, Christopher J; Barone, Vincenzo; Reiher, Markus
2017-08-08
Variational approaches for the calculation of vibrational wave functions and energies are a natural route to obtain highly accurate results with controllable errors. Here, we demonstrate how the density matrix renormalization group (DMRG) can be exploited to optimize vibrational wave functions (vDMRG) expressed as matrix product states. We study the convergence of these calculations with respect to the size of the local basis of each mode, the number of renormalized block states, and the number of DMRG sweeps required. We demonstrate the high accuracy achieved by vDMRG for small molecules that were intensively studied in the literature. We then proceed to show that the complete fingerprint region of the sarcosyn-glycin dipeptide can be calculated with vDMRG.
Dey, B.; Meyer, C. A.; Bellis, M.; ...
2014-05-27
High-statistics measurements of differential cross sections and spin density matrix elements for the reaction γ p → Φp have been made using the CLAS detector at Jefferson Lab. We cover center-of-mass energies (√s) from 1.97 to 2.84 GeV, with an extensive coverage in the Φ production angle. The high statistics of the data sample made it necessary to carefully account for the interplay between the Φ natural lineshape and effects of the detector resolution, that are found to be comparable in magnitude. We study both the charged- (Φ → K⁺K⁻) and neutral- (Φ → K0SK0L)more » $$K\\bar{K}$$ decay modes of the Φ. Further, for the charged mode, we differentiate between the cases where the final K⁻ track is directly detected or its momentum reconstructed as the total missing momentum in the event. The two charged-mode topologies and the neutral-mode have different resolutions and are calibrated against each other. Extensive usage is made of kinematic fitting to improve the reconstructed Φ mass resolution. Our final results are reported in 10- and mostly 30-MeV-wide √s bins for the charged- and the neutral-mode, respectively. Possible effects from K⁺Λ* channels with p$$K\\bar{K}$$ final-states are discussed. These present results constitute the most precise and extensive Φ photoproduction measurements to date and in conjunction with the ω photoproduction results recently published by CLAS, will greatly improve our understanding of low energy vector meson photoproduction.« less
NASA Astrophysics Data System (ADS)
Dey, B.; Meyer, C. A.; Bellis, M.; Williams, M.; Adhikari, K. P.; Adikaram, D.; Aghasyan, M.; Amaryan, M. J.; Anderson, M. D.; Anefalos Pereira, S.; Ball, J.; Baltzell, N. A.; Battaglieri, M.; Bedlinskiy, I.; Biselli, A. S.; Bono, J.; Boiarinov, S.; Briscoe, W. J.; Brooks, W. K.; Burkert, V. D.; Carman, D. S.; Celentano, A.; Chandavar, S.; Colaneri, L.; Cole, P. L.; Contalbrigo, M.; Cortes, O.; Crede, V.; D'Angelo, A.; Dashyan, N.; De Vita, R.; De Sanctis, E.; Deur, A.; Djalali, C.; Doughty, D.; Dugger, M.; Dupre, R.; El Alaoui, A.; El Fassi, L.; Elouadrhiri, L.; Fedotov, G.; Fegan, S.; Fleming, J. A.; Garçon, M.; Gevorgyan, N.; Ghandilyan, Y.; Gilfoyle, G. P.; Giovanetti, K. L.; Girod, F. X.; Glazier, D. I.; Goetz, J. T.; Gothe, R. W.; Griffioen, K. A.; Guidal, M.; Hafidi, K.; Hanretty, C.; Harrison, N.; Hattawy, M.; Hicks, K.; Ho, D.; Holtrop, M.; Hyde, C. E.; Ilieva, Y.; Ireland, D. G.; Ishkhanov, B. S.; Jenkins, D.; Jo, H. S.; Joo, K.; Keller, D.; Khandaker, M.; Kim, A.; Kim, W.; Klein, A.; Klein, F. J.; Koirala, S.; Kubarovsky, V.; Kuhn, S. E.; Kuleshov, S. V.; Lenisa, P.; Livingston, K.; Lu, H.; MacGregor, I. J. D.; Markov, N.; Mayer, M.; McCracken, M. E.; McKinnon, B.; Mineeva, T.; Mirazita, M.; Mokeev, V.; Montgomery, R. A.; Moriya, K.; Moutarde, H.; Munevar, E.; Munoz Camacho, C.; Nadel-Turonski, P.; Niccolai, S.; Niculescu, G.; Niculescu, I.; Osipenko, M.; Pappalardo, L. L.; Paremuzyan, R.; Park, K.; Pasyuk, E.; Peng, P.; Phillips, J. J.; Pisano, S.; Pogorelko, O.; Pozdniakov, S.; Price, J. W.; Procureur, S.; Protopopescu, D.; Puckett, A. J. R.; Rimal, D.; Ripani, M.; Ritchie, B. G.; Rizzo, A.; Rossi, P.; Roy, P.; Sabatié, F.; Saini, M. S.; Schott, D.; Schumacher, R. A.; Seder, E.; Senderovich, I.; Sharabian, Y. G.; Simonyan, A.; Smith, E. S.; Sober, D. I.; Sokhan, D.; Stepanyan, S. S.; Stoler, P.; Strakovsky, I. I.; Strauch, S.; Sytnik, V.; Taiuti, M.; Tang, W.; Tkachenko, S.; Ungaro, M.; Vernarsky, B.; Vlassov, A. V.; Voskanyan, H.; Voutier, E.; Walford, N. K.; Watts, D. P.; Zachariou, N.; Zana, L.; Zhang, J.; Zhao, Z. W.; Zonta, I.; CLAS Collaboration
2014-05-01
High-statistics measurements of differential cross sections and spin density matrix elements for the reaction γp →ϕp have been made using the CLAS detector at Jefferson Lab. We cover center-of-mass energies (√s ) from 1.97 to 2.84 GeV, with an extensive coverage in the ϕ production angle. The high statistics of the data sample made it necessary to carefully account for the interplay between the ϕ natural lineshape and effects of the detector resolution, that are found to be comparable in magnitude. We study both the charged- (ϕ →K+K-) and neutral- (ϕ →KS0KL0) KK ¯ decay modes of the ϕ. Further, for the charged mode, we differentiate between the cases where the final K- track is directly detected or its momentum reconstructed as the total missing momentum in the event. The two charged-mode topologies and the neutral-mode have different resolutions and are calibrated against each other. Extensive usage is made of kinematic fitting to improve the reconstructed ϕ mass resolution. Our final results are reported in 10- and mostly 30-MeV-wide √s bins for the charged- and the neutral-modes, respectively. Possible effects from K+Λ* channels with pKK ¯ final states are discussed. These present results constitute the most precise and extensive ϕ photoproduction measurements to date and in conjunction with the ω photoproduction results recently published by CLAS, will greatly improve our understanding of low energy vector meson photoproduction.
Dey, B.; Meyer, C. A.; Bellis, M.; Williams, M.; Adhikari, K. P.; Adikaram, D.; Aghasyan, M.; Amaryan, M. J.; Anderson, M. D.; Anefalos Pereira, S.; Ball, J.; Baltzell, N. A.; Battaglieri, M.; Bedlinskiy, I.; Biselli, A. S.; Bono, J.; Boiarinov, S.; Briscoe, W. J.; Brooks, W. K.; Burkert, V. D.; Carman, D. S.; Celentano, A.; Chandavar, S.; Colaneri, L.; Cole, P. L.; Contalbrigo, M.; Cortes, O.; Crede, V.; D'Angelo, A.; Dashyan, N.; De Vita, R.; De Sanctis, E.; Deur, A.; Djalali, C.; Doughty, D.; Dugger, M.; Dupre, R.; El Alaoui, A.; El Fassi, L.; Elouadrhiri, L.; Fedotov, G.; Fegan, S.; Fleming, J. A.; Garçon, M.; Gevorgyan, N.; Ghandilyan, Y.; Gilfoyle, G. P.; Giovanetti, K. L.; Girod, F. X.; Glazier, D. I.; Goetz, J. T.; Gothe, R. W.; Griffioen, K. A.; Guidal, M.; Hafidi, K.; Hanretty, C.; Harrison, N.; Hattawy, M.; Hicks, K.; Ho, D.; Holtrop, M.; Hyde, C. E.; Ilieva, Y.; Ireland, D. G.; Ishkhanov, B. S.; Jenkins, D.; Jo, H. S.; Joo, K.; Keller, D.; Khandaker, M.; Kim, A.; Kim, W.; Klein, A.; Klein, F. J.; Koirala, S.; Kubarovsky, V.; Kuhn, S. E.; Kuleshov, S. V.; Lenisa, P.; Livingston, K.; Lu, H.; MacGregor, I. J.D.; Markov, N.; Mayer, M.; McCracken, M. E.; McKinnon, B.; Mineeva, T.; Mirazita, M.; Mokeev, V.; Montgomery, R. A.; Moriya, K.; Moutarde, H.; Munevar, E.; Munoz Camacho, C.; Nadel-Turonski, P.; Niccolai, S.; Niculescu, G.; Niculescu, I.; Osipenko, M.; Pappalardo, L. L.; Paremuzyan, R.; Park, K.; Pasyuk, E.; Peng, P.; Phillips, J. J.; Pisano, S.; Pogorelko, O.; Pozdniakov, S.; Price, J. W.; Procureur, S.; Protopopescu, D.; Puckett, A. J. R.; Rimal, D.; Ripani, M.; Ritchie, B. G.; Rizzo, A.; Rossi, P.; Roy, P.; Sabatié, F.; Saini, M. S.; Schott, D.; Schumacher, R. A.; Seder, E.; Senderovich, I.; Sharabian, Y. G.; Simonyan, A.; Smith, E. S.; Sober, D. I.; Sokhan, D.; Stepanyan, S. S.; Stoler, P.; Strakovsky, I. I.; Strauch, S.; Sytnik, V.; Taiuti, M.; Tang, W.; Tkachenko, S.; Ungaro, M.; Vernarsky, B.; Vlassov, A. V.; Voskanyan, H.; Voutier, E.; Watts, D. P.; Zachariou, N.; Zana, L.; Zhang, J.; Zhao, Z. W.; Zonta, I.
2014-05-27
High-statistics measurements of differential cross sections and spin density matrix elements for the reaction γ p → Φp have been made using the CLAS detector at Jefferson Lab. We cover center-of-mass energies (√s) from 1.97 to 2.84 GeV, with an extensive coverage in the Φ production angle. The high statistics of the data sample made it necessary to carefully account for the interplay between the Φ natural lineshape and effects of the detector resolution, that are found to be comparable in magnitude. We study both the charged- (Φ → K⁺K⁻) and neutral- (Φ → K^{0}_{S}K^{0}_{L}) $K\\bar{K}$ decay modes of the Φ. Further, for the charged mode, we differentiate between the cases where the final K⁻ track is directly detected or its momentum reconstructed as the total missing momentum in the event. The two charged-mode topologies and the neutral-mode have different resolutions and are calibrated against each other. Extensive usage is made of kinematic fitting to improve the reconstructed Φ mass resolution. Our final results are reported in 10- and mostly 30-MeV-wide √s bins for the charged- and the neutral-mode, respectively. Possible effects from K⁺Λ* channels with p$K\\bar{K}$ final-states are discussed. These present results constitute the most precise and extensive Φ photoproduction measurements to date and in conjunction with the ω photoproduction results recently published by CLAS, will greatly improve our understanding of low energy vector meson photoproduction.
Direct Measurement of the Density Matrix of a Quantum System
NASA Astrophysics Data System (ADS)
Thekkadath, G. S.; Giner, L.; Chalich, Y.; Horton, M. J.; Banker, J.; Lundeen, J. S.
2016-09-01
One drawback of conventional quantum state tomography is that it does not readily provide access to single density matrix elements since it requires a global reconstruction. Here, we experimentally demonstrate a scheme that can be used to directly measure individual density matrix elements of general quantum states. The scheme relies on measuring a sequence of three observables, each complementary to the last. The first two measurements are made weak to minimize the disturbance they cause to the state, while the final measurement is strong. We perform this joint measurement on polarized photons in pure and mixed states to directly measure their density matrix. The weak measurements are achieved using two walk-off crystals, each inducing a polarization-dependent spatial shift that couples the spatial and polarization degrees of freedom of the photons. This direct measurement method provides an operational meaning to the density matrix and promises to be especially useful for large dimensional states.
Graphical evaluation of relativistic matrix elements
NASA Technical Reports Server (NTRS)
Huang, K. N.
1978-01-01
A graphical representation of angular momentum was used to evaluate relativistic matrix elements between antisymmetrized states of many particle configurations having any number of open shells. The antisymmetrized matrix element was expanded as a sum of semisymmetrized matrix elements. The diagram representing a semisymmetrized matrix element was composed of four diagram blocks; the bra block, the ket block, the spectator block, and the interaction block. The first three blocks indicate the couplings of the two interacting configurations while the last depends on the interaction and is the replaceable component. Interaction blocks for relativistic operators and commonly used potentials were summarized in ready to use forms. A simple step by step procedure was prescribed generally for calculating antisymmetrized matrix elements of one and two particle operators.
Comix, a New Matrix Element Generator
Gleisberg, Tanju; Hoche, Stefan; /Durham U., IPPP
2008-09-03
We present a new tree-level matrix element generator, based on the color dressed Berends-Giele recursive relations. We discuss two new algorithms for phase space integration, dedicated to be used with large multiplicities and color sampling.
Semiclassical matrix elements from periodic orbits
NASA Technical Reports Server (NTRS)
Eckhardt, B.; Fishman, S.; Mueller, K.; Wintgen, D.
1992-01-01
An extension of Gutzwiller's (1967, 1969, 1970, 1971, 1990) semiclassical theory for chaotic systems that allows a determination of matrix elements in terms of classical periodic orbits. Associated zeta functions are derived. The semiclassical predictions are found to be in good agreement with Fourier transforms of quantum spectra of hydrogen in a magnetic field. Expressions for off-diagonal matrix elements are derived that are extensions of the Bohr correspondence relations for integrable systems.
Semiclassical matrix elements from periodic orbits
NASA Technical Reports Server (NTRS)
Eckhardt, B.; Fishman, S.; Mueller, K.; Wintgen, D.
1992-01-01
An extension of Gutzwiller's (1967, 1969, 1970, 1971, 1990) semiclassical theory for chaotic systems that allows a determination of matrix elements in terms of classical periodic orbits. Associated zeta functions are derived. The semiclassical predictions are found to be in good agreement with Fourier transforms of quantum spectra of hydrogen in a magnetic field. Expressions for off-diagonal matrix elements are derived that are extensions of the Bohr correspondence relations for integrable systems.
Rolling Element Bearing Stiffness Matrix Determination (Presentation)
Guo, Y.; Parker, R.
2014-01-01
Current theoretical bearing models differ in their stiffness estimates because of different model assumptions. In this study, a finite element/contact mechanics model is developed for rolling element bearings with the focus of obtaining accurate bearing stiffness for a wide range of bearing types and parameters. A combined surface integral and finite element method is used to solve for the contact mechanics between the rolling elements and races. This model captures the time-dependent characteristics of the bearing contact due to the orbital motion of the rolling elements. A numerical method is developed to determine the full bearing stiffness matrix corresponding to two radial, one axial, and two angular coordinates; the rotation about the shaft axis is free by design. This proposed stiffness determination method is validated against experiments in the literature and compared to existing analytical models and widely used advanced computational methods. The fully-populated stiffness matrix demonstrates the coupling between bearing radial, axial, and tilting bearing deflections.
Matrix elements from moments of correlation functions
Chang, Chia Cheng; Bouchard, Chris; Orginos, Konstantinos; Richards, David G.
2016-10-01
Momentum-space derivatives of matrix elements can be related to their coordinate-space moments through the Fourier transform. We derive these expressions as a function of momentum transfer Q2 for asymptotic in/out states consisting of a single hadron. We calculate corrections to the finite volume moments by studying the spatial dependence of the lattice correlation functions. This method permits the computation of not only the values of matrix elements at momenta accessible on the lattice, but also the momentum-space derivatives, providing {\\it a priori} information about the Q2 dependence of form factors. As a specific application we use the method, at a single lattice spacing and with unphysically heavy quarks, to directly obtain the slope of the isovector form factor at various Q2, whence the isovector charge radius. The method has potential application in the calculation of any hadronic matrix element with momentum transfer, including those relevant to hadronic weak decays.
Renormalon ambiguities in NRQCD operator matrix elements
NASA Astrophysics Data System (ADS)
Bodwin, Geoffrey T.; Chen, Yu-Qi
1999-09-01
We analyze the renormalon ambiguities that appear in factorization formulas in QCD. Our analysis contains a simple argument that the ambiguities in the short-distance coefficients and operator matrix elements are artifacts of dimensional-regularization factorization schemes and are absent in cutoff schemes. We also present a method for computing the renormalon ambiguities in operator matrix elements and apply it to a computation of the ambiguities in the matrix elements that appear in the NRQCD factorization formulas for the annihilation decays of S-wave quarkonia. Our results, combined with those of Braaten and Chen for the short-distance coefficients, provide an explicit demonstration that the ambiguities cancel in the physical decay rates. In addition, we analyze the renormalon ambiguities in the Gremm-Kapustin relation and in various definitions of the heavy-quark mass.
Hwang, S H; Hicks, K; Ahn, J K; Nakano, T; Ahn, D S; Chang, W C; Chen, J Y; Daté, S; Ejiri, H; Fujimura, H; Fujiwara, M; Fukui, S; Gohn, W; Hotta, T; Imai, K; Ishikawa, T; Joo, K; Kato, Y; Kohri, H; Kon, Y; Lee, H S; Maeda, Y; Miyabe, M; Mibe, T; Morino, Y; Muramatsu, N; Nakatsugawa, Y; Niiyama, M; Noumi, H; Oh, Y; Ohashi, Y; Ohta, T; Oka, M; Parker, J; Rangacharyulu, C; Ryu, S Y; Sawada, T; Sugaya, Y; Sumihama, M; Tsunemi, T; Uchida, M; Ungaro, M; Yosoi, M
2012-03-02
The exclusive reaction γp→K(+)π(-)Σ(+) was measured for the first time using linearly polarized photons at beam energies from 1.85 to 2.96 GeV. Angular distributions in the rest frame of the K(+)π(-) system were fitted to extract spin-density matrix elements of the K(*0) decay. The measured parity spin asymmetry shows that natural-parity exchange is dominant in this reaction. This result clearly indicates the need for t-channel exchange of the κ(800) scalar meson.
Interaction picture density matrix quantum Monte Carlo
Malone, Fionn D. Lee, D. K. K.; Foulkes, W. M. C.; Blunt, N. S.; Shepherd, James J.; Spencer, J. S.
2015-07-28
The recently developed density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samples the N-body thermal density matrix and hence provides access to exact properties of many-particle quantum systems at arbitrary temperatures. We demonstrate that moving to the interaction picture provides substantial benefits when applying DMQMC to interacting fermions. In this first study, we focus on a system of much recent interest: the uniform electron gas in the warm dense regime. The basis set incompleteness error at finite temperature is investigated and extrapolated via a simple Monte Carlo sampling procedure. Finally, we provide benchmark calculations for a four-electron system, comparing our results to previous work where possible.
Microscopic method for E 0 transition matrix elements
NASA Astrophysics Data System (ADS)
Brown, B. A.; Garnsworthy, A. B.; Kibédi, T.; Stuchbery, A. E.
2017-01-01
We present a microscopic model for electric monopole (E 0 ) transition matrix elements by combining a configuration interaction model for orbital occupations with an energy-density functional model for the single-particle potential and radial wave functions. The configuration interaction model is used to constrain the orbital occupations for the diagonal and off-diagonal matrix elements. These are used in an energy-density functional calculation to obtain a self-consistent transition density. This density contains the valence contribution, as well as the polarization of the protons by the valence protons and neutrons. We show connections between E 0 matrix elements and isomer and isotope shifts of the charge radius. The spin-orbit correction to the charge density is important in some cases. This model accounts for a large part of the data over a wide region of the nuclear chart. It also accounts for the shape of the observed electron scattering form factors. The results depend on the Skyrme parameters used for the energy-density functional and might be used to provide new constraints for them.
NASA Astrophysics Data System (ADS)
Chen, Zhenhua; Chen, Xun; Wu, Wei
2013-04-01
In this paper, by applying the reduced density matrix (RDM) approach for nonorthogonal orbitals developed in the first paper of this series, efficient algorithms for matrix elements between VB structures and energy gradients in valence bond self-consistent field (VBSCF) method were presented. Both algorithms scale only as nm4 for integral transformation and d^2 n_β ^2 for VB matrix elements and 3-RDM evaluation, while the computational costs of other procedures are negligible, where n, m, d, and nβ are the numbers of variable occupied active orbitals, basis functions, determinants, and active β electrons, respectively. Using tensor properties of the energy gradients with respect to the orbital coefficients presented in the first paper of this series, a partial orthogonal auxiliary orbital set was introduced to reduce the computational cost of VBSCF calculation in which orbitals are flexibly defined. Test calculations on the Diels-Alder reaction of butadiene and ethylene have shown that the novel algorithm is very efficient for VBSCF calculations.
Chen, Zhenhua; Chen, Xun; Wu, Wei
2013-04-28
In this paper, by applying the reduced density matrix (RDM) approach for nonorthogonal orbitals developed in the first paper of this series, efficient algorithms for matrix elements between VB structures and energy gradients in valence bond self-consistent field (VBSCF) method were presented. Both algorithms scale only as nm(4) for integral transformation and d(2)n(β)(2) for VB matrix elements and 3-RDM evaluation, while the computational costs of other procedures are negligible, where n, m, d, and n(β )are the numbers of variable occupied active orbitals, basis functions, determinants, and active β electrons, respectively. Using tensor properties of the energy gradients with respect to the orbital coefficients presented in the first paper of this series, a partial orthogonal auxiliary orbital set was introduced to reduce the computational cost of VBSCF calculation in which orbitals are flexibly defined. Test calculations on the Diels-Alder reaction of butadiene and ethylene have shown that the novel algorithm is very efficient for VBSCF calculations.
The MOON project and DBD matrix elements
NASA Astrophysics Data System (ADS)
Ejiri, H.
2009-06-01
This is a brief report on experimental studies of double beta decays (DBD) in Japan, the MOON project for spectroscopic studies of neutrino-less DBD (0vββ) and on experimental studies of DBD nuclear matrix elements. Experimental DBD studies in Japan were made by geochemical methods on 130Te, 128Te and 96Zr and by a series of ELEGANT(EL) counting methods, EL III on 76Ge, EL IV, V on 100Mo, 116Cd, and EL VI on 48Ca. Future counter experiments are MOON, CANDLES, XMASS and DCBA. The MOON project, which is based on EL V, aims at studies of the Majorana nature of the neutrino (v) and the v-mass spectrum by spectroscopic 0vββ experiments with the v-mass sensitivity of < mmv > = 100-30 meV. The MOON detector is a super ensemble of multi-layer modules, each being composed by PL scintillator plates and position-sensitive detector planes. DBD nuclear matrix elements have been studied experimentally by using charge exchange reactions. The 2-neutrino DBD matrix elements are expressed by successive single-β matrix elements through low-lying intermediate states.
Status Report on Weak Matrix Element Calculations
NASA Astrophysics Data System (ADS)
Gupta, Rajan; Bhattacharya, Tanmoy
1996-03-01
This talk presents results of weak matrix elements calculated from simulations done on 170 32 3 × 64 lattices at β = 6.0 using quenched Wilson fermions. We discuss the extraction of pseudoscalar decay constants ƒπ, ƒ K, ƒ D, and f Ds, the form-factors for the rare decay B → K*γ, and the matrix elements of the 4-fermion operators relevant to B K, B7, B8. We present an analysis of the various sources of systematic errors, and show that these are now much larger than the statistical errors for each of these observables. Our main results are ƒ D = 186(29) MeV, ƒ Ds = 224(16) MeV, T1 = T2 = 0.24(1), B K( NDR,2 GeV) = 0.67(9), and B8 ( NDR, 2 GeV) = 0.81(1).
Lattice QCD calculations of weak matrix elements
NASA Astrophysics Data System (ADS)
Detar, Carleton
2017-01-01
Lattice QCD has become the method of choice for calculating the hadronic environment of the electroweak interactions of quarks. So it is now an essential tool in the search for new physics beyond the Standard Model. Advances in computing power and algorithms have resulted in increasingly precise predictions and increasingly stringent tests of the Standard Model. I review results of recent calculations of weak matrix elements and discuss their implications for new physics. Supported by US NSF grant PHY10-034278.
Twisted mass QCD for weak matrix elements
NASA Astrophysics Data System (ADS)
Pena, Carlos
2006-12-01
I report on the application of tmQCD techniques to the computation of hadronic matrix elements of four-fermion operators. Emphasis is put on the computation of BK in quenched QCD performed by the ALPHA Collaboration. The extension of tmQCD strategies to the study of neutral B- meson mixing is briefly discussed. Finally, some remarks are made concerning proposals to apply tmQCD to the computation of K → ππ amplitudes.
Measuring Entanglement Spectrum via Density Matrix Exponentiation
NASA Astrophysics Data System (ADS)
Zhu, Guanyu; Seif, Alireza; Pichler, Hannes; Zoller, Peter; Hafezi, Mohammad
Entanglement spectrum (ES), the eigenvalues of the reduced density matrix of a subsystem, serves as a powerful theoretical tool to study many-body systems. For example, the gap and degeneracies of the entanglement spectrum have been used to identify various topological phases. However, the usefulness of such a concept in real experiments has been debated, since it is believed that obtaining the ES requires full state tomography, at a cost which exponentially grows with the systems size. Inspired by a recent density matrix exponentiation technique, we propose a scheme to measure ES by evolving the system with a Hamiltonian that is the subsystem's own reduced density matrix. Such a time evolution can be induced by an ancilla photon that is coupled to multiple qubits at the same time. The phase associated with the time evolution can be detected and converted into ES through either a digital or an analogue scheme. The digital scheme involves a modified quantum phase estimation algorithm based on random time evolution, while the analogue scheme is in the spirit of Ramsey interferometry. Both schemes are not limited by the size of the system, and are especially sensitive to the gap and degeneracies. We also discuss the implementation in cavity/circuit-QED and ion trap systems.
Measuring Sparticles with the Matrix Element
Alwall, Johan; Freitas, Ayres; Mattelaer, Olivier; /INFN, Rome3 /Rome III U. /Louvain U.
2012-04-10
We apply the Matrix Element Method (MEM) to mass determination of squark pair production with direct decay to quarks and LSP at the LHC, showing that simultaneous mass determination of squarks and LSP is possible. We furthermore propose methods for inclusion of QCD radiation effects in the MEM. The goal of the LHC at CERN, scheduled to start this year, is to discover new physics through deviations from the Standard Model (SM) predictions. After discovery of deviations from the SM, the next step will be classification of the new physics. An important first goal in this process will be establishing a mass spectrum of the new particles. One of the most challenging scenarios is pair-production of new particles which decay to invisible massive particles, giving missing energy signals. Many methods have been proposed for mass determination in such scenarios (for a recent list of references, see e.g. [1]). In this proceeding, we report the first steps in applying the Matrix Element Method (MEM) in the context of supersymmetric scenarios giving missing energy signals. After a quick review of the MEM, we will focus on squark pair production, a process where other mass determination techniques have difficulties to simultaneously determine the LSP and squark masses. Finally, we will introduce methods to extend the range of validity of the MEM, by taking into account initial state radiation (ISR) in the method.
Polarizable Embedding Density Matrix Renormalization Group.
Hedegård, Erik D; Reiher, Markus
2016-09-13
The polarizable embedding (PE) approach is a flexible embedding model where a preselected region out of a larger system is described quantum mechanically, while the interaction with the surrounding environment is modeled through an effective operator. This effective operator represents the environment by atom-centered multipoles and polarizabilities derived from quantum mechanical calculations on (fragments of) the environment. Thereby, the polarization of the environment is explicitly accounted for. Here, we present the coupling of the PE approach with the density matrix renormalization group (DMRG). This PE-DMRG method is particularly suitable for embedded subsystems that feature a dense manifold of frontier orbitals which requires large active spaces. Recovering such static electron-correlation effects in multiconfigurational electronic structure problems, while accounting for both electrostatics and polarization of a surrounding environment, allows us to describe strongly correlated electronic structures in complex molecular environments. We investigate various embedding potentials for the well-studied first excited state of water with active spaces that correspond to a full configuration-interaction treatment. Moreover, we study the environment effect on the first excited state of a retinylidene Schiff base within a channelrhodopsin protein. For this system, we also investigate the effect of dynamical correlation included through short-range density functional theory.
The origin of linear scaling Fock matrix calculation with density prescreening
Mitin, Alexander V.
2015-12-31
A theorem was proven, which reads that the number of nonzero two-electron integrals scales linearly with respect to the number of basis functions for large molecular systems. This permits to show that linear scaling property of the Fock matrix calculation with using density prescreening arises due to linear scaling properties of the number of nonzero two-electron integrals and the number of leading matrix elements of density matrix. This property is reinforced by employing the density prescreening technique. The use of the density difference prescreening further improves the linear scaling property of the Fock matrix calculation method. As a result, the linear scaling regime of the Fock matrix calculation can begin from the number of basis functions of 2000–3000 in dependence on the basis function type in molecular calculations. It was also shown that the conventional algorithm of Fock matrix calculation from stored nonzero two-electron integrals with density prescreening possesses linear scaling property.
NASA Astrophysics Data System (ADS)
Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R.
2016-07-01
Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.
Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R
2016-07-07
Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.
Analytic Matrix Elements and Gradients with Shifted Correlated Gaussians
NASA Astrophysics Data System (ADS)
Fedorov, D. V.
2017-01-01
Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are shown to be analytic. Their gradients with respect to the non-linear parameters of the Gaussians are also analytic. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics.
Useful extremum principle for the variational calculation of matrix elements
NASA Technical Reports Server (NTRS)
Gerjuoy, E.; Rau, A. R. P.; Rosenberg, L.; Spruch, L.
1974-01-01
Variational principles are considered for the approximate evaluation of the diagonal matrix elements of an arbitrary known linear Hermitian operator. A method is derived that is immediately applicable to the variational determination of both the off-diagonal and diagonal matrix elements of normal and modified Green's functions.
Density matrix of radiation of a black hole with a fluctuating horizon
NASA Astrophysics Data System (ADS)
Iofa, Mikhail Z.
2016-09-01
The density matrix of Hawking radiation is calculated in the model of a black hole with a fluctuating horizon. Quantum fluctuations smear the classical horizon of a black hole and modify the density matrix of radiation producing the off-diagonal elements. The off-diagonal elements may store information on correlations between the radiation and the black hole. The smeared density matrix was constructed by convolution of the density matrix calculated with the instantaneous horizon with the Gaussian distribution over the instantaneous horizons. The distribution has the extremum at the classical radius of the black hole and the width of order of the Planck length. Calculations were performed in the model of a black hole formed by the thin collapsing shell which follows a trajectory that is a solution of the matching equations connecting the interior and exterior geometries.
Two-body density matrix of a normal Fermi fluid
NASA Astrophysics Data System (ADS)
Ristig, M. L.; Clark, J. W.
1990-05-01
The microscopic study of the two-body density matrix ρ2(r1,r2,r'1,r'2) initiated for uniform Bose fluids in an earlier paper is continued for the Fermi case. We present formal results on the structure of the generalized momentum distribution n(p,q)=Σk⁁<Ψ\\|a†k⁁+qa†p⁁-qap⁁ak⁁\\|Ψ>, and its Fourier inverse ρ2(r1,r2,r'1,r2)≡ρ2(r1,r2,r'1), based on a variational ground-state wave function of Jastrow-Slater form. The structural relations are inferred from the cluster expansions of these objects, from the asymptotic condition relating ρ2(r1,r2,r'1) to the particle density and the one-body density matrix ρ1(r1,r'1), and from formal diagrammatic connections with the Bose problem. The two-body density-matrix elements ρ2(r1,r2,r'1) are thereby expressed in closed form in terms of certain sums of irreducible cluster diagrams. Some of these diagram sums are familiar from the analogous theory of the one-body density matrix; all can be evaluated quantitatively by solving a set of Fermi-hypernetted-chain (FHNC) equations. Upon invoking the sequential relation between ρ2(r1,r2,r'1) and ρ1(r1,r'1), the corresponding result for the generalized momentum distribution n(p,q) effects a resolution into contributions from various scattering processes occurring in the many-body medium, specified by form factors that are susceptible to FHNC evaluation. This decomposition is comparable to that derived earlier for the Bose-fluid ground state but is complicated by contributions from exchange scattering and by a dynamically dressed Pauli kinematic correction. Silver has proposed a simple expression for the generalized momentum distribution n(p,q), a function which plays an essential role in his theory of final-state effects in deep-inelastic neutron scattering from the helium liquids. Based on the present microscopic treatment, the quality of Silver's estimate is assessed for the case of normal liquid He3, by evaluating the necessary distribution
Reduced density-matrix functionals from many-particle theory
NASA Astrophysics Data System (ADS)
Schade, Robert; Kamil, Ebad; Blöchl, Peter
2017-07-01
In materials with strong electron correlation the proper treatment of local atomic physics described by orbital occupations is crucial. Reduced density-matrix functional theory is a natural extension of density functional theory for systems that are dominated by orbital physics. We review the current state of reduced density-matrix functional theory (RDMFT). For atomic structure relaxations or ab-initio molecular dynamics the combination of density functional theory (DFT) and dynamical mean-field theory (DMFT) possesses a number of disadvantages, like the cumbersome evaluation of forces. We therefore describe a method, DFT+RDMFT, that combines many-particle effects based on reduced density-matrix functional theory with a density functional-like framework. A recent development is the construction of density-matrix functionals directly from many-particle theory such as methods from quantum chemistry or many-particle Green's functions. We present the underlying exact theorems and describe current progress towards quantitative functionals.
NASA Astrophysics Data System (ADS)
Abdul-Aziz, Ali; Ghosn, Louis J.; Baaklini, George Y.; Bhatt, Ramakrishna
2003-08-01
Ceramic matrix composites are being considered as candidate materials for high temperature aircraft engine components to replace the current high density metal alloys. The current Ceramic Matrix Composites (CMC) are engineered material composed of coated 2D woven high strength fiber tows and melt infiltrated ceramic matrix. Matrix voids are common anomalies generated during the melt infiltration process. The effects of these matrix porosities are usually associated with a reduction in the initial overall composite stiffness, and an increase in the thermal conductivity of the component. Furthermore, the role of the matrix as well as the coating is to protect the fibers from the harsh engine environment. Hence, the current design approach is to limit the design stress level of CMC components to be always below the first matrix cracking stress. In this study, the effects of matrix porosity on the initial component stiffness and the onset of matrix cracking are analyzed using a combined NDE/Finite-Element Technique. The Computed Tomography (CT) is utilized as the NDE technique to characterize the initial matrix porosity's locations and sizes in various CMC test specimens. The Finite Element is utilized to calculate the localized stress field around these pores based on the geometric modeling of the specimen's CT results, using image analysis and geometric modeling software. The same specimen was also scanned after tensile testing to a maximum nominal stress of 150 MPa to depict any growth of the previous observe voids. The post test CT scans depicted an enlargement and some coalescence of the existing voids.
Quenching of spin matrix elements in nuclei
NASA Astrophysics Data System (ADS)
Towner, I. S.
1987-11-01
Matrix elements of spin operators evaluated in a nuclear medium are systematically quenched compared to their values in free space. There are a number of contributing reasons for this. Foremost is the traditional nuclear structure difficulty of the inadequacy of the lowest-order shell-model wavefunctions. We use the Rayleigh-Schrödinger perturbation theory to correct for this, arguing that calculations must be carried through at least t o second order. This is a question of the appropriate effective interaction. We review the Landau-Migdal approach in which only RPA graphs are retained and discuss the strength of this interaction in the spin-isospin channel expressed in terms of the parameter g'. We also consider one-boson-exchange models and compare the two. The advantage of the OBEP models is that the two-nucleon meson-exchange current operators can be constructed to be consistent with the potential as required by the continuity equation for vector currents and the partial conservation (PCAC) equation for axial currents. We give a complete derivation of the MEC operators of heavy-meson range starting with the chiral Lagrangians used by Ivanov and Truhlik. Nonlocal terms are retained in the computations. We single out one class of MEC processes involving isobar excitation and demonstrate that in lowest order there is an equivalence between treating the isobar as an MEC correction and treating it as a nuclear constituent through the transition spin formalism. Differences occur in higher orders. There are a number of uncertainties in the isobar calculation involving the neglect of the isobar's natural width, the relativistic propagator being off the mass shell and the coupling constants not being known with any precision. We present a comprehensive calculation of core-polarisation, meson-exchange current and isobar-current corrections to low-energy M1 and Gamow-Teller transitions in closed-shell-plus-one nuclei (at LS and jj closed shells) expressing the results in
Rotordynamic Analysis with Shell Elements for the Transfer Matrix Method
1989-08-01
jACCESSION NO. 11. TITLE (Include Security Classification) (UNCLASSIFIED) ROTORDYNAMIC ANALYSIS WITH SHELL ELEMENTS FOR THE TRANSFER MATRIX METHOD 12...SECURITY CLASSIFICATION OF THIS PAGE AFIT/CI "OVERPRINT" iii ABSTRACT Rotordynamic Analysis with Shell Elements for the Transfer Matrix Method. (August...analysts in indus- try . ’ . ," Accesiu:, For NTIS CR,4i Fi FilC TA,: [3 0. fi A-1 B I ., ,.................. ,., ROTORDYNAMIC ANALYSIS WITH SHELL ELEMENTS
Excited State Effects in Nucleon Matrix Element Calculations
Constantia Alexandrou, Martha Constantinou, Simon Dinter, Vincent Drach, Karl Jansen, Theodoros Leontiou, Dru B Renner
2011-12-01
We perform a high-statistics precision calculation of nucleon matrix elements using an open sink method allowing us to explore a wide range of sink-source time separations. In this way the influence of excited states of nucleon matrix elements can be studied. As particular examples we present results for the nucleon axial charge g{sub A} and for the first moment of the isovector unpolarized parton distribution x{sub u-d}. In addition, we report on preliminary results using the generalized eigenvalue method for nucleon matrix elements. All calculations are performed using N{sub f} = 2+1+1 maximally twisted mass Wilson fermions.
Parameterized local hybrid functionals from density-matrix similarity metrics.
Janesko, Benjamin G; Scuseria, Gustavo E
2008-02-28
We recently proposed a real-space similarity metric comparing the Kohn-Sham one-particle density matrix to the local spin-density approximation model density matrix [Janesko and Scuseria, J. Chem. Phys. 127, 164117 (2007)]. This metric provides a useful ingredient for constructing local hybrid density functionals that locally mix exact exchange and semilocal density functional theory exchange. Here we present two lines of inquiry: An approximate similarity metric comparing exact versus generalized gradient approximation (GGA), exchange and parameterized mixing functions using these similarity metrics. This approach yields significantly improved thermochemistry, including GGA local hybrids whose thermochemical performance approaches GGA global hybrids.
Spectral density of the correlation matrix of factor models: a random matrix theory approach.
Lillo, F; Mantegna, R N
2005-07-01
We studied the eigenvalue spectral density of the correlation matrix of factor models of multivariate time series. By making use of the random matrix theory, we analytically quantified the effect of statistical uncertainty on the spectral density due to the finiteness of the sample. We considered a broad range of models, ranging from one-factor models to hierarchical multifactor models.
Vanishing of dipole matrix elements at level crossings.
NASA Technical Reports Server (NTRS)
Kocher, C. A.
1972-01-01
Demonstration that the vanishing of certain coupling matrix elements at level crossings follow from angular momentum commutation relations. A magnetic dipole transition having delta M = plus or minus 1, induced near a crossing of the levels in a nonzero magnetic field, is found to have a dipole matrix element comparable to or smaller than the quotient of the level separation and the field. This result also applies in the analogous electric field electric dipole case.
NASA Astrophysics Data System (ADS)
Casimir, J. B.; Kevorkian, S.; Vinh, T.
2005-10-01
This paper describes a procedure for building the dynamic stiffness matrix of two-dimensional elements with free edge boundary conditions. The dynamic stiffness matrix is the basis of the continuous element method. Then, the formulation is used to build a Kirchhoff rectangular plate element. Gorman's method of boundary condition decomposition and Levy's series are used to obtain the strong solution of the elementary problem. A symbolic computation software partially performs the construction of the dynamic stiffness matrix from this solution. The performances of the element are evaluated from comparisons with harmonic responses of plates obtained by the finite element method.
Information Theory Density Matrix for a Simple Quantum System.
ERIC Educational Resources Information Center
Titus, William J.
1979-01-01
Derives the density matrix that best describes, according to information theory, a one-dimensional single particle quantum system when the only information available is the values for the linear and quadratic position-momentum moments. (Author/GA)
Information Theory Density Matrix for a Simple Quantum System.
ERIC Educational Resources Information Center
Titus, William J.
1979-01-01
Derives the density matrix that best describes, according to information theory, a one-dimensional single particle quantum system when the only information available is the values for the linear and quadratic position-momentum moments. (Author/GA)
Deconstructing Wigner's density matrix concerning the mind-body question
NASA Astrophysics Data System (ADS)
Brandt, Howard E.
2002-06-01
In honor of the centennial of Eugene Wigner’s birth, a possible interpretation is given of the density matrix appearing in his classic paper, “Remarks on the mind-body question.” It is argued that nearinstantaneous vanishing of the quantum coherences of the reduced density matrix of the measured object would occur either in the case of Wigner’s friend, or in the case of any complex measuring automaton (conscious or not) making the measurement.
Stationary density matrix of a pumped polariton system.
Vera, Carlos Andrés; Cabo, Alejandro; González, Augusto
2009-03-27
The density matrix rho of a model polariton system is obtained numerically from a master equation which takes account of pumping and losses. In the stationary limit, the coherences between eigenstates of the Hamiltonian are 3 orders of magnitude smaller than the occupations, meaning that the stationary density matrix is approximately diagonal in the energy representation. A weakly distorted grand canonical Gibbs distribution fits well the occupations.
Edgar, Lowell T.; Hoying, James B.; Weiss, Jeffrey A.
2015-01-01
Mechanical interactions during angiogenesis, i.e., traction applied by neovessels to the extracellular matrix and the corresponding deformation, are important regulators of growth and neovascularization. We have previously designed, implemented, and validated a coupled model of angiogenesis in which a discrete microvessel growth model interacts with a continuous finite element mesh through the application of local remodeling sprout stresses (Edgar et al. in Biomech Model Mechanobiol, 2014). However, the initial implementation of this framework does not take matrix density into account when determined these remodeling stresses and is therefore insufficient for the study of angiogenesis within heterogeneous matrix environments such as those found in vivo. The objective of this study was to implement sensitivity to matrix density in the active stress generation within AngioFE in order to allow the study of angiogenic growth within a heterogeneous density environment. We accomplished this by scaling active sprout stresses relative to local matrix density using a scaling factor previously determined from experimental data. We then exercised the new functionality of the model by simulating angiogenesis within four different scenarios: homogeneous density, a narrow gap model, and matrix density gradient, and a construct subjected to repeated loading/unloading and preconditioning. These numerical experiments predicted heterogeneous matrix density in the initially homogeneous case, the closure and alignment of microvessels along a low-density gap, the formation of a unique cap-like structure during angiogenesis within a density gradient, and the alignment of microvessels in the absence of applied load due to preconditioning. The result of these in silico investigations demonstrate how matrix heterogeneity affects neovascularization and matrix deformation and provides a platform for studying angiogenesis in complicated and multi-faceted mechanical environments that
Smallwood, D.O.
1995-08-07
It is shown that the usual method for computing the coherence functions (ordinary, partial, and multiple) for a general multiple-input/multiple-output problem can be expressed as a modified form of Cholesky decomposition of the cross spectral density matrix of the inputs and outputs. The modified form of Cholesky decomposition used is G{sub zz} = LCL{prime}, where G is the cross spectral density matrix of inputs and outputs, L is a lower; triangular matrix with ones on the diagonal, and C is a diagonal matrix, and the symbol {prime} denotes the conjugate transpose. If a diagonal element of C is zero, the off diagonal elements in the corresponding column of L are set to zero. It is shown that the results can be equivalently obtained using singular value decomposition (SVD) of G{sub zz}. The formulation as a SVD problem suggests a way to order the inputs when a natural physical order of the inputs is absent.
Coulomb matrix elements in multi-orbital Hubbard models
NASA Astrophysics Data System (ADS)
Bünemann, Jörg; Gebhard, Florian
2017-04-01
Coulomb matrix elements are needed in all studies in solid-state theory that are based on Hubbard-type multi-orbital models. Due to symmetries, the matrix elements are not independent. We determine a set of independent Coulomb parameters for a d-shell and an f-shell and all point groups with up to 16 elements (O h , O, T d , T h , D 6h , and D 4h ). Furthermore, we express all other matrix elements as a function of the independent Coulomb parameters. Apart from the solution of the general point-group problem we investigate in detail the spherical approximation and first-order corrections to the spherical approximation.
Constraining neutrinoless double-beta decay matrix elements
NASA Astrophysics Data System (ADS)
Menendez, Javier
2015-10-01
Neutrinoless double-beta decay, if detected, would proof the Majorana nature of neutrinos. The decay lifetime is governed by the absolute neutrino masses and the nuclear matrix elements of the transition. Therefore accurate matrix elements are needed to asses the sensitivity of current and future experiments, and to determine the absolute neutrino masses and hierarchy with neutrinoless double-beta decay. However, present nuclear matrix element calculations show significant uncertainties. These affect the nuclear structure description of the mother and daughter nuclei, and also the treatment of the transition operator. In this talk I cover recent progress on neutrinoless double-beta decay nuclear matrix element calculations. On the one hand, I discuss the role of the size of the configuration space and of nuclear structure correlations. By comparing matrix elements obtained with different nuclear structure approaches and interactions, optimal strategies for improving the nuclear structure calculations capturing the most important correlations are identified. On the other hand, I describe first attempts to include two-body currents in the double-beta decay operator. They can be related to the ``quenching'' of the spin-isospin operator empirically found in nuclear structure studies.
Computer programs for the Boltzmann collision matrix elements
NASA Astrophysics Data System (ADS)
Das, P.
1989-09-01
When the distribution function in the kinetic theory of gases is expanded in a basis of orthogonal functions, the Boltzmann collision operators can be evaluated in terms of appropriate matrix elements. These matrix elements are usually given in terms of highly complex algebraic expressions. When Burnett functions, which consist of Sonine polynomials and spherical harmonics, are used as the basis, the irreducible tensor formalism provides expressions for the matrix elements that are algebraically simple, possess high symmetry, and are computationally more economical than in any other basis. The package reported here consists of routines to compute such matrix elements in a Burnett function basis for a mixture of hard sphere gases, as also the loss integral of a Burnett mode and the functions themselves. The matrix elements involve the Clebsch-Gordan and Brody-Moshinsky coefficients, both of which are used here for unusually high values of their arguments. For the purpose of validation both coefficients are computed using two different methods. Though written for hard sphere molecules the package can, with only slight modification, be adapted to more general molecular models as well.
Acceleration of matrix element computations for precision measurements
Brandt, Oleg; Gutierrez, Gaston; Wang, M. H.L.S.; Ye, Zhenyu
2014-11-25
The matrix element technique provides a superior statistical sensitivity for precision measurements of important parameters at hadron colliders, such as the mass of the top quark or the cross-section for the production of Higgs bosons. The main practical limitation of the technique is its high computational demand. Using the example of the top quark mass, we present two approaches to reduce the computation time of the technique by a factor of 90. First, we utilize low-discrepancy sequences for numerical Monte Carlo integration in conjunction with a dedicated estimator of numerical uncertainty, a novelty in the context of the matrix element technique. We then utilize a new approach that factorizes the overall jet energy scale from the matrix element computation, a novelty in the context of top quark mass measurements. The utilization of low-discrepancy sequences is of particular general interest, as it is universally applicable to Monte Carlo integration, and independent of the computing environment.
The matrix element method at next-to-leading order
NASA Astrophysics Data System (ADS)
Campbell, John M.; Giele, Walter T.; Williams, Ciaran
2012-11-01
This paper presents an extension of the matrix element method to next-to-leading order in perturbation theory, for electro-weak final states. To accomplish this we have developed a method to calculate next-to-leading order weights on an event-by-event basis. This allows for the definition of next-to-leading order likelihoods in exactly the same fashion as at leading order, thus extending the matrix element method to next-to-leading order. A welcome by-product of the method is the straightforward and efficient generation of unweighted next-to-leading order events. As examples of the application of our next-to-leading order matrix element method we consider the measurement of the mass of the Z boson and also the search for the Higgs boson in the four lepton channel.
Neutrinoless double-β decay and nuclear transition matrix elements
Rath, P. K.
2015-10-28
Within mechanisms involving the light Majorana neutrinos, squark-neutrino, Majorons, sterile neutrinos and heavy Majorana neutrino, nuclear transition matrix elements for the neutrinoless (β{sup −}β{sup −}){sub 0ν} decay of {sup 96}Zr, {sup 100}Mo, {sup 128,130}Te and {sup 150}Nd nuclei are calculated by employing the PHFB approach. Effects due to finite size of nucleons, higher order currents, short range correlations, and deformations of parent as well as daughter nuclei on the calculated matrix elements are estimated. Uncertainties in nuclear transition matrix elements within long-ranged mechanisms but for double Majoron accompanied (β{sup −}β{sup −}ϕϕ){sub 0ν} decay modes are 9%–15%. In the case of short ranged heavy Majorona neutrino exchange mechanism, the maximum uncertainty is about 35%. The maximum systematic error within the mechanism involving the exchange of light Majorana neutrino is about 46%.
The ab-initio density matrix renormalization group in practice
Olivares-Amaya, Roberto; Hu, Weifeng; Sharma, Sandeep; Yang, Jun; Chan, Garnet Kin-Lic; Nakatani, Naoki
2015-01-21
The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.
The ab-initio density matrix renormalization group in practice.
Olivares-Amaya, Roberto; Hu, Weifeng; Nakatani, Naoki; Sharma, Sandeep; Yang, Jun; Chan, Garnet Kin-Lic
2015-01-21
The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.
Discoveries far from the lamppost with matrix elements and ranking
Debnath, Dipsikha; Gainer, James S.; Matchev, Konstantin T.
2015-04-01
The prevalence of null results in searches for new physics at the LHC motivates the effort to make these searches as model-independent as possible. We describe procedures for adapting the Matrix Element Method for situations where the signal hypothesis is not known a priori. We also present general and intuitive approaches for performing analyses and presenting results, which involve the flattening of background distributions using likelihood information. The first flattening method involves ranking events by background matrix element, the second involves quantile binning with respect to likelihood (and other) variables, and the third method involves reweighting histograms by the inversemore » of the background distribution.« less
NASA Astrophysics Data System (ADS)
Todoroki, Akira; Omagari, Kazuomi
Carbon Fiber Reinforced Plastic (CFRP) laminates are adopted for fuel tank structures of next generation space rockets or automobiles. Matrix cracks may cause fuel leak or trigger fatigue damage. A monitoring system of the matrix crack density is required. The authors have developed an electrical resistance change method for the monitoring of delamination cracks in CFRP laminates. Reinforcement fibers are used as a self-sensing system. In the present study, the electric potential method is adopted for matrix crack density monitoring. Finite element analysis (FEA) was performed to investigate the possibility of monitoring matrix crack density using multiple electrodes mounted on a single surface of a specimen. The FEA reveals the matrix crack density increases electrical resistance for a target segment between electrodes. Experimental confirmation was also performed using cross-ply laminates. Eight electrodes were mounted on a single surface of a specimen using silver paste after polishing of the specimen surface with sandpaper. The two outermost electrodes applied electrical current, and the inner electrodes measured electric voltage changes. The slope of electrical resistance during reloading is revealed to be an appropriate index for the detection of matrix crack density.
A top quark mass measurement using a matrix element method
Linacre, Jacob Thomas
2009-01-01
A measurement of the mass of the top quark is presented, using top-antitop pair (t$\\bar{t}$) candidate events for the lepton+jets decay channel. The measurement makes use of Tevatron p$\\bar{p}$ collision data at centre-of-mass energy √s = 1.96 TeV, collected at the CDF detector. The top quark mass is measured by employing an unbinned maximum likelihood method where the event probability density functions are calculated using signal (t$\\bar{t}$) and background (W+jets) matrix elements, as well as a set of parameterised jet-to-parton mapping functions. The likelihood function is maximised with respect to the top quark mass, the fraction of signal events, and a correction to the jet energy scale (JES) of the calorimeter jets. The simultaneous measurement of the JES correction (Δ_{JES}) provides an in situ jet energy calibration based on the known mass of the hadronically decaying W boson. Using 578 lepton+jets candidate events corresponding to 3.2 fb ^{-1} of integrated luminosity, the top quark mass is measured to be m_{t} = 172.4± 1.4 (stat+Δ_{JES}) ±1.3 (syst) GeV=c^{2}, one of the most precise single measurements to date.
Revisting the Density Matrix Expansion with Regulated Chiral Interactions
NASA Astrophysics Data System (ADS)
Dyhdalo, Alexander; Furnstahl, Richard; Bogner, Scott; Schunck, Nicolas; Navarro Perez, Rodrigo
2016-09-01
The density matrix expansion provides a general way to map microscopic interactions to a local functional. Previous density matrix expansion formulations added unregulated chiral long-range potentials to a Skyrme-type functional, which accounted for the short-range contributions. We implement the expansion with new coordinate space regulators using the regulator cutoff as a tool to adiabatically turn on finite-range pion interactions. We discuss `smoking guns' for correct inclusion of 3-body forces, which are implemented in a normal-ordering prescription, and compare to ab initio calculations.
Spectral Density Matrix of a Single Photon Measured
NASA Astrophysics Data System (ADS)
Wasilewski, Wojciech; Kolenderski, Piotr; Frankowski, Robert
2007-09-01
We propose and demonstrate a method for measuring the spectral density matrix of a single photon pulse. The method is based on registering Hong-Ou-Mandel interference between a photon to be measured and a pair of attenuated and suitably delayed laser pulses described by a known spectral amplitude. The density matrix is retrieved from a two-dimensional interferogram of coincidence counts. The method has been implemented for a type-I down-conversion source, pumped by ultrashort laser pulses. The experimental results agree well with a theoretical model which takes into account the temporal as well as spatial effects in the source.
Spectral density matrix of a single photon measured.
Wasilewski, Wojciech; Kolenderski, Piotr; Frankowski, Robert
2007-09-21
We propose and demonstrate a method for measuring the spectral density matrix of a single photon pulse. The method is based on registering Hong-Ou-Mandel interference between a photon to be measured and a pair of attenuated and suitably delayed laser pulses described by a known spectral amplitude. The density matrix is retrieved from a two-dimensional interferogram of coincidence counts. The method has been implemented for a type-I down-conversion source, pumped by ultrashort laser pulses. The experimental results agree well with a theoretical model which takes into account the temporal as well as spatial effects in the source.
Interface Cohesive Elements to Model Matrix Crack Evolution in Composite Laminates
NASA Astrophysics Data System (ADS)
Shi, Y.; Pinna, C.; Soutis, C.
2014-02-01
In this paper, the transverse matrix (resin) cracking developed in multidirectional composite laminates loaded in tension was numerically investigated by a finite element (FE) model implemented in the commercially available software Abaqus/Explicit 6.10. A theoretical solution using the equivalent constraint model (ECM) of the damaged laminate developed by Soutis et al. was employed to describe matrix cracking evolution and compared to the proposed numerical approach. In the numerical model, interface cohesive elements were inserted between neighbouring finite elements that run parallel to fibre orientation in each lamina to simulate matrix cracking with the assumption of equally spaced cracks (based on experimental measurements and observations). The stress based traction-separation law was introduced to simulate initiation of matrix cracking and propagation under mixed-mode loading. The numerically predicted crack density was found to depend on the mesh size of the model and the material fracture parameters defined for the cohesive elements. Numerical predictions of matrix crack density as a function of applied stress are in a good agreement to experimentally measured and theoretically (ECM) obtained values, but some further refinement will be required in near future work.
NASA Astrophysics Data System (ADS)
Kumar, Deepak; Roy, Rene; Kweon, Jin-Hwe; Choi, Jin-ho
2016-06-01
Sub-laminate damage in the form of matrix cracking and delamination was simulated by using interface cohesive elements in the finite element (FE) software ABAQUS. Interface cohesive elements were inserted parallel to the fiber orientation in the transverse ply with equal spacing (matrix cracking) and between the interfaces (delamination). Matrix cracking initiation in the cohesive elements was based on stress traction separation laws and propagated under mixed-mode loading. We expanded the work of Shi et al. (Appl. Compos. Mater. 21, 57-70 2014) to include delamination and simulated additional [45/-45/0/90]s and [02/90n]s { n = 1,2,3} CFRP laminates and a [0/903]s GFRP laminate. Delamination damage was quantified numerically in terms of damage dissipative energy. We observed that transverse matrix cracks can propagate to the ply interface and initiate delamination. We also observed for [0/90n/0] laminates that as the number of 90° ply increases past n = 2, the crack density decreases. The predicted crack density evolution compared well with experimental results and the equivalent constraint model (ECM) theory. Empirical relationships were established between crack density and applied stress by linear curve fitting. The reduction of laminate elastic modulus due to cracking was also computed numerically and it is in accordance with reported experimental measurements.
Distributions of off-diagonal scattering matrix elements: Exact results
Nock, A. Kumar, S. Sommers, H.-J. Guhr, T.
2014-03-15
Scattering is a ubiquitous phenomenon which is observed in a variety of physical systems which span a wide range of length scales. The scattering matrix is the key quantity which provides a complete description of the scattering process. The universal features of scattering in chaotic systems is most generally modeled by the Heidelberg approach which introduces stochasticity to the scattering matrix at the level of the Hamiltonian describing the scattering center. The statistics of the scattering matrix is obtained by averaging over the ensemble of random Hamiltonians of appropriate symmetry. We derive exact results for the distributions of the real and imaginary parts of the off-diagonal scattering matrix elements applicable to orthogonally-invariant and unitarily-invariant Hamiltonians, thereby solving a long standing problem. -- Highlights: •Scattering problem in complex or chaotic systems. •Heidelberg approach to model the chaotic nature of the scattering center. •A novel route to the nonlinear sigma model based on the characteristic function. •Exact results for the distributions of off-diagonal scattering-matrix elements. •Universal aspects of the scattering-matrix fluctuations.
Some measurements for determining strangeness matrix elements in the nucleon
Henley, E.M.; Pollock, S.J.; Ying, S.; Frederico, T.; Krein,; Williams, A.G.
1991-12-31
Some experiments to measure strangeness matrix elements of the proton are proposed. Two of these suggestions are described in some detail, namely electro-production of phi mesons and the difference between neutrino and antineutrino scattering for isospin zero targets such as deuterium.
Some measurements for determining strangeness matrix elements in the nucleon
Henley, E.M.; Pollock, S.J.; Ying, S. ); Frederico, T. , Sao Jose dos Campos, SP . Inst. de Estudos Avancados); Krein, . Inst. de Fisica Teorica); Williams, A.G. )
1991-01-01
Some experiments to measure strangeness matrix elements of the proton are proposed. Two of these suggestions are described in some detail, namely electro-production of phi mesons and the difference between neutrino and antineutrino scattering for isospin zero targets such as deuterium.
Precision Measurement of Transition Matrix Elements via Light Shift Cancellation
2012-12-14
two zeros, so that simultaneous fits to both zeros accurately determine R6p, independent of the other pa - rameters. With the addition of sufficiently...data set. The extracted matrix elements are insensitive to the exclusion value. [35] U. Volz and H. Schmoranzer, Phys. Scr. T65, 48 (1996). [36] See
Auxiliary Density Matrix Methods for Hartree-Fock Exchange Calculations.
Guidon, Manuel; Hutter, Jürg; VandeVondele, Joost
2010-08-10
The calculation of Hartree-Fock exchange (HFX) is computationally demanding for large systems described with high-quality basis sets. In this work, we show that excellent performance and good accuracy can nevertheless be obtained if an auxiliary density matrix is employed for the HFX calculation. Several schemes to derive an auxiliary density matrix from a high-quality density matrix are discussed. Key to the accuracy of the auxiliary density matrix methods (ADMM) is the use of a correction based on standard generalized gradient approximations for HFX. ADMM integrates seamlessly in existing HFX codes and, in particular, can be employed in linear scaling implementations. Demonstrating the performance of the method, the effect of HFX on the structure of liquid water is investigated in detail using Born-Oppenheimer molecular dynamics simulations (300 ps) of a system of 64 molecules. Representative for large systems are calculations on a solvated protein (Rubredoxin), for which ADMM outperforms the corresponding standard HFX implementation by approximately a factor 20.
Communication: Four-component density matrix renormalization group
Knecht, Stefan Reiher, Markus; Legeza, Örs
2014-01-28
We present the first implementation of the relativistic quantum chemical two- and four-component density matrix renormalization group algorithm that includes a variational description of scalar-relativistic effects and spin–orbit coupling. Numerical results based on the four-component Dirac–Coulomb Hamiltonian are presented for the standard reference molecule for correlated relativistic benchmarks: thallium hydride.
Rovibrational matrix elements of the quadrupole moment of N2 in a solid parahydrogen matrix
NASA Astrophysics Data System (ADS)
Mishra, Adya P.; Balasubramanian, T. K.
2008-11-01
The present work pertains to the study of the rotational dynamics of N2 molecules solvated in a matrix of solid para-H2. It is shown that the mixing of the rotational states due to the anisotropic part of the N2-H2 pair potential in the solid gives rise to an additional 5.4% contribution to the intensity of quadrupole-induced double transitions involving N2-H2 pair. Hence the recently reported quadrupole moment matrix element of N2 in a solid para-H2 crystal [A. P. Mishra and T. K. Balasubramanian, J. Chem. Phys. 125, 124507 (2006)], which was deduced from a comparison of the theoretical intensity (with rotational mixing of states neglected) with the measured value is larger by ˜2.7%. The ground electronic state rovibrational matrix elements ⟨v'J'|Q2(r)|vJ⟩ of N2 molecule in a solid parahydrogen matrix for v,v'≤1 and J,J'≤4 have also been computed by taking into account the changes in the intramolecular potential of N2 due to the intermolecular interaction in the matrix. The computed quadrupole moment matrix elements agree well with a few available values (for v =v'=0) deduced from the observed transitions.
Improved density matrix expansion for spin-unsaturated nuclei
Gebremariam, B.; Bogner, S. K.; Duguet, T.
2010-07-15
A current objective of low-energy nuclear theory is to build nonempirical nuclear energy density functionals (EDFs) from underlying internucleon interactions and many-body perturbation theory (MBPT). The density matrix expansion (DME) of Negele and Vautherin is a convenient method to map highly nonlocal Hartree-Fock expressions into the form of a quasi-local Skyrme functional with density-dependent couplings. In this work, we assess the accuracy of the DME at reproducing the nonlocal exchange (Fock) contribution to the energy. In contrast to the scalar part of the density matrix for which the original formulation of Negele and Vautherin is reasonably accurate, we demonstrate the necessity to reformulate the DME for the vector part of the density matrix, which is needed for an accurate description of spin-unsaturated nuclei. Phase-space-averaging techniques are shown to yield a significant improvement for the vector part of the density matrix compared to the original formulation of Negele and Vautherin. The key to the improved accuracy is to take into account the anisotropy that characterizes the local momentum distribution in the surface region of finite Fermi systems. Optimizing separately the DME for the central, tensor, and spin-orbit contributions to the Fock energy, one reaches a few-percent accuracy over a representative set of semi-magic nuclei. With such an accuracy at hand, one can envision using the corresponding Skyrme-like energy functional as a microscopically constrained starting point around which future phenomenological parametrizations can be built and refined.
Smallwood, D. O.
1996-01-01
It is shown that the usual method for estimating the coherence functions (ordinary, partial, and multiple) for a general multiple-input! multiple-output problem can be expressed as a modified form of Cholesky decomposition of the cross-spectral density matrix of the input and output records. The results can be equivalently obtained using singular value decomposition (SVD) of the cross-spectral density matrix. Using SVD suggests a new form of fractional coherence. The formulation as a SVD problem also suggests a way to order the inputs when a natural physical order of the inputs is absent.
Some New Elements for the Matrix Displacement Method
1968-10-01
OCT 1968 2. REPORT TYPE 3. DATES COVERED 00-00-1968 to 00-00-1968 4. TITLE AND SUBTITLE Some New Elements for the Matrix Displacement Method 5a...ORGANIZATION NAME(S) AND ADDRESS(ES) Air Force Flight Dynamics Laboratory,Wright Patterson AFB,OH,45433 8. PERFORMING ORGANIZATION REPORT NUMBER 9...on Matrix Methods in Structural Mechanics (2nd) Held at Wright-Patterson Air Force Base, Ohio, on 15-17 October 1968. 14. ABSTRACT 15. SUBJECT TERMS
Covariances from Light-Element R-Matrix Analyses
Hale, G.M.
2008-12-15
We review the method for obtaining covariance information for light-element reactions using R-matrix theory. The general LANL R-matrix analysis code EDA provides accurate covariances for the resonance parameters at a solution due to the search algorithm it uses to find a local minimum of the chi-square surface. This information is used, together with analytically calculated sensitivity derivatives, in the first-order error propagation equation to obtain cross-section covariances for all reactions included in the analysis. Examples are given of the covariances obtained from the EDA analyses for n-p scattering and for the n+{sup 6}Li reactions used in the latest light-element standard cross section evaluation. Also discussed is a method of defining 'pure theory' correlations that could be useful for extensions to higher energies and heavier systems.
Nuclear matrix elements for double-β decay
NASA Astrophysics Data System (ADS)
Barea, J.; Kotila, J.; Iachello, F.
2013-01-01
Background: Direct determination of the neutrino mass through double-β decay is at the present time one of the most important areas of experimental and theoretical research in nuclear and particle physics.Purpose: We calculate nuclear matrix elements for the extraction of the average neutrino mass in neutrinoless double-β decay.Methods: The microscopic interacting boson model (IBM-2) is used.Results: Nuclear matrix elements in the closure approximation are calculated for 48Ca, 76Ge, 82Se, 96Zr, 100Mo, 110Pd, 116Cd, 124Sn, 128Te, 130Te, 148Nd, 150Nd, 154Sm, 160Gd, and 198Pt decay.Conclusions: Realistic predictions for the expected half-lives in neutrinoless double-β decay with light and heavy neutrino exchange in terms of neutrino masses are made and limits are set from current experiments.
Magic wavelengths, matrix elements, polarizabilities, and lifetimes of Cs
NASA Astrophysics Data System (ADS)
Safronova, M. S.; Safronova, U. I.; Clark, Charles W.
2016-07-01
Motivated by recent interest in their applications, we report a systematic study of Cs atomic properties calculated by a high-precision relativistic all-order method. Excitation energies, reduced matrix elements, transition rates, and lifetimes are determined for levels with principal quantum numbers n ≤12 and orbital angular momentum quantum numbers l ≤3 . Recommended values and estimates of uncertainties are provided for a number of electric-dipole transitions and the electric dipole polarizabilities of the n s , n p , and n d states. We also report a calculation of the electric quadrupole polarizability of the ground state. We display the dynamic polarizabilities of the 6 s and 7 p states for optical wavelengths between 1160 and 1800 nm and identify corresponding magic wavelengths for the 6 s -7 p1 /2 and 6 s -7 p3 /2 transitions. The values of relevant matrix elements needed for polarizability calculations at other wavelengths are provided.
Calculation of transition matrix elements by nonsingular orbital transformations
NASA Astrophysics Data System (ADS)
Kývala, Mojmír
A general strategy is described for the evaluation of transition matrix elements between pairs of full class CI wave functions built up from mutually nonorthogonal molecular orbitals. A new method is proposed for the counter-transformation of the linear expansion coefficients of a full CI wave function under a nonsingular transformation of the molecular-orbital basis. The method, which consists in a straightforward application of the Cauchy-Binet formula to the definition of a Slater determinant, is shown to be simple and suitable for efficient implementation on current high-performance computers. The new method appears mainly beneficial to the calculation of miscellaneous transition matrix elements among individually optimized CASSCF states and to the re-evaluation of the CASCI expansion coefficients in Slater-determinant bases formed from arbitrarily rotated (e.g., localized or, conversely, delocalized) active molecular orbitals.
Disk level S-matrix elements at eikonal Regge limit
NASA Astrophysics Data System (ADS)
Garousi, Mohammad R.
2011-01-01
We examine the calculation of the color-ordered disk level S-matrix element of massless scalar vertex operators for the special case that some of the Mandelstam variables for which there are no open string channel in the amplitude, are set to zero. By explicit calculation we show that the string form factors in the 2n-point functions reduce to one at the eikonal Regge limit.
A stochastic method for computing hadronic matrix elements
Alexandrou, Constantia; Constantinou, Martha; Dinter, Simon; ...
2014-01-24
In this study, we present a stochastic method for the calculation of baryon 3-point functions which is an alternative to the typically used sequential method offering more versatility. We analyze the scaling of the error of the stochastically evaluated 3-point function with the lattice volume and find a favorable signal to noise ratio suggesting that the stochastic method can be extended to large volumes providing an efficient approach to compute hadronic matrix elements and form factors.
Calculating weak matrix elements using HYP staggered fermions
T. Bhattacharya; G. T. Fleming; G. Kilcup; R. Gupta; W. Lee; S. Sharpe
2004-03-01
We present preliminary results of weak matrix elements relevant to CP violation calculated using the HYP (II) staggered fermions. Since the complete set of matching coefficients at the one-loop level became available recently, we have constructed lattice operators with all the g{sup 2} corrections included. The main results include both {Delta}I = 3/2 and {Delta}I = 1/2 contributions.
[Electron transfer between globular proteins. Evaluation of a matrix element].
Lakhno, V D; Chuev, G N; Ustinin, M N
1998-01-01
The dependence of the matrix element of the probability of interprotein electron transfer on the mutual orientation of the donor and acceptor centers and the distance between them was calculated. The calculations were made under the assumption that electron transfer proceeds mainly by a collective excitation of polaron nature, like a solvated electron state. The results obtained are consistent with experimental data and indicate the nonexponential behavior of this dependence in the case when the distance transfer is less than 20 A.
Reweighting QCD matrix-element and parton-shower calculations
NASA Astrophysics Data System (ADS)
Bothmann, Enrico; Schönherr, Marek; Schumann, Steffen
2016-11-01
We present the implementation and validation of the techniques used to efficiently evaluate parametric and perturbative theoretical uncertainties in matrix-element plus parton-shower simulations within the Sherpa event-generator framework. By tracing the full α _s and PDF dependences, including the parton-shower component, as well as the fixed-order scale uncertainties, we compute variational event weights on-the-fly, thereby greatly reducing the computational costs to obtain theoretical-uncertainty estimates.
A real-space stochastic density matrix approach for density functional electronic structure.
Beck, Thomas L
2015-12-21
The recent development of real-space grid methods has led to more efficient, accurate, and adaptable approaches for large-scale electrostatics and density functional electronic structure modeling. With the incorporation of multiscale techniques, linear-scaling real-space solvers are possible for density functional problems if localized orbitals are used to represent the Kohn-Sham energy functional. These methods still suffer from high computational and storage overheads, however, due to extensive matrix operations related to the underlying wave function grid representation. In this paper, an alternative stochastic method is outlined that aims to solve directly for the one-electron density matrix in real space. In order to illustrate aspects of the method, model calculations are performed for simple one-dimensional problems that display some features of the more general problem, such as spatial nodes in the density matrix. This orbital-free approach may prove helpful considering a future involving increasingly parallel computing architectures. Its primary advantage is the near-locality of the random walks, allowing for simultaneous updates of the density matrix in different regions of space partitioned across the processors. In addition, it allows for testing and enforcement of the particle number and idempotency constraints through stabilization of a Feynman-Kac functional integral as opposed to the extensive matrix operations in traditional approaches.
Localized density matrix minimization and linear-scaling algorithms
NASA Astrophysics Data System (ADS)
Lai, Rongjie; Lu, Jianfeng
2016-06-01
We propose a convex variational approach to compute localized density matrices for both zero temperature and finite temperature cases, by adding an entry-wise ℓ1 regularization to the free energy of the quantum system. Based on the fact that the density matrix decays exponentially away from the diagonal for insulating systems or systems at finite temperature, the proposed ℓ1 regularized variational method provides an effective way to approximate the original quantum system. We provide theoretical analysis of the approximation behavior and also design convergence guaranteed numerical algorithms based on Bregman iteration. More importantly, the ℓ1 regularized system naturally leads to localized density matrices with banded structure, which enables us to develop approximating algorithms to find the localized density matrices with computation cost linearly dependent on the problem size.
Double-β decay matrix elements from lattice quantum chromodynamics
NASA Astrophysics Data System (ADS)
Tiburzi, Brian C.; Wagman, Michael L.; Winter, Frank; Chang, Emmanuel; Davoudi, Zohreh; Detmold, William; Orginos, Kostas; Savage, Martin J.; Shanahan, Phiala E.; Nplqcd Collaboration
2017-09-01
A lattice quantum chromodynamics (LQCD) calculation of the nuclear matrix element relevant to the n n →p p e e ν¯eν¯e transition is described in detail, expanding on the results presented in Ref. [P. E. Shanahan et al., Phys. Rev. Lett. 119, 062003 (2017), 10.1103/PhysRevLett.119.062003]. This matrix element, which involves two insertions of the weak axial current, is an important input for phenomenological determinations of double-β decay rates of nuclei. From this exploratory study, performed using unphysical values of the quark masses, the long-distance deuteron-pole contribution to the matrix element is separated from shorter-distance hadronic contributions. This polarizability, which is only accessible in double-weak processes, cannot be constrained from single-β decay of nuclei, and is found to be smaller than the long-distance contributions in this calculation, but non-negligible. In this work, technical aspects of the LQCD calculations, and of the relevant formalism in the pionless effective field theory, are described. Further calculations of the isotensor axial polarizability, in particular near and at the physical values of the light-quark masses, are required for precise determinations of both two-neutrino and neutrinoless double-β decay rates in heavy nuclei.
ARPES matrix element and the waterfall effect in the cuprates.
NASA Astrophysics Data System (ADS)
Basak, Susmita; Das, Tanmoy; Nieminen, Jouko; Lindroos, Matti; Lin, Hsin; Markiewicz, Robert; Bansil, Arun
2009-03-01
The high-energy kink (HEK) or the 'waterfall' effect as seen in angle-resolved photoemission spectra (ARPES) in the cuprates has the potential of revealing important information about the dressing of quasiparticles by electronic excitations [1,2,3]. However, recently it has been suggested that matrix element effects radically modify the experimental spectra in Bi2Sr2CaCu2O8 (Bi2212), and it has been questioned whether the HEK exists [4]. Here we discuss how the interplay between the matrix element and self-energy effects shapes the ARPES spectra. Both the ARPES matrix element and the self-energy are found to be necessary for understanding the experimental spectra. Work supported in part by the USDOE. [1] R. S. Markiewicz et al., Phys. Rev. B 76, 174514 (2007). [2] A. Macridin et al.,Phys. Rev. Lett. 99, 237001 (2007). [3] Tanmoy Das et al., cond-mat:0807.4257. [4] D.S. Inosov et al., Phys. Rev. Lett. 99, 237002 (2007).
Algebraic evaluation of matrix elements in the Laguerre function basis
NASA Astrophysics Data System (ADS)
McCoy, A. E.; Caprio, M. A.
2016-02-01
The Laguerre functions constitute one of the fundamental basis sets for calculations in atomic and molecular electron-structure theory, with applications in hadronic and nuclear theory as well. While similar in form to the Coulomb bound-state eigenfunctions (from the Schrödinger eigenproblem) or the Coulomb-Sturmian functions (from a related Sturm-Liouville problem), the Laguerre functions, unlike these former functions, constitute a complete, discrete, orthonormal set for square-integrable functions in three dimensions. We construct the SU(1, 1) × SO(3) dynamical algebra for the Laguerre functions and apply the ideas of factorization (or supersymmetric quantum mechanics) to derive shift operators for these functions. We use the resulting algebraic framework to derive analytic expressions for matrix elements of several basic radial operators (involving powers of the radial coordinate and radial derivative) in the Laguerre function basis. We illustrate how matrix elements for more general spherical tensor operators in three dimensional space, such as the gradient, may then be constructed from these radial matrix elements.
Magnesium Matrix Composite Foams-Density, Mechanical Properties, and Applications
2012-07-24
known that the effect of particle-matrix interfacial bonding is much less significant under compression compared to under tension [33,34]. One of the...parameter). Some syntactic foam composites are found to have less than 0.4 g/cc density in Figure 9. These data points belong to foams that contain...syntactic foams containing porosity only inside hollow particles. The yield strength values for various types of MMSFs, including aluminum, titanium , and
Multi-jet Merging with NLO Matrix Elements
Siegert, Frank; Hoche, Stefan; Krauss, Frank; Schonherr, Marek; /Dresden, Tech. U.
2011-08-18
In the algorithm presented here, the ME+PS approach to merge samples of tree-level matrix elements into inclusive event samples is combined with the POWHEG method, which includes exact next-to-leading order matrix elements in the parton shower. The advantages of the method are discussed and the quality of its implementation in SHERPA is exemplified by results for e{sup +}e{sup -} annihilation into hadrons at LEP, for deep-inelastic lepton-nucleon scattering at HERA, for Drell-Yan lepton-pair production at the Tevatron and for W{sup +}W{sup -}-production at LHC energies. The simulation of hard QCD radiation in parton-shower Monte Carlos has seen tremendous progress over the last years. It was largely stimulated by the need for more precise predictions at LHC energies where the large available phase space allows additional hard QCD radiation alongside known Standard Model processes or even signals from new physics. Two types of algorithms have been developed, which allow to improve upon the soft-collinear approximations made in the parton shower, such that hard radiation is simulated according to exact matrix elements. In the ME+PS approach [1] higher-order tree-level matrix elements for different final-state jet multiplicity are merged with each other and with subsequent parton shower emissions to generate an inclusive sample. Such a prescription is invaluable for analyses which are sensitive to final states with a large jet multiplicity. The only remaining deficiency of such tree-level calculations is the large uncertainty stemming from scale variations. The POWHEG method [2] solves this problem for the lowest multiplicity subprocess by combining full NLO matrix elements with the parton shower. While this leads to NLO accuracy in the inclusive cross section and the exact radiation pattern for the first emission, it fails to describe higher-order emissions with improved accuracy. Thus it is not sufficient if final states with high jet multiplicities are considered
Weak matrix elements on the lattice - Circa 1995
Soni, A.
1995-10-03
Status of weak matrix elements is reviewed. In particular, e{prime}/e, B {yields} K*{gamma}, B{sub B} and B{sub B}, are discussed and the overall situation with respect to the lattice effort and some of its phenomenological implications are summarised. For e{prime}/e the need for the relevant matrix elements is stressed in view of the forthcoming improved experiments. For some of the operators, (e.g. O{sub 6}), even bound on their matrix elements would be very helpful. On B {yields} K{degrees}{gamma}, a constant behavior of T{sub 2} appears disfavored although dependence of T{sub 2} could, of course, be milder than a simple pole. Improved data is badly needed to settle this important issue firmly, especially in view of its ramification for extractions of V{sub td} from B {yields} {rho}{gamma}. On B{sub {kappa}}, the preliminary result from JLQCD appears to contradict Sharpe et al. JLQCD data seems to fit very well to linear {alpha} dependence and leads to an appreciably lower value of B{sub {kappa}}. Four studies of B{sub {kappa}} in the {open_quotes}full{close_quotes} (n{sub f} = 2) theory indicate very little quenching effects on B{sub {kappa}}; the full theory value seems to be just a little less than the quenched result. Based on expectations from HQET, analysis of B-parameter (B{sub h}{ell}) for the heavy-light mesons via B{sub h}{ell}) = constant + constants{prime}/m{sub h}{ell} is suggested. A summary of an illustrative sample of hadron matrix elements is given and constraints on CKM parameters (e.g. V{sub td}/V{sub ts}, on the unitarity triangle and on x{sub s}/x{sub d}, emerging from the lattice calculations along with experimental results are briefly discussed. In quite a few cases, for the first time, some indication of quenching errors on weak matrix elements are now becoming available.
Jordan, Daniel K; Mazziotti, David A
2005-02-22
Two classes of linear-scaling methods to replace diagonalization of the one-particle Hamiltonian matrix in density functional theory are compared to each other. Purification takes a density matrix with the correct eigenfunctions and corrects the occupation numbers; density matrix minimization takes a density matrix with correct occupation numbers and corrects the eigenfunctions by rotating the orbitals. Computational comparisons are performed through modification of the MondoSCF program on water clusters and the protein endothelin. A purification scheme and a density matrix minimization scheme, based on the 1,2-contracted Schrodinger equation [D. A. Mazziotti, J. Chem. Phys. 115, 8305 (2001)] are implemented in large systems.
Uncertainty evaluation for the matrix ``solidified state'' of fissionable elements
NASA Astrophysics Data System (ADS)
Iliescu, Elena; Iancso, Georgeta
2012-09-01
In case of the analysis of the radioactive liquid samples, no matter the relative physical analysis method used, two impediments act that belong to the behavior in time of the dispersion state of the liquid samples to be analyzed and of the standard used in the analysis. That is, one of them refers to the state of the sample to be analyzed when being sampled, which "alter" during the time elapsed from sampling up to the analysis of the sample. The other impediment is the natural change of the dispersion state of the standard radioactive solutions, due to the occurrence and evolution in time of the radiocolloidal and pseudo-radiocolloidal states. These radiocolloidal states are states of aggregation and they lead to the destruction of the homogeneity of the solutions. Taking into consideration the advantages offered by the relative physical methods of analysis as against the chemical or the radiochemical ones, different ways of eliminating these impediments have been tried. We eliminated these impediments processing the liquid reference materials (the solutions calibrated in radionuclides of interest), immediately after the preparation. This processing changes the liquid physical state of the reference materials in a "solidified state". Through this procedure the dispersion states of the samples, practically, can no longer be essentially modified in time and also ensure the uniform distribution of the radionuclides of interest in the elemental matrix of the samples "state solidified". The homogeneity of the distribution of the atoms of the radionuclides from the samples "solidified state" was checked up through the track micromapping technique of the alpha particles. Through this technique, in the chemically etched track detectors that were put in direct contact with the sample for a determined period of time, the alpha exposure time of the detectors, micromaps of alpha tracks were obtained. These micromaps are retorts through tracks of the distributions atoms of
Uncertainty evaluation for the matrix 'solidified state' of fissionable elements
Iliescu, Elena; Iancso, Georgeta
2012-09-06
In case of the analysis of the radioactive liquid samples, no matter the relative physical analysis method used, two impediments act that belong to the behavior in time of the dispersion state of the liquid samples to be analyzed and of the standard used in the analysis. That is, one of them refers to the state of the sample to be analyzed when being sampled, which 'alter' during the time elapsed from sampling up to the analysis of the sample. The other impediment is the natural change of the dispersion state of the standard radioactive solutions, due to the occurrence and evolution in time of the radiocolloidal and pseudo-radiocolloidal states. These radiocolloidal states are states of aggregation and they lead to the destruction of the homogeneity of the solutions. Taking into consideration the advantages offered by the relative physical methods of analysis as against the chemical or the radiochemical ones, different ways of eliminating these impediments have been tried. We eliminated these impediments processing the liquid reference materials (the solutions calibrated in radionuclides of interest), immediately after the preparation. This processing changes the liquid physical state of the reference materials in a 'solidified state'. Through this procedure the dispersion states of the samples, practically, can no longer be essentially modified in time and also ensure the uniform distribution of the radionuclides of interest in the elemental matrix of the samples 'state solidified'. The homogeneity of the distribution of the atoms of the radionuclides from the samples 'solidified state' was checked up through the track micromapping technique of the alpha particles. Through this technique, in the chemically etched track detectors that were put in direct contact with the sample for a determined period of time, the alpha exposure time of the detectors, micromaps of alpha tracks were obtained. These micromaps are retorts through tracks of the distributions atoms of
Acceleration of matrix element computations for precision measurements
Brandt, Oleg; Gutierrez, Gaston; Wang, M. H.L.S.; ...
2014-11-25
The matrix element technique provides a superior statistical sensitivity for precision measurements of important parameters at hadron colliders, such as the mass of the top quark or the cross-section for the production of Higgs bosons. The main practical limitation of the technique is its high computational demand. Using the example of the top quark mass, we present two approaches to reduce the computation time of the technique by a factor of 90. First, we utilize low-discrepancy sequences for numerical Monte Carlo integration in conjunction with a dedicated estimator of numerical uncertainty, a novelty in the context of the matrix elementmore » technique. We then utilize a new approach that factorizes the overall jet energy scale from the matrix element computation, a novelty in the context of top quark mass measurements. The utilization of low-discrepancy sequences is of particular general interest, as it is universally applicable to Monte Carlo integration, and independent of the computing environment.« less
Molarity (Aromic Density) of the Elements as Pure Crystals.
ERIC Educational Resources Information Center
Pauling, Linus; Herman, Zelek S.
1985-01-01
Provides background information for teachers on the atomic density of the elements as pure crystals. Atomic density is defined as the reciprocal of the atomic volume. Includes atomic-density diagrams which were prepared using the atomic-volume values given by Singman, supplemented by additional values for some allotropes. (JN)
Molarity (Aromic Density) of the Elements as Pure Crystals.
ERIC Educational Resources Information Center
Pauling, Linus; Herman, Zelek S.
1985-01-01
Provides background information for teachers on the atomic density of the elements as pure crystals. Atomic density is defined as the reciprocal of the atomic volume. Includes atomic-density diagrams which were prepared using the atomic-volume values given by Singman, supplemented by additional values for some allotropes. (JN)
Density Functional Approach and Random Matrix Theory in Proteogenesis
NASA Astrophysics Data System (ADS)
Yamanaka, Masanori
2017-02-01
We study the energy-level statistics of amino acids by random matrix theory. The molecular orbital and the Kohn-Sham orbital energies are calculated using ab initio and density-functional formalisms for 20 different amino acids. To generate statistical data, we performed a multipoint calculation on 10000 molecular structures produced via a molecular dynamics simulation. For the valence orbitals, the energy-level statistics exhibit repulsion, but the universality in the random matrix cannot be determined. For the unoccupied orbitals, the energy-level statistics indicate an intermediate distribution between the Gaussian orthogonal ensemble and the semi-Poisson statistics for all 20 different amino acids. These amino acids are considered to be in a type of critical state.
Kaon matrix elements and CP violation from quenched lattice QCD
NASA Astrophysics Data System (ADS)
Cristian, Calin-Radu
We report the results of a calculation of the K → pipi matrix elements relevant for the DeltaI = 1/2 rule and epsilon '/epsilon in quenched lattice QCD using domain wall fermions at a fixed lattice spacing of a-1 ˜ 2 GeV. Working in the three-quark effective theory, where only the u, d and s quarks enter and which is known perturbatively to next-to-leading order; we calculate the lattice K → pi and K → |0> matrix elements of dimension six, four-fermion operators. Through lowest order chiral perturbation theory these yield K → pipi matrix elements, which we then normalize to continuum values through a non-perturbative renormalization technique. For the Delta I = 1/2 rule we find a value of 25.3 +/- 1.8 (statistical error only) compared to the experimental value of 22.2, with individual isospin amplitudes 10--20% below the experimental values. For epsilon '/epsilon; using known central values for standard model parameters, we calculate (-4.0 +/- 2.3) x 10-4 (statistical error only) compared to the current experimental average of (17.2 +/- 1.8) x 10-4. Because we find a large cancellation between the I = 0 and I = 2 contributions to epsilon'/epsilon, the result may be very sensitive to the approximations employed. Among these are the use of: quenched QCD, lowest order chiral perturbation theory and continuum perturbation theory below 1.3 GeV. We have also calculated the kaon B parameter, BK and find BK(2 GeV) = 0.532(11). Although currently unable to give a reliable systematic error; we have control over statistical errors and more simulations will yield information about the effects of the approximations on this first-principles determination of these important quantities.
Separable approximation to two-body matrix elements
Robledo, Luis M.
2010-04-15
Two-body matrix elements of arbitrary local interactions are written as the sum of separable terms in a way that is well suited for the exchange and pairing channels present in mean-field calculations. The expansion relies on the transformation to center of mass and relative coordinate (in the spirit of Talmi's method) and therefore it is only useful (finite number of expansion terms) for harmonic oscillator single particle states. The converge of the expansion with the number of terms retained is studied for a Gaussian two body interaction. The limit of a contact (delta) force is also considered. Ways to handle the general case are also discussed.
Weak matrix elements efforts on the lattice: Status and prospects
Soni, A.
1995-01-01
Lattice approach to weak matrix elements is reviewed. Recent progress in treating heavy quarks on the lattice is briefly discussed. Illustrative sample of results obtained so far is given. Among them I elaborate on B{sub K}, {line_integral}{sub B} and B {yields} K*{sub {gamma}}. Experimental implications especially with regard to constraints on the Standard Model (i.e. Wolfenstein) parameters, V{sub td} measurements and expectations for B{sub s}-{bar B}{sub s}, oscillations are briefly discussed.
The Matrix Element Method in the LHC era
NASA Astrophysics Data System (ADS)
Wertz, Sébastien
2017-03-01
The Matrix Element Method (MEM) is a powerful multivariate method allowing to maximally exploit the experimental and theoretical information available to an analysis. The method is reviewed in depth, and several recent applications of the MEM at LHC experiments are discussed, such as searches for rare processes and measurements of Standard Model observables in Higgs and Top physics. Finally, a new implementation of the MEM is presented. This project builds on established phase-space parametrisations known to greatly improve the speed of the calculations, and aims at a much improved modularity and maintainability compared to previous software, easing the use of the MEM for high-statistics data analyses.
Density matrix renormalization group numerical study of the kagome antiferromagnet.
Jiang, H C; Weng, Z Y; Sheng, D N
2008-09-12
We numerically study the spin-1/2 antiferromagnetic Heisenberg model on the kagome lattice using the density-matrix renormalization group method. We find that the ground state is a magnetically disordered spin liquid, characterized by an exponential decay of spin-spin correlation function in real space and a magnetic structure factor showing system-size independent peaks at commensurate magnetic wave vectors. We obtain a spin triplet excitation gap DeltaE(S=1)=0.055+/-0.005 by extrapolation based on the large size results, and confirm the presence of gapless singlet excitations. The physical nature of such an exotic spin liquid is also discussed.
Relativistic description of nuclear matrix elements in neutrinoless double-β decay
NASA Astrophysics Data System (ADS)
Song, L. S.; Yao, J. M.; Ring, P.; Meng, J.
2014-11-01
Background: Neutrinoless double-β (0 ν β β ) decay is related to many fundamental concepts in nuclear and particle physics beyond the standard model. Currently there are many experiments searching for this weak process. An accurate knowledge of the nuclear matrix element for the 0 ν β β decay is essential for determining the effective neutrino mass once this process is eventually measured. Purpose: We report the first full relativistic description of the 0 ν β β decay matrix element based on a state-of-the-art nuclear structure model. Methods: We adopt the full relativistic transition operators which are derived with the charge-changing nucleonic currents composed of the vector coupling, axial-vector coupling, pseudoscalar coupling, and weak-magnetism coupling terms. The wave functions for the initial and final nuclei are determined by the multireference covariant density functional theory (MR-CDFT) based on the point-coupling functional PC-PK1. Correlations beyond the mean field are introduced by configuration mixing of both angular momentum and particle number projected quadrupole deformed mean-field wave functions. Results: The low-energy spectra and electric quadrupole transitions in 150Nd and its daughter nucleus 150Sm are well reproduced by the MR-CDFT calculations. The 0 ν β β decay matrix elements for both the 01+→01+ and 01+→02+ decays of 150Nd are evaluated. The effects of particle number projection, static and dynamic deformations, and the full relativistic structure of the transition operators on the matrix elements are studied in detail. Conclusions: The resulting 0 ν β β decay matrix element for the 01+→01+ transition is 5.60 , which gives the most optimistic prediction for the next generation of experiments searching for the 0 ν β β decay in 150Nd.
Nuclear matrix element of neutrinoless double-β decay: Relativity and short-range correlations
NASA Astrophysics Data System (ADS)
Song, L. S.; Yao, J. M.; Ring, P.; Meng, J.
2017-02-01
Background:The discovery of neutrinoless double-β (0 ν β β ) decay would demonstrate the nature of neutrinos, have profound implications for our understanding of matter-antimatter mystery, and solve the mass hierarchy problem of neutrinos. The calculations for the nuclear matrix elements M0 ν of 0 ν β β decay are crucial for the interpretation of this process. Purpose: We study the effects of relativity and nucleon-nucleon short-range correlations on the nuclear matrix elements M0 ν by assuming the mechanism of exchanging light or heavy neutrinos for the 0 ν β β decay. Methods:The nuclear matrix elements M0 ν are calculated within the framework of covariant density functional theory, where the beyond-mean-field correlations are included in the nuclear wave functions by configuration mixing of both angular-momentum and particle-number projected quadrupole deformed mean-field states. Results: The nuclear matrix elements M0 ν are obtained for ten 0 ν β β -decay candidate nuclei. The impact of relativity is illustrated by adopting relativistic or nonrelativistic decay operators. The effects of short-range correlations are evaluated. Conclusions: The effects of relativity and short-range correlations play an important role in the mechanism of exchanging heavy neutrinos though the influences are marginal for light neutrinos. Combining the nuclear matrix elements M0 ν with the observed lower limits on the 0 ν β β -decay half-lives, the predicted strongest limits on the effective masses are |
Effect of truncated cone roughness element density on hydrodynamic drag
NASA Astrophysics Data System (ADS)
Womack, Kristofer; Schultz, Michael; Meneveau, Charles
2016-11-01
An experimental study was conducted on rough-wall, turbulent boundary layer flow. Varying planform densities of truncated cone roughness elements were investigated. Element densities studied ranged from 10% to 57%. Detailed turbulent boundary layer velocity statistics were recorded with a two-component LDV system on a three-axis traverse. Hydrodynamic roughness length (z0) and skin-friction coefficient (Cf) were determined and compared with the estimates from existing roughness element drag prediction models including Macdonald et al. (1998) and Yang et al. (2015). The roughness elements used in this work model idealized barnacles, so implications of this data set for ship powering are considered. Office of Naval Research.
Fractional spin in reduced density-matrix functional theory.
Helbig, N; Theodorakopoulos, G; Lathiotakis, N N
2011-08-07
We study the behavior of different functionals of the one-body reduced density matrix (1RDM) for systems with fractional z-component of the total spin. We define these systems as ensembles of integer spin states. It is shown that, similarly to density functional theory, the error in the dissociation of diatomic molecules is directly related to the deviation from constancy of the atomic total energies as functions of the fractional spin. However, several functionals of the 1RDM show a size inconsistency which leads to additional errors. We also investigate the difference between a direct evaluation of the energy of an ensemble of integer-spin systems and a direct minimization of the energy of a fractional-spin system.
The problem of the universal density functional and the density matrix functional theory
Bobrov, V. B. Trigger, S. A.
2013-04-15
The analysis in this paper shows that the Hohenberg-Kohn theorem is the constellation of two statements: (i) the mathematically rigorous Hohenberg-Kohn lemma, which demonstrates that the same ground-state density cannot correspond to two different potentials of an external field, and (ii) the hypothesis of the existence of the universal density functional. Based on the obtained explicit expression for the nonrel-ativistic particle energy in a local external field, we prove that the energy of the system of more than two non-interacting electrons cannot be a functional of the inhomogeneous density. This result is generalized to the system of interacting electrons. It means that the Hohenberg-Kohn lemma cannot provide justification of the universal density functional for fermions. At the same time, statements of the density functional theory remain valid when considering any number of noninteracting ground-state bosons due to the Bose condensation effect. In the framework of the density matrix functional theory, the hypothesis of the existence of the universal density matrix functional corresponds to the cases of noninteracting particles and to interaction in the Hartree-Fock approximation.
Extracting electron transfer coupling elements from constrained density functional theory
NASA Astrophysics Data System (ADS)
Wu, Qin; Van Voorhis, Troy
2006-10-01
Constrained density functional theory (DFT) is a useful tool for studying electron transfer (ET) reactions. It can straightforwardly construct the charge-localized diabatic states and give a direct measure of the inner-sphere reorganization energy. In this work, a method is presented for calculating the electronic coupling matrix element (Hab) based on constrained DFT. This method completely avoids the use of ground-state DFT energies because they are known to irrationally predict fractional electron transfer in many cases. Instead it makes use of the constrained DFT energies and the Kohn-Sham wave functions for the diabatic states in a careful way. Test calculations on the Zn2+ and the benzene-Cl atom systems show that the new prescription yields reasonable agreement with the standard generalized Mulliken-Hush method. We then proceed to produce the diabatic and adiabatic potential energy curves along the reaction pathway for intervalence ET in the tetrathiafulvalene-diquinone (Q-TTF-Q) anion. While the unconstrained DFT curve has no reaction barrier and gives Hab≈17kcal /mol, which qualitatively disagrees with experimental results, the Hab calculated from constrained DFT is about 3kcal /mol and the generated ground state has a barrier height of 1.70kcal/mol, successfully predicting (Q-TTF-Q)- to be a class II mixed-valence compound.
Improved lattice computation of proton decay matrix elements
NASA Astrophysics Data System (ADS)
Aoki, Yasumichi; Izubuchi, Taku; Shintani, Eigo; Soni, Amarjit
2017-07-01
We present an improved result for the lattice computation of the proton decay matrix elements in Nf=2 +1 QCD. In this study, by adopting the error reduction technique of all-mode-averaging, a significant improvement of the statistical accuracy is achieved for the relevant form factor of proton (and also neutron) decay on the gauge ensemble of Nf=2 +1 domain-wall fermions with mπ=0.34 - 0.69 GeV on a 2.7 fm3 lattice, as used in our previous work [1]. We improve the total accuracy of matrix elements to 10-15% from 30-40% for p →π e+ or from 20-40% for p →K ν ¯. The accuracy of the low-energy constants α and β in the leading-order baryon chiral perturbation theory (BChPT) of proton decay are also improved. The relevant form factors of p →π estimated through the "direct" lattice calculation from the three-point function appear to be 1.4 times smaller than those from the "indirect" method using BChPT with α and β . It turns out that the utilization of our result will provide a factor 2-3 larger proton partial lifetime than that obtained using BChPT. We also discuss the use of these parameters in a dark matter model.
A new formulation to calculate general HFB matrix elements through the Pfaffian
NASA Astrophysics Data System (ADS)
Mizusaki, Takahiro; Oi, Makito
2012-08-01
A new formula is presented for the calculation of matrix elements between multi-quasiparticle Hartree-Fock-Bogoliubov (HFB) states. The formula is expressed in terms of the Pfaffian, and is derived by using Fermion coherent states with Grassmann numbers. It turns out that the formula corresponds to an extension of the generalized Wick's theorem and simplifies the combinatorial complexity resulting from practical applications of the generalized Wick's theorem by unifying the transition density and the transition pairing tensor in HFB theory. The resultant formula is simpler and more compact than the traditional description of matrix elements of general many-body operators. In addition, through the derivation of our new formula, we found that the Pfaffian version of the Lewis Carroll formula corresponds to a relation suggested by Balian and Brezin for HFB theory in 1969.
Generalized Pauli constraints in reduced density matrix functional theory
Theophilou, Iris; Helbig, Nicole; Lathiotakis, Nektarios N.; Marques, Miguel A. L.
2015-04-21
Functionals of the one-body reduced density matrix (1-RDM) are routinely minimized under Coleman’s ensemble N-representability conditions. Recently, the topic of pure-state N-representability conditions, also known as generalized Pauli constraints, received increased attention following the discovery of a systematic way to derive them for any number of electrons and any finite dimensionality of the Hilbert space. The target of this work is to assess the potential impact of the enforcement of the pure-state conditions on the results of reduced density-matrix functional theory calculations. In particular, we examine whether the standard minimization of typical 1-RDM functionals under the ensemble N-representability conditions violates the pure-state conditions for prototype 3-electron systems. We also enforce the pure-state conditions, in addition to the ensemble ones, for the same systems and functionals and compare the correlation energies and optimal occupation numbers with those obtained by the enforcement of the ensemble conditions alone.
Development and application of a density dependent matrix ...
Ranging along the Atlantic coast from US Florida to the Maritime Provinces of Canada, the Atlantic killifish (Fundulus heteroclitus) is an important and well-studied model organism for understanding the effects of pollutants and other stressors in estuarine and marine ecosystems. Matrix population models are useful tools for ecological risk assessment because they integrate effects across the life cycle, provide a linkage between endpoints observed in the individual and ecological risk to the population as a whole, and project outcomes for many generations in the future. We developed a density dependent matrix population model for Atlantic killifish by modifying a model developed for fathead minnow (Pimephales promelas) that has proved to be extremely useful, e.g. to incorporate data from laboratory studies and project effects of endocrine disrupting chemicals. We developed a size-structured model (as opposed to one that is based upon developmental stages or age class structure) so that we could readily incorporate output from a Dynamic Energy Budget (DEB) model, currently under development. Due to a lack of sufficient data to accurately define killifish responses to density dependence, we tested a number of scenarios realistic for other fish species in order to demonstrate the outcome of including this ecologically important factor. We applied the model using published data for killifish exposed to dioxin-like compounds, and compared our results to those using
Density matrix embedding in an antisymmetrized geminal power bath
Tsuchimochi, Takashi; Welborn, Matthew; Van Voorhis, Troy
2015-07-14
Density matrix embedding theory (DMET) has emerged as a powerful tool for performing wave function-in-wave function embedding for strongly correlated systems. In traditional DMET, an accurate calculation is performed on a small impurity embedded in a mean field bath. Here, we extend the original DMET equations to account for correlation in the bath via an antisymmetrized geminal power (AGP) wave function. The resulting formalism has a number of advantages. First, it allows one to properly treat the weak correlation limit of independent pairs, which DMET is unable to do with a mean-field bath. Second, it associates a size extensive correlation energy with a given density matrix (for the models tested), which AGP by itself is incapable of providing. Third, it provides a reasonable description of charge redistribution in strongly correlated but non-periodic systems. Thus, AGP-DMET appears to be a good starting point for describing electron correlation in molecules, which are aperiodic and possess both strong and weak electron correlation.
Watching excitons move: the time-dependent transition density matrix
NASA Astrophysics Data System (ADS)
Ullrich, Carsten
2012-02-01
Time-dependent density-functional theory allows one to calculate excitation energies and the associated transition densities in principle exactly. The transition density matrix (TDM) provides additional information on electron-hole localization and coherence of specific excitations of the many-body system. We have extended the TDM concept into the real-time domain in order to visualize the excited-state dynamics in conjugated molecules. The time-dependent TDM is defined as an implicit density functional, and can be approximately obtained from the time-dependent Kohn-Sham orbitals. The quality of this approximation is assessed in simple model systems. A computational scheme for real molecular systems is presented: the time-dependent Kohn-Sham equations are solved with the OCTOPUS code and the time-dependent Kohn-Sham TDM is calculated using a spatial partitioning scheme. The method is applied to show in real time how locally created electron-hole pairs spread out over neighboring conjugated molecular chains. The coupling mechanism, electron-hole coherence, and the possibility of charge separation are discussed.
SYMBMAT: Symbolic computation of quantum transition matrix elements
NASA Astrophysics Data System (ADS)
Ciappina, M. F.; Kirchner, T.
2012-08-01
We have developed a set of Mathematica notebooks to compute symbolically quantum transition matrices relevant for atomic ionization processes. The utilization of a symbolic language allows us to obtain analytical expressions for the transition matrix elements required in charged-particle and laser induced ionization of atoms. Additionally, by using a few simple commands, it is possible to export these symbolic expressions to standard programming languages, such as Fortran or C, for the subsequent computation of differential cross sections or other observables. One of the main drawbacks in the calculation of transition matrices is the tedious algebraic work required when initial states other than the simple hydrogenic 1s state need to be considered. Using these notebooks the work is dramatically reduced and it is possible to generate exact expressions for a large set of bound states. We present explicit examples of atomic collisions (in First Born Approximation and Distorted Wave Theory) and laser-matter interactions (within the Dipole and Strong Field Approximations and different gauges) using both hydrogenic wavefunctions and Slater-Type Orbitals with arbitrary nlm quantum numbers as initial states. Catalogue identifier: AEMI_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMI_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 71 628 No. of bytes in distributed program, including test data, etc.: 444 195 Distribution format: tar.gz Programming language: Mathematica Computer: Single machines using Linux or Windows (with cores with any clock speed, cache memory and bits in a word) Operating system: Any OS that supports Mathematica. The notebooks have been tested under Windows and Linux and with versions 6.x, 7.x and 8.x Classification: 2.6 Nature of problem
Closed String S-matrix Elements in Open String Field Theory
NASA Astrophysics Data System (ADS)
Garousi, Mohammad R.; Maktabdaran, G. R.
2005-03-01
We study the S-matrix elements of the gauge invariant operators corresponding to on-shell closed strings, in open string field theory. In particular, we calculate the tree level S-matrix element of two arbitrary closed strings, and the S-matrix element of one closed string and two open strings. By mapping the world-sheet of these amplitudes to the upper half z-plane, and by evaluating explicitly the correlators in the ghost part, we show that these S-matrix elements are exactly identical to the corresponding disk level S-matrix elements in perturbative string theory.
Hermitian one-particle density matrix through a semiclassical gradient expansion
NASA Astrophysics Data System (ADS)
Bencheikh, K.; Räsänen, E.
2016-01-01
We carry out the semiclassical expansion of the one-particle density matrix up to the second order in {{\\hslash }}. We use the method of Grammaticos and Voros based on the Wigner transform of operators. We show that the resulting density matrix is Hermitian and idempotent in contrast with the well-known result of the semiclassical Kirzhnits expansion. Our density matrix leads to the same particle density and kinetic energy density as in the literature, and it satisfies the consistency criterion of the Euler equation. The derived Hermitian density matrix clarifies the ambiguity in the usefulness of gradient expansion approximations and might reignite the development of density functionals with semiclassical methods.
Ferromagnetic elements by epitaxial growth: A density functional prediction
NASA Astrophysics Data System (ADS)
Schönecker, Stephan; Richter, Manuel; Koepernik, Klaus; Eschrig, Helmut
2012-01-01
The periodic table contains only six natural elements with a ferromagnetic ground state. For example, the metal uranium, which is magnetically ordered in many compounds, is paramagnetic in all its known elemental bulk phases. Also, the iron-group elements ruthenium and osmium are known to be bulk paramagnets. We predict by means of density functional calculations that epitaxial growth of uranium, ruthenium, or osmium on suitable substrates may allow stabilization of bulklike films with tetragonal structures showing ferromagnetic order.
NASA Astrophysics Data System (ADS)
Craggs, A.
1989-08-01
When making an acoustic finite element model of a duct system, the resulting matrices can be very large due to the length of ductwork, the complex changes in geometry and the numerous junctions, and a full model may require several thousand nodes. In this paper two techniques are given for reducing the size of the matrices; the transfer matrix method and the condensed stiffness matrix approach—both of which lead to equations expressed in terms of the input and output nodes only. The methods are demonstrated with examples on a straight section of duct and a branched duct network. The substantial reductions in computer memory shown imply that duct acoustic problems can be studied using a desktop work station.
The Matrix Element Method: Past, Present, and Future
Gainer, James S.; Lykken, Joseph; Matchev, Konstantin T.; Mrenna, Stephen; Park, Myeonghun
2013-07-12
The increasing use of multivariate methods, and in particular the Matrix Element Method (MEM), represents a revolution in experimental particle physics. With continued exponential growth in computing capabilities, the use of sophisticated multivariate methods-- already common-- will soon become ubiquitous and ultimately almost compulsory. While the existence of sophisticated algorithms for disentangling signal and background might naively suggest a diminished role for theorists, the use of the MEM, with its inherent connection to the calculation of differential cross sections will benefit from collaboration between theorists and experimentalists. In this white paper, we will briefly describe the MEM and some of its recent uses, note some current issues and potential resolutions, and speculate about exciting future opportunities.
Matrix product density operators: Renormalization fixed points and boundary theories
NASA Astrophysics Data System (ADS)
Cirac, J. I.; Pérez-García, D.; Schuch, N.; Verstraete, F.
2017-03-01
We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced in (Verstraete et al., 2005) and characterize the tensors corresponding to the fixed points. We relate them to the states possessing zero correlation length, saturation of the area law, as well as to those which generate ground states of local and commuting Hamiltonians. For mixed states, we introduce the concept of renormalization fixed points and characterize the corresponding tensors. We also relate them to concepts like finite correlation length, saturation of the area law, as well as to those which generate Gibbs states of local and commuting Hamiltonians. One of the main result of this work is that the resulting fixed points can be associated to the boundary theories of two-dimensional topological states, through the bulk-boundary correspondence introduced in (Cirac et al., 2011).
Unified quantum density matrix description of coherence and polarization
NASA Astrophysics Data System (ADS)
de Lima Bernardo, Bertúlio
2017-07-01
The properties of coherence and polarization of light has been the subject of intense investigations and form the basis of many technological applications. These concepts which historically have been treated independently can now be formulated under a single classical theory. Here, we derive a quantum counterpart for this theory, with basis on a density matrix formulation, which describes jointly the coherence and polarization properties of an ensemble of photons. The method is used to show how the degree of polarization of a specific class of mixed states changes on propagation in free space, and how an interacting environment can suppress the coherence and polarization degrees of a general state. This last application can be particularly useful in the analysis of decoherence effects in optical quantum information implementations.
Reduced density matrix and order parameters of a topological insulator
NASA Astrophysics Data System (ADS)
Yu, Wing Chi; Li, Yan Chao; Sacramento, P. D.; Lin, Hai-Qing
2016-12-01
It has been recently proposed that the reduced density matrix may be used to derive the order parameter of a condensed matter system. Here we propose order parameters for the phases of a topological insulator, specifically a spinless Su-Schrieffer-Heeger (SSH) model, and consider the effect of short-range interactions. All the derived order parameters and their possible corresponding quantum phases are verified by the entanglement entropy and electronic configuration analysis results. The order parameter appropriate to the topological regions is further proved by calculating the Berry phase under twisted boundary conditions. It is found that the topological nontrivial phase is robust to the introduction of repulsive intersite interactions and can appear in the topological trivial parameter region when appropriate interactions are added.
Sliced Basis Density Matrix Renormalization Group for Electronic Structure
NASA Astrophysics Data System (ADS)
Stoudenmire, E. Miles; White, Steven R.
2017-07-01
We introduce a hybrid approach to applying the density matrix renormalization group to continuous systems, combining a grid approximation along one direction with a finite Gaussian basis set for the remaining two directions. This approach is especially useful for chainlike molecules, where the grid is used in the long direction. For hydrogen chain systems, the computational time scales approximately linearly with the number of atoms, as we show with near-exact minimal basis set calculations with up to 1000 atoms. The linear scaling comes from both the localization of the basis and a compression method for the long-ranged two-electron interaction. For shorter hydrogen chains, we show results with up to triple-ζ bases.
Determination of CKM Matrix Elements with Superallowed Fermi Decays^*.
NASA Astrophysics Data System (ADS)
Fujikawa, Brian
1996-10-01
The u-d element (V_ud) of the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix is a fundamental parameter of the Standard Model of Electroweak Interactions. Its most precise determination comes from nuclear physics experiments, in particular, from measurements of superallowed Fermi beta decays. Precise knowledge of V_ud will allow a variety of tests of the Standard Model, in addition to placing a number of important constraints on astrophysics and cosmology. These measurements, which require both precision nuclear physics experiments and state of the art theoretical nuclear physics calculations, have been made for a variety of nuclei ranging from ^14O to ^54Co. The u-d element obtained from these measurements are in statistical agreement and the average value obtained implies a non-unitary CKM matrix, which if correct, would require exotic extensions to the Standard Model. Unfortunately the theoretical calculations of the isospin breaking corrections, which are necessary to extract V_ud, are controversial. In order to resolve this controversy, much effort has recently been invested in measuring V_ud from the superallowed Fermi decay of ^10C, where the isospin breaking corrections are expected to be small. This is a very challenging experiment, since it requires the precision measurement of very small branching ratios in a high background environment. I will report on the current status of the determination of V_ud emphasizing the recent experimental effort to measure V_ud from the superallowed Fermi decay of ^10C. ^*Supported by the U.S. D.O.E. under Contracts No. W-31-109-ENG-38 and No. DE-AC03-76SF00098.
Fabrication of synthetic diffractive elements using advanced matrix laser lithography
NASA Astrophysics Data System (ADS)
Škereň, M.; Svoboda, J.; Květoň, M.; Fiala, P.
2013-02-01
In this paper we present a matrix laser writing device based on a demagnified projection of a micro-structure from a computer driven spatial light modulator. The device is capable of writing completely aperiodic micro-structures with resolution higher than 200 000 DPI. An optical system is combined with ultra high precision piezoelectric stages with an elementary step ~ 4 nm. The device operates in a normal environment, which significantly decreases the costs compared to competitive technologies. Simultaneously, large areas can be exposed up to 100 cm2. The capabilities of the constructed device will be demonstrated on particular elements fabricated for real applications. The optical document security is the first interesting field, where the synthetic image holograms are often combined with sophisticated aperiodic micro-structures. The proposed technology can easily write simple micro-gratings creating the color and kinetic visual effects, but also the diffractive cryptograms, waveguide couplers, and other structures recently used in the field of optical security. A general beam shaping elements and special photonic micro-structures are another important applications which will be discussed in this paper.
NASA Technical Reports Server (NTRS)
Newman, M. B.; Filstrup, A. W.
1973-01-01
Linear (8 node), parabolic (20 node), cubic (32 node) and mixed (some edges linear, some parabolic and some cubic) have been inserted into NASTRAN, level 15.1. First the dummy element feature was used to check out the stiffness matrix generation routines for the linear element in NASTRAN. Then, the necessary modules of NASTRAN were modified to include the new family of elements. The matrix assembly was changed so that the stiffness matrix of each isoparametric element is only generated once as the time to generate these higher order elements tends to be much longer than the other elements in NASTRAN. This paper presents some of the experiences and difficulties of inserting a new element or family of elements into NASTRAN.
Efficient perturbation theory to improve the density matrix renormalization group
NASA Astrophysics Data System (ADS)
Tirrito, Emanuele; Ran, Shi-Ju; Ferris, Andrew J.; McCulloch, Ian P.; Lewenstein, Maciej
2017-02-01
The density matrix renormalization group (DMRG) is one of the most powerful numerical methods available for many-body systems. It has been applied to solve many physical problems, including the calculation of ground states and dynamical properties. In this work, we develop a perturbation theory of the DMRG (PT-DMRG) to greatly increase its accuracy in an extremely simple and efficient way. Using the canonical matrix product state (MPS) representation for the ground state of the considered system, a set of orthogonal basis functions {| ψi> } is introduced to describe the perturbations to the ground state obtained by the conventional DMRG. The Schmidt numbers of the MPS that are beyond the bond dimension cutoff are used to define these perturbation terms. The perturbed Hamiltonian is then defined as H˜i j=< ψi| H ̂|ψj> ; its ground state permits us to calculate physical observables with a considerably improved accuracy compared to the original DMRG results. We benchmark the second-order perturbation theory with the help of a one-dimensional Ising chain in a transverse field and the Heisenberg chain, where the precision of the DMRG is shown to be improved O (10 ) times. Furthermore, for moderate L the errors of the DMRG and PT-DMRG both scale linearly with L-1 (with L being the length of the chain). The linear relation between the dimension cutoff of the DMRG and that of the PT-DMRG at the same precision shows a considerable improvement in efficiency, especially for large dimension cutoffs. In the thermodynamic limit we show that the errors of the PT-DMRG scale with √{L-1}. Our work suggests an effective way to define the tangent space of the ground-state MPS, which may shed light on the properties beyond the ground state. This second-order PT-DMRG can be readily generalized to higher orders, as well as applied to models in higher dimensions.
NASA Astrophysics Data System (ADS)
Wouters, Sebastian; Nakatani, Naoki; Van Neck, Dimitri; Chan, Garnet Kin-Lic
2013-08-01
The similarities between Hartree-Fock (HF) theory and the density matrix renormalization group (DMRG) are explored. Both methods can be formulated as the variational optimization of a wave-function Ansatz. Linearization of the time-dependent variational principle near a variational minimum allows to derive the random phase approximation (RPA). We show that the nonredundant parameterization of the matrix product state (MPS) tangent space [J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde, and F. Verstraete, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.107.070601 107, 070601 (2011)] leads to the Thouless theorem for MPS, i.e., an explicit nonredundant parameterization of the entire MPS manifold, starting from a specific MPS reference. Excitation operators are identified, which extends the analogy between HF and DMRG to the Tamm-Dancoff approximation (TDA), the configuration interaction (CI) expansion, and coupled cluster theory. For a small one-dimensional Hubbard chain, we use a CI-MPS Ansatz with single and double excitations to improve on the ground state and to calculate low-lying excitation energies. For a symmetry-broken ground state of this model, we show that RPA-MPS allows to retrieve the Goldstone mode. We also discuss calculations of the RPA-MPS correlation energy. With the long-range quantum chemical Pariser-Parr-Pople Hamiltonian, low-lying TDA-MPS and RPA-MPS excitation energies for polyenes are obtained.
Determination of the weak magnetism matrix element in {sup 14}C beta decay
Zeuli, A.R.; Ahmad, I.; Coulter, K.P.; Greene, J.P.; Schiffer, J.P.; Freedman, S.J.; Fujikawa, B.K.; Mortara, J.L.
1993-10-01
Higher order beta decay matrix elements, such as weak magnetism, will introduce small departures (a shape factor) from the allowed beta decay electron energy spectrum. The value of the weak magnetism matrix element is predicted by the Conserved Vector Current (CVC) hypothesis and an experimental determination of the weak magnetism matrix element can be interpreted as a test of CVC. We have determined the weak magnetism matrix element from the {sup 14}C shape factor, which was measured using an apparatus incorporating a high resolution solid state detector and a super conducting solenoid. The results of our measurement will be presented.
Neutrinoless Double Beta Nuclear Matrix Elements Around Mass 80 in the Nuclear Shell Model
NASA Astrophysics Data System (ADS)
Yoshinaga, Naotaka; Higashiyama, Koji; Taguchi, Daisuke; Teruya, Eri
The observation of the neutrinoless double-beta decay can determine whether the neutrino is a Majorana particle or not. In its theoretical nuclear side it is particularly important to estimate three types of nuclear matrix elements, namely, Fermi (F), Gamow-Teller (GT), and tensor (T) types matrix elements. The shell model calculations and also the pair-truncated shell model calculations are carried out to check the model dependence on nuclear matrix elements. In this work the neutrinoless double-beta decay for mass A = 82 nuclei is studied. It is found that the matrix elements are quite sensitive to the ground state wavefunctions.
Density matrix reconstruction of a large angular momentum
NASA Astrophysics Data System (ADS)
Klose, Gerd
2001-10-01
A complete description of the quantum state of a physical system is the fundamental knowledge necessary to statistically predict the outcome of measurements. In turning this statement around, Wolfgang Pauli raised already in 1933 the question, whether an unknown quantum state could be uniquely determined by appropriate measurements-a problem that has gained new relevance in recent years. In order to harness the prospects of quantum computing, secure communication, teleportation, and the like, the development of techniques to accurately control and measure quantum states has now become a matter of practical as well as fundamental interest. However, there is no general answer to Pauli's very basic question, and quantum state reconstruction algorithms have been developed and experimentally demonstrated only for a few systems so far. This thesis presents a novel experimental method to measure the unknown and generally mixed quantum state for an angular momentum of arbitrary magnitude. The (2F + 1) x (2F + 1) density matrix describing the quantum state is hereby completely determined from a set of Stern-Gerlach measurements with (4F + 1) different orientations of the quantization axis. This protocol is implemented for laser cooled Cesium atoms in the 6S1/2(F = 4) hyperfine ground state manifold, and is applied to a number of test states prepared by optical pumping and Larmor precession. A comparison of the input and the measured states shows successful reconstructions with fidelities of about 0.95.
Reduced density matrix hybrid approach: Application to electronic energy transfer
Berkelbach, Timothy C.; Reichman, David R.; Markland, Thomas E.
2012-02-28
Electronic energy transfer in the condensed phase, such as that occurring in photosynthetic complexes, frequently occurs in regimes where the energy scales of the system and environment are similar. This situation provides a challenge to theoretical investigation since most approaches are accurate only when a certain energetic parameter is small compared to others in the problem. Here we show that in these difficult regimes, the Ehrenfest approach provides a good starting point for a dynamical description of the energy transfer process due to its ability to accurately treat coupling to slow environmental modes. To further improve on the accuracy of the Ehrenfest approach, we use our reduced density matrix hybrid framework to treat the faster environmental modes quantum mechanically, at the level of a perturbative master equation. This combined approach is shown to provide an efficient and quantitative description of electronic energy transfer in a model dimer and the Fenna-Matthews-Olson complex and is used to investigate the effect of environmental preparation on the resulting dynamics.
Density Matrix Embedding: A Strong-Coupling Quantum Embedding Theory.
Knizia, Gerald; Chan, Garnet Kin-Lic
2013-03-12
We extend our density matrix embedding theory (DMET) [Phys. Rev. Lett.2012, 109, 186404] from lattice models to the full chemical Hamiltonian. DMET allows the many-body embedding of arbitrary fragments of a quantum system, even when such fragments are open systems and strongly coupled to their environment (e.g., by covalent bonds). In DMET, empirical approaches to strong coupling, such as link atoms or boundary regions, are replaced by a small, rigorous quantum bath designed to reproduce the entanglement between a fragment and its environment. We describe the theory and demonstrate its feasibility in strongly correlated hydrogen ring and grid models; these are not only beyond the scope of traditional embeddings but even challenge conventional quantum chemistry methods themselves. We find that DMET correctly describes the notoriously difficult symmetric dissociation of a 4 × 3 hydrogen atom grid, even when the treated fragments are as small as single hydrogen atoms. We expect that DMET will open up new ways of treating complex strongly coupled, strongly correlated systems in terms of their individual fragments.
Matrix element method for high performance computing platforms
NASA Astrophysics Data System (ADS)
Grasseau, G.; Chamont, D.; Beaudette, F.; Bianchini, L.; Davignon, O.; Mastrolorenzo, L.; Ochando, C.; Paganini, P.; Strebler, T.
2015-12-01
Lot of efforts have been devoted by ATLAS and CMS teams to improve the quality of LHC events analysis with the Matrix Element Method (MEM). Up to now, very few implementations try to face up the huge computing resources required by this method. We propose here a highly parallel version, combining MPI and OpenCL, which makes the MEM exploitation reachable for the whole CMS datasets with a moderate cost. In the article, we describe the status of two software projects under development, one focused on physics and one focused on computing. We also showcase their preliminary performance obtained with classical multi-core processors, CUDA accelerators and MIC co-processors. This let us extrapolate that with the help of 6 high-end accelerators, we should be able to reprocess the whole LHC run 1 within 10 days, and that we have a satisfying metric for the upcoming run 2. The future work will consist in finalizing a single merged system including all the physics and all the parallelism infrastructure, thus optimizing implementation for best hardware platforms.
Controlling excited-state contamination in nucleon matrix elements
Yoon, Boram; Gupta, Rajan; Bhattacharya, Tanmoy; Engelhardt, Michael; Green, Jeremy; Joo, Balint; Lin, Huey -Wen; Negele, John; Orginos, Kostas; Pochinsky, Andrew; Richards, David; Syritsyn, Sergey; Winter, Frank
2016-06-08
We present a detailed analysis of methods to reduce statistical errors and excited-state contamination in the calculation of matrix elements of quark bilinear operators in nucleon states. All the calculations were done on a 2+1-flavor ensemble with lattices of size 32^{3} × 64 generated using the rational hybrid Monte Carlo algorithm at a = 0.081 fm and with M_{π} = 312 MeV. The statistical precision of the data is improved using the all-mode-averaging method. We compare two methods for reducing excited-state contamination: a variational analysis and a 2-state fit to data at multiple values of the source-sink separation t_{sep}. We show that both methods can be tuned to significantly reduce excited-state contamination and discuss their relative advantages and cost effectiveness. As a result, a detailed analysis of the size of source smearing used in the calculation of quark propagators and the range of values of t_{sep} needed to demonstrate convergence of the isovector charges of the nucleon to the t_{sep} → ∞ estimates is presented.
Controlling excited-state contamination in nucleon matrix elements
Yoon, Boram; Gupta, Rajan; Bhattacharya, Tanmoy; ...
2016-06-08
We present a detailed analysis of methods to reduce statistical errors and excited-state contamination in the calculation of matrix elements of quark bilinear operators in nucleon states. All the calculations were done on a 2+1-flavor ensemble with lattices of size 323 × 64 generated using the rational hybrid Monte Carlo algorithm at a = 0.081 fm and with Mπ = 312 MeV. The statistical precision of the data is improved using the all-mode-averaging method. We compare two methods for reducing excited-state contamination: a variational analysis and a 2-state fit to data at multiple values of the source-sink separation tsep. Wemore » show that both methods can be tuned to significantly reduce excited-state contamination and discuss their relative advantages and cost effectiveness. As a result, a detailed analysis of the size of source smearing used in the calculation of quark propagators and the range of values of tsep needed to demonstrate convergence of the isovector charges of the nucleon to the tsep → ∞ estimates is presented.« less
Controlling excited-state contamination in nucleon matrix elements
Yoon, Boram; Gupta, Rajan; Bhattacharya, Tanmoy; Engelhardt, Michael; Green, Jeremy; Joo, Balint; Lin, Huey -Wen; Negele, John; Orginos, Kostas; Pochinsky, Andrew; Richards, David; Syritsyn, Sergey; Winter, Frank
2016-06-08
We present a detailed analysis of methods to reduce statistical errors and excited-state contamination in the calculation of matrix elements of quark bilinear operators in nucleon states. All the calculations were done on a 2+1-flavor ensemble with lattices of size 32^{3} × 64 generated using the rational hybrid Monte Carlo algorithm at a = 0.081 fm and with M_{π} = 312 MeV. The statistical precision of the data is improved using the all-mode-averaging method. We compare two methods for reducing excited-state contamination: a variational analysis and a 2-state fit to data at multiple values of the source-sink separation t_{sep}. We show that both methods can be tuned to significantly reduce excited-state contamination and discuss their relative advantages and cost effectiveness. As a result, a detailed analysis of the size of source smearing used in the calculation of quark propagators and the range of values of t_{sep} needed to demonstrate convergence of the isovector charges of the nucleon to the t_{sep} → ∞ estimates is presented.
Controlling excited-state contamination in nucleon matrix elements
Yoon, Boram; Gupta, Rajan; Bhattacharya, Tanmoy; Engelhardt, Michael; Green, Jeremy; Joó, Bálint; Lin, Huey-Wen; Negele, John; Orginos, Kostas; Pochinsky, Andrew; Richards, David; Syritsyn, Sergey; Winter, Frank
2016-06-01
We present a detailed analysis of methods to reduce statistical errors and excited-state contamination in the calculation of matrix elements of quark bilinear operators in nucleon states. All the calculations were done on a 2+1 flavor ensemble with lattices of size $32^3 \\times 64$ generated using the rational hybrid Monte Carlo algorithm at $a=0.081$~fm and with $M_\\pi=312$~MeV. The statistical precision of the data is improved using the all-mode-averaging method. We compare two methods for reducing excited-state contamination: a variational analysis and a two-state fit to data at multiple values of the source-sink separation $t_{\\rm sep}$. We show that both methods can be tuned to significantly reduce excited-state contamination and discuss their relative advantages and cost-effectiveness. A detailed analysis of the size of source smearing used in the calculation of quark propagators and the range of values of $t_{\\rm sep}$ needed to demonstrate convergence of the isovector charges of the nucleon to the $t_{\\rm sep} \\to \\infty $ estimates is presented.
Configuration interaction matrix elements for the quantum Hall effect
NASA Astrophysics Data System (ADS)
Wooten, Rachel; Macek, Joseph
2015-03-01
In the spherical model of the quantum Hall system, the two-body matrix elements and pseudopotentials can be found analytically in terms of a general scalar pair interaction potential by expressing the pair interaction as a weighted sum over Legendre polynomials. For non-infinite systems, only a finite set of terms in the potential expansion contribute to the interactions; the contributing terms define an effective spatial potential for the system. The connection between the effective spatial potential and the pseudopotential is one-to-one for finite systems, and any completely defined model pseudopotential can be analytically inverted to give a unique corresponding spatial potential. This technique of inverting the pseudopotential to derive effective spatial potentials may be of use for developing accurate model spatial potentials for quantum Monte Carlo simulations. We demonstrate the technique and the corresponding spatial potentials for a few example model pseudopotentials. Supported by Office of Basic Energy Sciences, U.S. DOE, Grant DE-FG02-02ER15283 to the University of Tennessee.
NASA Astrophysics Data System (ADS)
Baker, Thomas E.; Wagner, Lucas O.; Stoudenmire, E. Miles; White, Steven R.; Burke, Kieron
2014-03-01
Kohn-Sham Density Functional Theory (DFT) is a mathematically exact method that requires approximation to the exchange correlation energy which may exclude features seen in experiment or provide inadequate estimates. Meanwhile, we may use Density Matrix Renormalization Group (DMRG), a numerical method which can accurately treat strongly correlated electrons in one dimension, to find exact DFT quantities such as the Kohn-Sham potential. We use DMRG in one dimension as a benchmark to test new functionals. Further, recommendations for calculations in two and three dimensional systems are discussed as well as computational proof of principles. We graciously acknowledge the support of the Department of Energy (DE-SC0008696). L.O.W. also thanks the Korean Global Research Network Grant (No. NRF-2010-220-C00017).
NASA Astrophysics Data System (ADS)
Parson, William W.; Warshel, Arieh
2004-01-01
from P* to B, including stepwise formation of the product during the period when the system retains vibrational coherences. Although the rate does not depend strongly on whether P* is prepared coherently or incoherently, speeding up vibrational relaxations decreases the rate. At least part of the adverse effect of rapid relaxations can be viewed as a manifestation of the quantum Zeno paradox, which arises when off-diagonal elements of the density matrix decay very rapidly.
NASA Technical Reports Server (NTRS)
Ko, William L.; Olona, Timothy; Muramoto, Kyle M.
1990-01-01
Different finite element models previously set up for thermal analysis of the space shuttle orbiter structure are discussed and their shortcomings identified. Element density criteria are established for the finite element thermal modelings of space shuttle orbiter-type large, hypersonic aircraft structures. These criteria are based on rigorous studies on solution accuracies using different finite element models having different element densities set up for one cell of the orbiter wing. Also, a method for optimization of the transient thermal analysis computer central processing unit (CPU) time is discussed. Based on the newly established element density criteria, the orbiter wing midspan segment was modeled for the examination of thermal analysis solution accuracies and the extent of computation CPU time requirements. The results showed that the distributions of the structural temperatures and the thermal stresses obtained from this wing segment model were satisfactory and the computation CPU time was at the acceptable level. The studies offered the hope that modeling the large, hypersonic aircraft structures using high-density elements for transient thermal analysis is possible if a CPU optimization technique was used.
Reduced density-matrix functional theory: Correlation and spectroscopy
Di Sabatino, S.; Romaniello, P.; Berger, J. A.; Reining, L.
2015-07-14
In this work, we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the calculation of total energies, occupation numbers, removal/addition energies, and spectral functions. We use the exactly solvable Hubbard dimer at 1/4 and 1/2 fillings as test systems. This allows us to analyze the underlying physics and to elucidate the origin of the observed trends. For comparison, we also report the results of the GW approximation, where the self-energy functional is approximated, but no further hypothesis is made concerning the approximations of the observables. In particular, we focus on the atomic limit, where the two sites of the dimer are pulled apart and electrons localize on either site with equal probability, unless a small perturbation is present: this is the regime of strong electron correlation. In this limit, using the Hubbard dimer at 1/2 filling with or without a spin-symmetry-broken ground state allows us to explore how degeneracies and spin-symmetry breaking are treated in RDMFT. We find that, within the used approximations, neither in RDMFT nor in GW, the signature of strong correlation is present, when looking at the removal/addition energies and spectral function from the spin-singlet ground state, whereas both give the exact result for the spin-symmetry broken case. Moreover, we show how the spectroscopic properties change from one spin structure to the other.
Pair 2-electron reduced density matrix theory using localized orbitals
NASA Astrophysics Data System (ADS)
Head-Marsden, Kade; Mazziotti, David A.
2017-08-01
Full configuration interaction (FCI) restricted to a pairing space yields size-extensive correlation energies but its cost scales exponentially with molecular size. Restricting the variational two-electron reduced-density-matrix (2-RDM) method to represent the same pairing space yields an accurate lower bound to the pair FCI energy at a mean-field-like computational scaling of O (r3) where r is the number of orbitals. In this paper, we show that localized molecular orbitals can be employed to generate an efficient, approximately size-extensive pair 2-RDM method. The use of localized orbitals eliminates the substantial cost of optimizing iteratively the orbitals defining the pairing space without compromising accuracy. In contrast to the localized orbitals, the use of canonical Hartree-Fock molecular orbitals is shown to be both inaccurate and non-size-extensive. The pair 2-RDM has the flexibility to describe the spectra of one-electron RDM occupation numbers from all quantum states that are invariant to time-reversal symmetry. Applications are made to hydrogen chains and their dissociation, n-acene from naphthalene through octacene, and cadmium telluride 2-, 3-, and 4-unit polymers. For the hydrogen chains, the pair 2-RDM method recovers the majority of the energy obtained from similar calculations that iteratively optimize the orbitals. The localized-orbital pair 2-RDM method with its mean-field-like computational scaling and its ability to describe multi-reference correlation has important applications to a range of strongly correlated phenomena in chemistry and physics.
Application of the Finite-Element Z-Matrix Method to e-H2 Collisions
NASA Technical Reports Server (NTRS)
Huo, Winifred M.; Brown, David; Langhoff, Stephen R. (Technical Monitor)
1997-01-01
The present study adapts the Z-matrix formulation using a mixed basis of finite elements and Gaussians. This is a energy-independent basis which allows flexible boundary conditions and is amenable to efficient algorithms for evaluating the necessary matrix elements with molecular targets.
NASA Astrophysics Data System (ADS)
Ender, I. A.; Bakaleinikov, L. A.; Flegontova, E. Yu.; Gerasimenko, A. B.
2017-08-01
We have proposed an algorithm for the sequential construction of nonisotropic matrix elements of the collision integral, which are required to solve the nonlinear Boltzmann equation using the moments method. The starting elements of the matrix are isotropic and assumed to be known. The algorithm can be used for an arbitrary law of interactions for any ratio of the masses of colliding particles.
Element orbitals for Kohn-Sham density functional theory
Lin, Lin; Ying, Lexing
2012-05-08
We present a method to discretize the Kohn-Sham Hamiltonian matrix in the pseudopotential framework by a small set of basis functions automatically contracted from a uniform basis set such as planewaves. Each basis function is localized around an element, which is a small part of the global domain containing multiple atoms. We demonstrate that the resulting basis set achieves meV accuracy for 3D densely packed systems with a small number of basis functions per atom. The procedure is applicable to insulating and metallic systems.
Localization in band random matrix models with and without increasing diagonal elements.
Wang, Wen-ge
2002-06-01
It is shown that localization of eigenfunctions in the Wigner band random matrix model with increasing diagonal elements can be related to localization in a band random matrix model with random diagonal elements. The relation is obtained by making use of a result of a generalization of Brillouin-Wigner perturbation theory, which shows that reduced Hamiltonian matrices with relatively small dimensions can be introduced for nonperturbative parts of eigenfunctions, and by employing intermediate basis states, which can improve the method of the reduced Hamiltonian matrix. The latter model deviates from the standard band random matrix model mainly in two aspects: (i) the root mean square of diagonal elements is larger than that of off-diagonal elements within the band, and (ii) statistical distributions of the matrix elements are close to the Lévy distribution in their central parts, except in the high top regions.
Chiral random matrix theory for two-color QCD at high density
Kanazawa, Takuya; Yamamoto, Naoki; Wettig, Tilo
2010-04-15
We identify a non-Hermitian chiral random matrix theory that corresponds to two-color QCD at high density. We show that the partition function of the random matrix theory coincides with the partition function of the finite-volume effective theory at high density, and that the Leutwyler-Smilga-type spectral sum rules of the random matrix theory are identical to those derived from the effective theory. The microscopic Dirac spectrum of the theory is governed by the BCS gap, rather than the conventional chiral condensate. We also show that with a different choice of a parameter the random matrix theory yields the effective partition function at low density.
Energy density matrix formalism for interacting quantum systems: a quantum Monte Carlo study
Krogel, Jaron T; Kim, Jeongnim; Reboredo, Fernando A
2014-01-01
We develop an energy density matrix that parallels the one-body reduced density matrix (1RDM) for many-body quantum systems. Just as the density matrix gives access to the number density and occupation numbers, the energy density matrix yields the energy density and orbital occupation energies. The eigenvectors of the matrix provide a natural orbital partitioning of the energy density while the eigenvalues comprise a single particle energy spectrum obeying a total energy sum rule. For mean-field systems the energy density matrix recovers the exact spectrum. When correlation becomes important, the occupation energies resemble quasiparticle energies in some respects. We explore the occupation energy spectrum for the finite 3D homogeneous electron gas in the metallic regime and an isolated oxygen atom with ground state quantum Monte Carlo techniques imple- mented in the QMCPACK simulation code. The occupation energy spectrum for the homogeneous electron gas can be described by an effective mass below the Fermi level. Above the Fermi level evanescent behavior in the occupation energies is observed in similar fashion to the occupation numbers of the 1RDM. A direct comparison with total energy differences demonstrates a quantita- tive connection between the occupation energies and electron addition and removal energies for the electron gas. For the oxygen atom, the association between the ground state occupation energies and particle addition and removal energies becomes only qualitative. The energy density matrix provides a new avenue for describing energetics with quantum Monte Carlo methods which have traditionally been limited to total energies.
Finite element analysis of metal matrix composite blade
NASA Astrophysics Data System (ADS)
Isai Thamizh, R.; Velmurugan, R.; Jayagandhan, R.
2016-10-01
In this work, compressor rotor blade of a gas turbine engine has been analyzed for stress, maximum displacement and natural frequency using ANSYS software for determining its failure strength by simulating the actual service conditions. Static stress analysis and modal analysis have been carried out using Ti-6Al-4V alloy, which is currently used in compressor blade. The results are compared with those obtained using Ti matrix composites reinforced with SiC. The advantages of using metal matrix composites in the gas turbine compressor blades are investigated. From the analyses carried out, it seems that composite rotor blades have lesser mass, lesser tip displacement and lower maximum stress values.
Status and future of nuclear matrix elements for neutrinoless double-beta decay: a review
NASA Astrophysics Data System (ADS)
Engel, Jonathan; Menéndez, Javier
2017-04-01
The nuclear matrix elements that govern the rate of neutrinoless double beta decay must be accurately calculated if experiments are to reach their full potential. Theorists have been working on the problem for a long time but have recently stepped up their efforts as ton-scale experiments have begun to look feasible. Here we review past and recent work on the matrix elements in a wide variety of nuclear models and discuss work that will be done in the near future. Ab initio nuclear-structure theory, which is developing rapidly, holds out hope of more accurate matrix elements with quantifiable error bars.
Status and future of nuclear matrix elements for neutrinoless double-beta decay: a review.
Engel, Jonathan; Menéndez, Javier
2017-04-01
The nuclear matrix elements that govern the rate of neutrinoless double beta decay must be accurately calculated if experiments are to reach their full potential. Theorists have been working on the problem for a long time but have recently stepped up their efforts as ton-scale experiments have begun to look feasible. Here we review past and recent work on the matrix elements in a wide variety of nuclear models and discuss work that will be done in the near future. Ab initio nuclear-structure theory, which is developing rapidly, holds out hope of more accurate matrix elements with quantifiable error bars.
Leonard Gamberg, Asmita Mukherjee, Piet J. Mulders
2011-04-01
Gluonic pole matrix elements explain the appearance of single spin asymmetries (SSA) in high-energy scattering processes. They involve a combination of operators which are odd under time reversal (T-odd). Such matrix elements appear in principle both for parton distribution functions and parton fragmentation functions. We show that for parton fragmentation functions these gluonic pole matrix elements vanish as a consequence of the analytic structure of scattering amplitudes in Quantum Chromodynamics. This result is important in the study of the universality of transverse momentum dependent (TMD) fragmentation functions.
NASA Astrophysics Data System (ADS)
Lü, Ling; Liu, Shuo; Li, Gang; Zhao, Guannan; Gu, Jiajia; Tian, Jing; Wang, Zhouyang
2016-11-01
In this paper, we research the outer synchronization among discrete networks with different topologies. Based on Lyapunov theorem, a novel synchronization technique is designed. Further, the control inputs of the networks and the adaptive laws of configuration matrix element are obtained. In the end, a numerical example is given to illustrate the effectiveness of the synchronization technique. It is found that the designed control input of the networks ensures the convergence of the errors among the networks to zero. And the designed adaptive law of configuration matrix element can replace effectively configuration matrix element in networks.
Multivariate and matrix-variate analogues of Maxwell-Boltzmann and Raleigh densities
NASA Astrophysics Data System (ADS)
Mathai, A. M.; Princy, T.
2017-02-01
The Maxwell-Boltzmann and Raleigh densities are basic densities in many problems in Physics. A multivariate analogue and a rectangular matrix-variate analogue of these densities are explored in this article. The results may become useful in extending the usual theories, where these densities for the real scalar variable case occur, to multivariate and matrix variable situations. Various properties are studied and connection to the volumes of parallelotopes determined by p linearly independent random points in Euclidean n-space, n ≥ p, is also established. Structural decompositions of these random determinants and pathway extensions of Maxwell-Boltzmann and Raleigh densities are also considered.
EH3 matrix mineralogy with major and trace element composition compared to chondrules
NASA Astrophysics Data System (ADS)
Lehner, S. W.; McDonough, W. F.; NéMeth, P.
2014-12-01
We investigated the matrix mineralogy in primitive EH3 chondrites Sahara 97072, ALH 84170, and LAR 06252 with transmission electron microscopy; measured the trace and major element compositions of Sahara 97072 matrix and ferromagnesian chondrules with laser-ablation, inductively coupled, plasma mass spectrometry (LA-ICPMS); and analyzed the bulk composition of Sahara 97072 with LA-ICPMS, solution ICPMS, and inductively coupled plasma atomic emission spectroscopy. The fine-grained matrix of EH3 chondrites is unlike that in other chondrite groups, consisting primarily of enstatite, cristobalite, troilite, and kamacite with a notable absence of olivine. Matrix and pyroxene-rich chondrule compositions differ from one another and are distinct from the bulk meteorite. Refractory lithophile elements are enriched by a factor of 1.5-3 in chondrules relative to matrix, whereas the matrix is enriched in moderately volatile elements. The compositional relation between the chondrules and matrix is reminiscent of the difference between EH3 pyroxene-rich chondrules and EH3 Si-rich, highly sulfidized chondrules. Similar refractory element ratios between the matrix and the pyroxene-rich chondrules suggest the fine-grained material primarily consists of the shattered, sulfidized remains of the formerly pyroxene-rich chondrules with the minor addition of metal clasts. The matrix, chondrule, and metal-sulfide nodule compositions are probably complementary, suggesting all the components of the EH3 chondrites came from the same nebular reservoir.
Design of a shielded coil element of a matrix gradient coil
NASA Astrophysics Data System (ADS)
Jia, Feng; Littin, Sebastian; Layton, Kelvin J.; Kroboth, Stefan; Yu, Huijun; Zaitsev, Maxim
2017-08-01
The increasing interest in spatial encoding with non-linear magnetic fields has intensified the need for coils that generates such fields. Matrix coils consisting of multiple coil elements appear to offer a high flexibility in generating customized encoding fields and are particularly promising for localized high resolution imaging applications. However, coil elements of existing matrix coils were primarily designed and constructed for better shimming and therefore are not expected to achieve an optimal performance for local spatial encoding. Moreover, eddy current properties of such coil elements were not fully explored. In this work, an optimization problem is formulated based on the requirement of local non-linear encoding and eddy current reduction that results in novel designs of coil elements for an actively-shielded matrix gradient coil. Two metrics are proposed to assess the performance of different coil element designs. The results are analyzed to reveal new insights into coil element design.
Calculation of Radiative Corrections to E1 matrix elements in the Neutral Alkalis
Sapirstein, J; Cheng, K T
2004-09-28
Radiative corrections to E1 matrix elements for ns-np transitions in the alkali metal atoms lithium through francium are evaluated. They are found to be small for the lighter alkalis but significantly larger for the heavier alkalis, and in the case of cesium much larger than the experimental accuracy. The relation of the matrix element calculation to a recent decay rate calculation for hydrogenic ions is discussed, and application of the method to parity nonconservation in cesium is described.
Neutrinoless double beta nuclear matrix elements around mass 80 in the nuclear shell-model
NASA Astrophysics Data System (ADS)
Yoshinaga, N.; Higashiyama, K.; Taguchi, D.; Teruya, E.
2015-05-01
The observation of the neutrinoless double-beta decay can determine whether the neutrino is a Majorana particle or not. For theoretical nuclear physics it is particularly important to estimate three types of matrix elements, namely Fermi (F), Gamow-Teller (GT), and tensor (T) matrix elements. In this paper, we carry out shell-model calculations and also pair-truncated shell-model calculations to check the model dependence in the case of mass A=82 nuclei.
Open-Ended Recursive Approach for the Calculation of Multiphoton Absorption Matrix Elements
2015-01-01
We present an implementation of single residues for response functions to arbitrary order using a recursive approach. Explicit expressions in terms of density-matrix-based response theory for the single residues of the linear, quadratic, cubic, and quartic response functions are also presented. These residues correspond to one-, two-, three- and four-photon transition matrix elements. The newly developed code is used to calculate the one-, two-, three- and four-photon absorption cross sections of para-nitroaniline and para-nitroaminostilbene, making this the first treatment of four-photon absorption in the framework of response theory. We find that the calculated multiphoton absorption cross sections are not very sensitive to the size of the basis set as long as a reasonably large basis set with diffuse functions is used. The choice of exchange–correlation functional, however, significantly affects the calculated cross sections of both charge-transfer transitions and other transitions, in particular, for the larger para-nitroaminostilbene molecule. We therefore recommend the use of a range-separated exchange–correlation functional in combination with the augmented correlation-consistent double-ζ basis set aug-cc-pVDZ for the calculation of multiphoton absorption properties. PMID:25821415
Open-Ended Recursive Approach for the Calculation of Multiphoton Absorption Matrix Elements.
Friese, Daniel H; Beerepoot, Maarten T P; Ringholm, Magnus; Ruud, Kenneth
2015-03-10
We present an implementation of single residues for response functions to arbitrary order using a recursive approach. Explicit expressions in terms of density-matrix-based response theory for the single residues of the linear, quadratic, cubic, and quartic response functions are also presented. These residues correspond to one-, two-, three- and four-photon transition matrix elements. The newly developed code is used to calculate the one-, two-, three- and four-photon absorption cross sections of para-nitroaniline and para-nitroaminostilbene, making this the first treatment of four-photon absorption in the framework of response theory. We find that the calculated multiphoton absorption cross sections are not very sensitive to the size of the basis set as long as a reasonably large basis set with diffuse functions is used. The choice of exchange-correlation functional, however, significantly affects the calculated cross sections of both charge-transfer transitions and other transitions, in particular, for the larger para-nitroaminostilbene molecule. We therefore recommend the use of a range-separated exchange-correlation functional in combination with the augmented correlation-consistent double-ζ basis set aug-cc-pVDZ for the calculation of multiphoton absorption properties.
USDA-ARS?s Scientific Manuscript database
Ecological edge effects are sensitive to landscape context. In particular, edge effects can be altered by matrix type and by the presence of other nearby edges. We experimentally altered patch configurations in an African savanna to determine how edge density and matrix type influence edge effect de...
Linear-scaling density matrix perturbation treatment of electric fields in solids.
Xiang, H J; Yang, Jinlong; Hou, J G; Zhu, Qingshi
2006-12-31
We develop a novel linear-scaling [O(N)] algorithm for calculating the optical dielectric constant and Born effective charge. Our method relies on the fact that only the sum of the nondiagonal parts of the electric field perturbation in solids contributes to the first-order derivative density matrix, which can then be obtained through the density-matrix perturbation method. The optical dielectric constant of amorphous SiO(2) is computed using a realistic model for the first time.
Bartkiewicz, Karol; Černoch, Antonín; Lemr, Karel; Miranowicz, Adam
2016-01-21
In standard optical tomographic methods, the off-diagonal elements of a density matrix ρ are measured indirectly. Thus, the reconstruction of ρ, even if it is based on linear inversion, typically magnifies small errors in the experimental data. Recently, an optimal tomography solution measuring all the elements of ρ one-by-one without error magnification has been theoretically proposed. We implemented this method for two-qubit polarization states. For comparison, we also experimentally implemented other well-known tomographic protocols, either based solely on local measurements (of, e.g., the Pauli operators and James-Kwiat-Munro-White projectors) or with mutually unbiased bases requiring both local and global measurements. We reconstructed seventeen separable, partially and maximally entangled two-qubit polarization states. Our experiments show that our method has the highest stability against errors in comparison to other quantum tomographies. In particular, we demonstrate that each optimally-reconstructed state is embedded in an uncertainty circle of the smallest radius, both in terms of trace distance and disturbance. We explain how to experimentally estimate uncertainty radii for all the implemented tomographies and show that, for each reconstructed state, the relevant uncertainty circles intersect indicating the approximate location of the corresponding physical density matrix.
Mesh refinement in finite element analysis by minimization of the stiffness matrix trace
NASA Technical Reports Server (NTRS)
Kittur, Madan G.; Huston, Ronald L.
1989-01-01
Most finite element packages provide means to generate meshes automatically. However, the user is usually confronted with the problem of not knowing whether the mesh generated is appropriate for the problem at hand. Since the accuracy of the finite element results is mesh dependent, mesh selection forms a very important step in the analysis. Indeed, in accurate analyses, meshes need to be refined or rezoned until the solution converges to a value so that the error is below a predetermined tolerance. A-posteriori methods use error indicators, developed by using the theory of interpolation and approximation theory, for mesh refinements. Some use other criterions, such as strain energy density variation and stress contours for example, to obtain near optimal meshes. Although these methods are adaptive, they are expensive. Alternatively, a priori methods, until now available, use geometrical parameters, for example, element aspect ratio. Therefore, they are not adaptive by nature. An adaptive a-priori method is developed. The criterion is that the minimization of the trace of the stiffness matrix with respect to the nodal coordinates, leads to a minimization of the potential energy, and as a consequence provide a good starting mesh. In a few examples the method is shown to provide the optimal mesh. The method is also shown to be relatively simple and amenable to development of computer algorithms. When the procedure is used in conjunction with a-posteriori methods of grid refinement, it is shown that fewer refinement iterations and fewer degrees of freedom are required for convergence as opposed to when the procedure is not used. The mesh obtained is shown to have uniform distribution of stiffness among the nodes and elements which, as a consequence, leads to uniform error distribution. Thus the mesh obtained meets the optimality criterion of uniform error distribution.
NASA Astrophysics Data System (ADS)
Cheng, Wei; Xu, Fang; Li, Hua; Wang, Gang
2014-04-01
Given the density matrix of a bipartite quantum state, could we decide whether it is separable, free entangled, or PPT entangled? Here, we give a negative answer to this question by providing a lot of concrete examples of density matrices, some of which are well known. We find that both separability and distillability are dependent on the decomposition of the density matrix. To be more specific, we show that if a given matrix is considered as the density operators of different composite systems, their entanglement properties might be different. In the case of density matrices, we can look them as both and bipartite quantum states and show that their entanglement properties (i.e., separable, free entangled, or PPT entangled) are completely irrelevant to each other.
Matrix elements and duality for type 2 unitary representations of the Lie superalgebra gl(m|n)
Werry, Jason L.; Gould, Mark D.; Isaac, Phillip S.
2015-12-15
The characteristic identity formalism discussed in our recent articles is further utilized to derive matrix elements of type 2 unitary irreducible gl(m|n) modules. In particular, we give matrix element formulae for all gl(m|n) generators, including the non-elementary generators, together with their phases on finite dimensional type 2 unitary irreducible representations which include the contravariant tensor representations and an additional class of essentially typical representations. Remarkably, we find that the type 2 unitary matrix element equations coincide with the type 1 unitary matrix element equations for non-vanishing matrix elements up to a phase.
Element-specific density profiles in interacting biomembrane models
NASA Astrophysics Data System (ADS)
Schneck, Emanuel; Rodriguez-Loureiro, Ignacio; Bertinetti, Luca; Marin, Egor; Novikov, Dmitri; Konovalov, Oleg; Gochev, Georgi
2017-03-01
Surface interactions involving biomembranes, such as cell-cell interactions or membrane contacts inside cells play important roles in numerous biological processes. Structural insight into the interacting surfaces is a prerequisite to understand the interaction characteristics as well as the underlying physical mechanisms. Here, we work with simplified planar experimental models of membrane surfaces, composed of lipids and lipopolymers. Their interaction is quantified in terms of pressure-distance curves using ellipsometry at controlled dehydrating (interaction) pressures. For selected pressures, their internal structure is investigated by standing-wave x-ray fluorescence (SWXF). This technique yields specific density profiles of the chemical elements P and S belonging to lipid headgroups and polymer chains, as well as counter-ion profiles for charged surfaces.
Matrix density mediates polarization and lumen formation of endothelial sprouts in VEGF gradients.
Shamloo, Amir; Heilshorn, Sarah C
2010-11-21
Endothelial cell (EC) sprouting morphogenesis is a critical step during angiogenesis, the formation of new blood vessels from existing conduits. Here, three-dimensional sprouting morphogenesis was examined using in vitro microfluidic devices that enabled the separate and simultaneous tuning of biomechanical and soluble biochemical stimuli. Quantitative analysis of endothelial sprout formation demonstrated that the ability of vascular endothelial growth factor (VEGF) to regulate stable sprout formation was mediated by the density of the surrounding collagen/fibronectin matrix. The coordinated migration and proliferation of multiple ECs to form stable sprouts were enhanced at intermediate matrix densities (1.2-1.9 mg ml(-1)), while lower densities resulted in uncoordinated migration (0.3-0.7 mg ml(-1)) and higher densities resulted in broad cell clusters that did not elongate (2.7 mg ml(-1)). Within the permissive range of matrix biomechanics, higher density matrices resulted in shorter, thicker, and slower-growing sprouts. The sprouts in higher density matrices also were more likely to polarize towards higher VEGF concentrations, included more cells per cross-sectional area, and demonstrated more stable lumen formation compared to sprouts in lower density matrices. These results quantitatively demonstrate that matrix density mediates VEGF-induced sprout polarization and lumen formation, potentially by regulating the balance between EC migration rate and proliferation rate.
Hedegård, Erik Donovan Knecht, Stefan; Reiher, Markus; Kielberg, Jesper Skau; Jensen, Hans Jørgen Aagaard
2015-06-14
We present a new hybrid multiconfigurational method based on the concept of range-separation that combines the density matrix renormalization group approach with density functional theory. This new method is designed for the simultaneous description of dynamical and static electron-correlation effects in multiconfigurational electronic structure problems.
Construct order parameters from the reduced density matrix spectra
Gu, Shi-Jian; Yu, Wing Chi; Lin, Hai-Qing
2013-09-15
In this paper, we try to establish a connection between a quantum information concept, i.e., the mutual information, and the conventional order parameter in condensed matter physics. We show that non-vanishing mutual information between two subsystems separated by a long distance means the existence of long-range orders in the system. By analyzing the spectra of the reduced density matrices that are used to calculate the mutual information, we show how to derive the local order operators that identify various ordered phases in condensed matter physics. -- Highlights: •Discussed the relation between long-range order and the mutual information (MI). •Pointed out how to check the existence of long-range order from MI. •Proposed a scheme to derive the diagonal and off-diagonal order parameter. •Gave three examples to show the effectiveness of the scheme.
NASA Technical Reports Server (NTRS)
Bhatt, Ramakrishna T.; Kiser, Lames D.
1990-01-01
The room temperature mechanical properties were measured for SiC fiber reinforced reaction-bonded silicon nitride composites (SiC/RBSN) of different densities. The composites consisted of approx. 30 vol percent uniaxially aligned 142 micron diameter SiC fibers (Textron SCS-6) in a reaction-bonded Si3N4 matrix. The composite density was varied by changing the consolidation pressure during RBSN processing and by hot isostatically pressing the SiC/RBSN composites. Results indicate that as the consolidation pressure was increased from 27 to 138 MPa, the average pore size of the nitrided composites decreased from 0.04 to 0.02 microns and the composite density increased from 2.07 to 2.45 gm/cc. Nonetheless, these improvements resulted in only small increases in the first matrix cracking stress, primary elastic modulus, and ultimate tensile strength values of the composites. In contrast, HIP consolidation of SiC/RBSN resulted in a fully dense material whose first matrix cracking stress and elastic modulus were approx. 15 and 50 percent higher, respectively, and ultimate tensile strength values were approx. 40 percent lower than those for unHIPed SiC/RBSN composites. The modulus behavior for all specimens can be explained by simple rule-of-mixture theory. Also, the loss in ultimate strength for the HIPed composites appears to be related to a degradation in fiber strength at the HIP temperature. However, the density effect on matrix fracture strength was much less than would be expected based on typical monolithic Si3N4 behavior, suggesting that composite theory is indeed operating. Possible practical implications of these observations are discussed.
NASA Technical Reports Server (NTRS)
Bhatt, Ramakrishna T.; Kiser, Lames D.
1990-01-01
The room temperature mechanical properties were measured for SiC fiber reinforced reaction-bonded silicon nitride composites (SiC/RBSN) of different densities. The composites consisted of approx. 30 vol percent uniaxially aligned 142 micron diameter SiC fibers (Textron SCS-6) in a reaction-bonded Si3N4 matrix. The composite density was varied by changing the consolidation pressure during RBSN processing and by hot isostatically pressing the SiC/RBSN composites. Results indicate that as the consolidation pressure was increased from 27 to 138 MPa, the average pore size of the nitrided composites decreased from 0.04 to 0.02 microns and the composite density increased from 2.07 to 2.45 gm/cc. Nonetheless, these improvements resulted in only small increases in the first matrix cracking stress, primary elastic modulus, and ultimate tensile strength values of the composites. In contrast, HIP consolidation of SiC/RBSN resulted in a fully dense material whose first matrix cracking stress and elastic modulus were approx. 15 and 50 percent higher, respectively, and ultimate tensile strength values were approx. 40 percent lower than those for unHIPed SiC/RBSN composites. The modulus behavior for all specimens can be explained by simple rule-of-mixture theory. Also, the loss in ultimate strength for the HIPed composites appears to be related to a degradation in fiber strength at the HIP temperature. However, the density effect on matrix fracture strength was much less than would be expected based on typical monolithic Si3N4 behavior, suggesting that composite theory is indeed operating. Possible practical implications of these observations are discussed.
Matrix elements of Δ B =0 operators in heavy hadron chiral perturbation theory
NASA Astrophysics Data System (ADS)
Lee, Jong-Wan
2015-05-01
We study the light-quark mass and spatial volume dependence of the matrix elements of Δ B =0 four-quark operators relevant for the determination of Vu b and the lifetime ratios of single-b hadrons. To this end, one-loop diagrams are computed in the framework of heavy hadron chiral perturbation theory with partially quenched formalism for three light-quark flavors in the isospin limit; flavor-connected and -disconnected diagrams are carefully analyzed. These calculations include the leading light-quark flavor and heavy-quark spin symmetry breaking effects in the heavy hadron spectrum. Our results can be used in the chiral extrapolation of lattice calculations of the matrix elements to the physical light-quark masses and to infinite volume. To provide insight on such chiral extrapolation, we evaluate the one-loop contributions to the matrix elements containing external Bd, Bs mesons and Λb baryon in the QCD limit, where sea and valence quark masses become equal. In particular, we find that the matrix elements of the λ3 flavor-octet operators with an external Bd meson receive the contributions solely from connected diagrams in which current lattice techniques are capable of precise determination of the matrix elements. Finite volume effects are at most a few percent for typical lattice sizes and pion masses.
Insights into Nuclear Triaxiality from Interference Effects in E2 Matrix Elements
NASA Astrophysics Data System (ADS)
Allmond, J. M.; Wood, J. L.; Kulp, W. D.
2007-10-01
Recently, we have introduced [1] a triaxial rotor model with independent inertia and E2 tensors. The E2 matrix elements [2] of the osmium isotopes (186, 188, 190, and 192) are studied in the framework of this model (59 of 84 E2 matrix elements deviate by 30% or less). It is shown that interference effects in the inertia tensor (K-mixing) and the E2 tensor can lead to significant reductions in the diagonal E2 matrix elements. In some instances, the diagonal E2 matrix elements may decrease with increasing spin. Additionally, a sum rule for diagonal E2 matrix elements is shown and used to explore missing strength from K-admixtures. [1] J.L. Wood, A-M. Oros-Peusquens, R. Zaballa, J.M. Allmond, and W.D. Kulp, Phys. Rev. C 70, 024308 (2004). [2] C.Y. Wu, D. Cline, T. Czosnyka, A. Backlin, C. Baktash, R.M. Diamond, G.D. Dracoulis, L. Hasselgren, H. Kluge, et al., Nucl. Phys. A607, 178 (1996).
A Surrogate Measure of Cortical Bone Matrix Density by Long T2-Suppressed MRI
Seifert, Alan C.; Li, Cheng; Wehrli, Suzanne L.; Wehrli, Felix W.
2015-01-01
Magnetic resonance has the potential to image and quantify two pools of water within bone: free water within the Haversian pore system (transverse relaxation time, T2 > 1 ms), and water hydrogen-bonded to matrix collagen (T2 ~ 300–400 µs). While total bone water concentration quantified by MRI has been shown to scale with porosity, greater insight into bone matrix density and porosity may be gained by relaxation-based separation of bound and pore water fractions. The objective of this study was to evaluate a recently developed surrogate measurement for matrix density, single adiabatic inversion recovery (SIR) zero echo-time (ZTE) MRI, in human bone. Specimens of tibial cortical bone from 15 donors (27–97 y/o, eight female and seven male) were examined at 9.4T field strength using two methods: (1) 1H ZTE MRI, to capture total 1H signal, and (2) 1H SIR-ZTE MRI, to selectively image matrix-associated 1H signal. Total water, bone matrix, and bone mineral densities were also quantified gravimetrically, and porosity was measured by micro-CT. ZTE apparent total water 1H concentration was 32.7±3.2 M (range: 28.5–40.3 M), and was correlated positively with porosity (R2 = 0.80) and negatively with matrix and mineral densities (R2 = 0.90 and 0.82, respectively). SIR-ZTE apparent bound water 1H concentration was 32.9±3.9 M (range: 24.4–39.8 M), and its correlations were opposite to those of apparent total water: negative with porosity (R2 = 0.73) and positive with matrix density (R2 = 0.74) and mineral density (R2 = 0.72). Porosity was strongly correlated with gravimetric matrix density (R2 = 0.91, negative) and total water density (R2 = 0.92, positive). The strong correlations of SIR-ZTE-derived apparent bound water 1H concentration with ground-truth measurements suggest that this quantitative solid-state MRI method provides a nondestructive surrogate measure of bone matrix density. PMID:26085307
A Surrogate Measure of Cortical Bone Matrix Density by Long T2 -Suppressed MRI.
Seifert, Alan C; Li, Cheng; Wehrli, Suzanne L; Wehrli, Felix W
2015-12-01
Magnetic resonance has the potential to image and quantify two pools of water within bone: free water within the Haversian pore system (transverse relaxation time, T2 > 1 ms), and water hydrogen-bonded to matrix collagen (T2 ∼ 300 to 400 μs). Although total bone water concentration quantified by MRI has been shown to scale with porosity, greater insight into bone matrix density and porosity may be gained by relaxation-based separation of bound and pore water fractions. The objective of this study was to evaluate a recently developed surrogate measurement for matrix density, single adiabatic inversion recovery (SIR) zero echo-time (ZTE) MRI, in human bone. Specimens of tibial cortical bone from 15 donors (aged 27 to 97 years; 8 female and 7 male) were examined at 9.4T field strength using two methods: (1) (1)H ZTE MRI, to capture total (1)H signal, and (2) (1)H SIR-ZTE MRI, to selectively image matrix-associated (1)H signal. Total water, bone matrix, and bone mineral densities were also quantified gravimetrically, and porosity was measured by micro-CT. ZTE apparent total water (1)H concentration was 32.7 ± 3.2 M (range 28.5 to 40.3 M), and was correlated positively with porosity (R(2) = 0.80) and negatively with matrix and mineral densities (R(2) = 0.90 and 0.82, respectively). SIR-ZTE apparent bound water (1)H concentration was 32.9 ± 3.9 M (range 24.4 to 39.8 M), and its correlations were opposite to those of apparent total water: negative with porosity (R(2) = 0.73) and positive with matrix density (R(2) = 0.74) and mineral density (R(2) = 0.72). Porosity was strongly correlated with gravimetric matrix density (R(2) = 0.91, negative) and total water density (R(2) = 0.92, positive). The strong correlations of SIR-ZTE-derived apparent bound water (1)H concentration with ground-truth measurements suggest that this quantitative solid-state MRI method provides a nondestructive surrogate measure of bone matrix density
NASA Astrophysics Data System (ADS)
Spiegel, J. Dominik; Lyskov, Igor; Kleinschmidt, Martin; Marian, Christel M.
2017-01-01
BODIPY-based dyads serve as model systems for the investigation of excitation energy transfer (EET). Through-space EET is brought about by direct and exchange interactions between the transition densities of donor and acceptor localized states. The presence of a molecular linker gives rise to additional charge transfer (CT) contributions. Here, we present a novel approach for the calculation of the excitonic coupling matrix element (ECME) including CT contributions which is based on supermolecular one-electron transition density matrices (STD). The validity of the approach is assessed for a model system of two π -stacked ethylene molecules at varying intermolecular separation. Wave functions and electronic excitation energies of five EET cassettes comprising anthracene as exciton donor and BODIPY as exciton acceptor are obtained by the redesigned combined density functional theory and multireference configuration interaction (DFT/MRCI-R) method. CT contributions to the ECME are shown to be important in the covalently linked EET cassettes.
Large-scale All-electron Density Functional Theory Calculations using Enriched Finite Element Method
NASA Astrophysics Data System (ADS)
Kanungo, Bikash; Gavini, Vikram
We present a computationally efficient method to perform large-scale all-electron density functional theory calculations by enriching the Lagrange polynomial basis in classical finite element (FE) discretization with atom-centered numerical basis functions, which are obtained from the solutions of the Kohn-Sham (KS) problem for single atoms. We term these atom-centered numerical basis functions as enrichment functions. The integrals involved in the construction of the discrete KS Hamiltonian and overlap matrix are computed using an adaptive quadrature grid based on gradients in the enrichment functions. Further, we propose an efficient scheme to invert the overlap matrix by exploiting its LDL factorization and employing spectral finite elements along with Gauss-Lobatto quadrature rules. Finally, we use a Chebyshev polynomial based acceleration technique to compute the occupied eigenspace in each self-consistent iteration. We demonstrate the accuracy, efficiency and scalability of the proposed method on various metallic and insulating benchmark systems, with systems ranging in the order of 10,000 electrons. We observe a 50-100 fold reduction in the overall computational time when compared to classical FE calculations while being commensurate with the desired chemical accuracy. We acknowledge the support of NSF (Grant No. 1053145) and ARO (Grant No. W911NF-15-1-0158) in conducting this work.
1983-12-15
T TAVIS UCASIFIED 15 DEC 83 TR-0 84(4925-03)-1 SD-TR-83-75 F/G 20/5 NENLS OE 0 ONE so hiE EhhhhhhhhhhhhE ImI INShIhIhhhhE . 1.8 11111 I2 fl...Amplification 00C in a Double Heterostructure GaAs Device Using the Density Matrix Approach M. T. TAVIS Electronics Research Laboratory Laboratory Operations... Tavis F04701-83-C-0084 9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT, TASK The Aerospace Corporation AE OKUI UBR El Segundo
Quenched domain wall QCD with DBW2 gauge action toward nucleon decay matrix element calculation
NASA Astrophysics Data System (ADS)
Aoki, Yasumichi
2001-10-01
The domain wall fermion action is a promising way to control chiral symmetry in lattice gauge theory. By the good chiral symmetry of this approach even at finite lattice spacing, one is able to extract hadronic matrix elements, like kaon weak matrix elements, for which the symmetry is extremely important. Ordinary fermions with poor chiral symmetry make calculation difficult because of the large mixing of operators with different chiral structure. Even though the domain wall fermion action with the simple Wilson gauge action has a good chiral symmetry, one can further improve the symmetry by using a different gauge action. We take a non-perturbatively improved action, the DBW2 action of the QCD Taro group. Hadron masses are systematically examined for a range of parameters. Application to nucleon decay matrix element is also discussed.
Liu, C; Liu, J; Yao, Y X; Wu, P; Wang, C Z; Ho, K M
2016-10-11
We recently proposed the correlation matrix renormalization (CMR) theory to treat the electronic correlation effects [Phys. Rev. B 2014, 89, 045131 and Sci. Rep. 2015, 5, 13478] in ground state total energy calculations of molecular systems using the Gutzwiller variational wave function (GWF). By adopting a number of approximations, the computational effort of the CMR can be reduced to a level similar to Hartree-Fock calculations. This paper reports our recent progress in minimizing the error originating from some of these approximations. We introduce a novel sum-rule correction to obtain a more accurate description of the intersite electron correlation effects in total energy calculations. Benchmark calculations are performed on a set of molecules to show the reasonable accuracy of the method.
B(s) 0-mixing matrix elements from lattice QCD for the Standard Model and beyond
NASA Astrophysics Data System (ADS)
Bazavov, A.; Bernard, C.; Bouchard, C. M.; Chang, C. C.; DeTar, C.; Du, Daping; El-Khadra, A. X.; Freeland, E. D.; Gámiz, E.; Gottlieb, Steven; Heller, U. M.; Kronfeld, A. S.; Laiho, J.; Mackenzie, P. B.; Neil, E. T.; Simone, J.; Sugar, R.; Toussaint, D.; Van de Water, R. S.; Zhou, Ran; Fermilab Lattice; MILC Collaborations
2016-06-01
We calculate—for the first time in three-flavor lattice QCD—the hadronic matrix elements of all five local operators that contribute to neutral B0- and Bs-meson mixing in and beyond the Standard Model. We present a complete error budget for each matrix element and also provide the full set of correlations among the matrix elements. We also present the corresponding bag parameters and their correlations, as well as specific combinations of the mixing matrix elements that enter the expression for the neutral B -meson width difference. We obtain the most precise determination to date of the SU(3)-breaking ratio ξ =1.206 (18 )(6 ), where the second error stems from the omission of charm-sea quarks, while the first encompasses all other uncertainties. The threefold reduction in total uncertainty, relative to the 2013 Flavor Lattice Averaging Group results, tightens the constraint from B mixing on the Cabibbo-Kobayashi-Maskawa (CKM) unitarity triangle. Our calculation employs gauge-field ensembles generated by the MILC Collaboration with four lattice spacings and pion masses close to the physical value. We use the asqtad-improved staggered action for the light-valence quarks and the Fermilab method for the bottom quark. We use heavy-light meson chiral perturbation theory modified to include lattice-spacing effects to extrapolate the five matrix elements to the physical point. We combine our results with experimental measurements of the neutral B -meson oscillation frequencies to determine the CKM matrix elements |Vt d|=8.00 (34 )(8 )×10-3, |Vt s|=39.0 (1.2 )(0.4 )×10-3, and |Vt d/Vt s|=0.2052 (31 )(10 ), which differ from CKM-unitarity expectations by about 2 σ . These results and others from flavor-changing-neutral currents point towards an emerging tension between weak processes that are mediated at the loop and tree levels.
Nonequilibrium density-matrix description of steady-state quantum transport.
Dhar, Abhishek; Saito, Keiji; Hänggi, Peter
2012-01-01
With this work we investigate the stationary nonequilibrium density matrix of current carrying nonequilibrium steady states of in-between quantum systems that are connected to reservoirs. We describe the analytical procedure to obtain the explicit result for the reduced density matrix of quantum transport when the system, the connecting reservoirs, and the system-reservoir interactions are described by quadratic Hamiltonians. Our procedure is detailed for both electronic transport described by the tight-binding Hamiltonian and for phonon transport described by harmonic Hamiltonians. For the special case of weak system-reservoir couplings, a more detailed description of the steady-state density matrix is obtained. Several paradigm transport setups for interelectrode electron transport and low-dimensional phonon heat flux are elucidated.
NASA Astrophysics Data System (ADS)
Cave, Robert J.; Newton, Marshall D.
1996-01-01
A new method for the calculation of the electronic coupling matrix element for electron transfer processes is introduced and results for several systems are presented. The method can be applied to ground and excited state systems and can be used in cases where several states interact strongly. Within the set of states chosen it is a non-perturbative treatment, and can be implemented using quantities obtained solely in terms of the adiabatic states. Several applications based on quantum chemical calculations are briefly presented. Finally, since quantities for adiabatic states are the only input to the method, it can also be used with purely experimental data to estimate electron transfer matrix elements.
Semiclassical matrix elements for a chaotic propagator in the scar function basis
NASA Astrophysics Data System (ADS)
Rivas, Alejandro M. F.
2013-04-01
A semiclassical approximation for the matrix elements of a quantum chaotic propagator in the scar function basis has been derived. The obtained expression is solely expressed in terms of canonical invariant objects. For our purpose, we have used the recently developed, semiclassical matrix elements of the propagator in coherent states, together with the linearization of the flux in the neighborhood of a classically unstable periodic orbit of chaotic two-dimensional systems. The expression derived here is successfully verified to be exact for a (linear) cat map, after the theory is adapted to a discrete phase space appropriate to a quantized torus.
Calculation of radiative corrections to E1 matrix elements in the neutral alkali metals
Sapirstein, J.; Cheng, K.T.
2005-02-01
Radiative corrections to E1 matrix elements for ns-np transitions in the alkali-metal atoms lithium through francium are evaluated. They are found to be small for the lighter alkali metals but significantly larger for the heavier alkali metals, and in the case of cesium much larger than the experimental accuracy. The relation of the matrix element calculation to a recent decay rate calculation for hydrogenic ions is discussed, and application of the method to parity nonconservation in cesium is described.
Axial-Current Matrix Elements in Light Nuclei from Lattice QCD
Savage, Martin; Shanahan, Phiala E.; Tiburzi, Brian C.; Wagman, Michael L.; Winter, Frank T.; Beane, Silas; Chang, Emmanuel; Davoudi, Zohreh; Detmold, William; Orginos, Konstantinos
2016-12-01
I present results from the first lattice QCD calculations of axial-current matrix elements in light nuclei, performed by the NPLQCD collaboration. Precision calculations of these matrix elements, and the subsequent extraction of multi-nucleon axial-current operators, are essential in refining theoretical predictions of the proton-proton fusion cross section, neutrino-nucleus cross sections and $\\beta\\beta$-decay rates of nuclei. In addition, they are expected to shed light on the phenomenological quenching of $g_A$ that is required in nuclear many-body calculations.
Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n)
Gould, Mark D.; Isaac, Phillip S.; Werry, Jason L.
2014-01-15
Using our recent results on eigenvalues of invariants associated to the Lie superalgebra gl(m|n), we use characteristic identities to derive explicit matrix element formulae for all gl(m|n) generators, particularly non-elementary generators, on finite dimensional type 1 unitary irreducible representations. We compare our results with existing works that deal with only subsets of the class of type 1 unitary representations, all of which only present explicit matrix elements for elementary generators. Our work therefore provides an important extension to existing methods, and thus highlights the strength of our techniques which exploit the characteristic identities.
Analytic matrix elements for the two-electron atomic basis with logarithmic terms
Liverts, Evgeny Z.; Barnea, Nir
2014-08-01
The two-electron problem for the helium-like atoms in S-state is considered. The basis containing the integer powers of ln r, where r is a radial variable of the Fock expansion, is studied. In this basis, the analytic expressions for the matrix elements of the corresponding Hamiltonian are presented. These expressions include only elementary and special functions, what enables very fast and accurate computation of the matrix elements. The decisive contribution of the correct logarithmic terms to the behavior of the two-electron wave function in the vicinity of the triple-coalescence point is reaffirmed.
Double β-decay nuclear matrix elements for the A=48 and A=58 systems
NASA Astrophysics Data System (ADS)
Skouras, L. D.; Vergados, J. D.
1983-11-01
The nuclear matrix elements entering the double β decays of the 48Ca-48Ti and 58Ni-58Fe systems have been calculated using a realistic two nucleon interaction and realistic shell model spaces. Effective transition operators corresponding to a variety of gauge theory models have been considered. The stability of such matrix elements against variations of the nuclear parameters is examined. Appropriate lepton violating parameters are extracted from the A=48 data and predictions are made for the lifetimes of the positron decays of the A=58 system. RADIOACTIVITY Double β decay. Gauge theories. Lepton nonconservation. Neutrino mass. Shell model calculations.
Nonmonotonic Recursive Polynomial Expansions for Linear Scaling Calculation of the Density Matrix.
Rubensson, Emanuel H
2011-05-10
As it stands, density matrix purification is a powerful tool for linear scaling electronic structure calculations. The convergence is rapid and depends only weakly on the band gap. However, as will be shown in this letter, there is room for improvements. The key is to allow for nonmonotonicity in the recursive polynomial expansion. On the basis of this idea, new purification schemes are proposed that require only half the number of matrix-matrix multiplications compared to previous schemes. The speedup is essentially independent of the location of the chemical potential and increases with decreasing band gap.
Matrix Element Effects in the ARPES Spectra of High-Tc's
NASA Astrophysics Data System (ADS)
Bansil, A.; Lindroos, M.
1998-03-01
We have extended our first-principles photointensity computations [see, e.g., Lindroos and Bansil, Phys. Rev. Letters 75, 1182(1995)] to treat the complex Bi2212 structure. Results for emission from the (001) surface along high symmetry directions in the Brillouin zone are discussed. Although the calculations are implicitly based on the LDA wavefunctions, we have carried out a number of simulations to mimic correlation effects in order to assess the robustness of our results. The total weight of the spectral peak associated with the CuO2 plane bands is found to vary anisotropically as one moves away from the zone center in remarkable overall accord with the corresponding experimental observations [Ding et al., Phys. Rev. Letters 76, 1533(1996)]. The photon-energy, polarization and k-dependencies of the spectra in the vicinity of the M-point are analyzed in some detail with an eye towards identifying signatures of one vs two CuO2 plane bands in the spectra. Our study shows clearly that matrix element effects are important in interpreting the ARPES spectra of the high-Tc's and that caution should be exercised in making direct comparisons between the observed features and the computed one-particle spectral density functions. Work supported in part by the DOE and the Academy of Finland.
Matrix sublimation method for the formation of high-density amorphous ice
NASA Astrophysics Data System (ADS)
Kouchi, A.; Hama, T.; Kimura, Y.; Hidaka, H.; Escribano, R.; Watanabe, N.
2016-08-01
A novel method for the formation of amorphous ice involving matrix sublimation has been developed. A CO-rich CO:H2O mixed ice was deposited at 8-10 K under ultra-high vacuum condition, which was then allowed to warm. After the sublimation of matrix CO at 35 K, amorphous ice remained. The amorphous ice formed exhibits a highly porous microscale texture; however, it also rather exhibits a density similar to that of high-density amorphous ice formed under high pressure. Furthermore, unlike conventional vapor-deposited amorphous ice, the amorphous ice is stable up to 140 K, where it transforms directly to cubic ice Ic.
Entangled electron and nuclear spin states in 15N@C60: Density matrix tomography
NASA Astrophysics Data System (ADS)
Scherer, Werner; Mehring, Michael
2008-02-01
Procedures of the preparation and detection of entangled electron-nuclear spin states in N15@C60 by combining electron spin resonance and electron nuclear double resonance pulse techniques are presented. A quantitative evaluation of the complete density matrix is obtained by a special density matrix tomography. All four Bell states of a two qubit subsystem were analyzed and experimental decoherence times are presented. In addition, we estimate a quantum critical temperature of Tq=7.76K for this system at an electron spin resonance frequency of 95GHz.
NASA Astrophysics Data System (ADS)
Qi, Xianfei; Gao, Ting; Yan, Fengli
2017-09-01
We present a necessary and sufficient product criterion for bipartite quantum states based on the rank of realignment matrix of density matrix. Then, this approach is generalized to multipartite systems. We first introduce the concept of semiproduct in a similar manner to the semiseparable and prove that semiproduct is equivalent to fully product. Therefore, a quantum state is bipartite product with respect to all possible partitions implies fully product which is different from the case of separability. For pure states, it can easily be seen that several necessary and sufficient separability criteria for multipartite systems are derived as a special case of our results. Several specific examples illustrate that our criteria are convenient and operational.
Edgar, Lowell T.; Underwood, Clayton J.; Guilkey, James E.; Hoying, James B.; Weiss, Jeffrey A.
2014-01-01
Angiogenesis is regulated by the local microenvironment, including the mechanical interactions between neovessel sprouts and the extracellular matrix (ECM). However, the mechanisms controlling the relationship of mechanical and biophysical properties of the ECM to neovessel growth during sprouting angiogenesis are just beginning to be understood. In this research, we characterized the relationship between matrix density and microvascular topology in an in vitro 3D organ culture model of sprouting angiogenesis. We used these results to design and calibrate a computational growth model to demonstrate how changes in individual neovessel behavior produce the changes in vascular topology that were observed experimentally. Vascularized gels with higher collagen densities produced neovasculatures with shorter vessel lengths, less branch points, and reduced network interconnectivity. The computational model was able to predict these experimental results by scaling the rates of neovessel growth and branching according to local matrix density. As a final demonstration of utility of the modeling framework, we used our growth model to predict several scenarios of practical interest that could not be investigated experimentally using the organ culture model. Increasing the density of the ECM significantly reduced angiogenesis and network formation within a 3D organ culture model of angiogenesis. Increasing the density of the matrix increases the stiffness of the ECM, changing how neovessels are able to deform and remodel their surroundings. The computational framework outlined in this study was capable of predicting this observed experimental behavior by adjusting neovessel growth rate and branching probability according to local ECM density, demonstrating that altering the stiffness of the ECM via increasing matrix density affects neovessel behavior, thereby regulated vascular topology during angiogenesis. PMID:24465500
Computing the Density Matrix in Electronic Structure Theory on Graphics Processing Units.
Cawkwell, M J; Sanville, E J; Mniszewski, S M; Niklasson, Anders M N
2012-11-13
The self-consistent solution of a Schrödinger-like equation for the density matrix is a critical and computationally demanding step in quantum-based models of interatomic bonding. This step was tackled historically via the diagonalization of the Hamiltonian. We have investigated the performance and accuracy of the second-order spectral projection (SP2) algorithm for the computation of the density matrix via a recursive expansion of the Fermi operator in a series of generalized matrix-matrix multiplications. We demonstrate that owing to its simplicity, the SP2 algorithm [Niklasson, A. M. N. Phys. Rev. B2002, 66, 155115] is exceptionally well suited to implementation on graphics processing units (GPUs). The performance in double and single precision arithmetic of a hybrid GPU/central processing unit (CPU) and full GPU implementation of the SP2 algorithm exceed those of a CPU-only implementation of the SP2 algorithm and traditional matrix diagonalization when the dimensions of the matrices exceed about 2000 × 2000. Padding schemes for arrays allocated in the GPU memory that optimize the performance of the CUBLAS implementations of the level 3 BLAS DGEMM and SGEMM subroutines for generalized matrix-matrix multiplications are described in detail. The analysis of the relative performance of the hybrid CPU/GPU and full GPU implementations indicate that the transfer of arrays between the GPU and CPU constitutes only a small fraction of the total computation time. The errors measured in the self-consistent density matrices computed using the SP2 algorithm are generally smaller than those measured in matrices computed via diagonalization. Furthermore, the errors in the density matrices computed using the SP2 algorithm do not exhibit any dependence of system size, whereas the errors increase linearly with the number of orbitals when diagonalization is employed.
Juxtaposing density matrix and classical path-based wave packet dynamics
Aghtar, Mortaza; Liebers, Jörg; Strümpfer, Johan; Schulten, Klaus; Kleinekathöfer, Ulrich
2012-01-01
In many physical, chemical, and biological systems energy and charge transfer processes are of utmost importance. To determine the influence of the environment on these transport processes, equilibrium molecular dynamics simulations become more and more popular. From these simulations, one usually determines the thermal fluctuations of certain energy gaps, which are then either used to perform ensemble-averaged wave packet simulations, also called Ehrenfest dynamics, or to employ a density matrix approach via spectral densities. These two approaches are analyzed through energy gap fluctuations that are generated to correspond to a predetermined spectral density. Subsequently, density matrix and wave packet simulations are compared through population dynamics and absorption spectra for different parameter regimes. Furthermore, a previously proposed approach to enforce the correct long-time behavior in the wave packet simulations is probed and an improvement is proposed. PMID:22697524
Kinetic equations for a density matrix describing nonlinear effects in spectral line wings
Parkhomenko, A. I. Shalagin, A. M.
2011-11-15
Kinetic quantum equations are derived for a density matrix with collision integrals describing nonlinear effects in spectra line wings. These equations take into account the earlier established inequality of the spectral densities of Einstein coefficients for absorption and stimulated radiation emission by a two-level quantum system in the far wing of a spectral line in the case of frequent collisions. The relationship of the absorption and stimulated emission probabilities with the characteristics of radiation and an elementary scattering event is found.
NASA Astrophysics Data System (ADS)
Briceño, Raúl A.; Hansen, Maxwell T.; Monahan, Christopher J.
2017-07-01
Lattice quantum chromodynamics (QCD) provides the only known systematic, nonperturbative method for first-principles calculations of nucleon structure. However, for quantities such as light-front parton distribution functions (PDFs) and generalized parton distributions (GPDs), the restriction to Euclidean time prevents direct calculation of the desired observable. Recently, progress has been made in relating these quantities to matrix elements of spatially nonlocal, zero-time operators, referred to as quasidistributions. Still, even for these time-independent matrix elements, potential subtleties have been identified in the role of the Euclidean signature. In this work, we investigate the analytic behavior of spatially nonlocal correlation functions and demonstrate that the matrix elements obtained from Euclidean lattice QCD are identical to those obtained using the Lehmann-Symanzik-Zimmermann reduction formula in Minkowski space. After arguing the equivalence on general grounds, we also show that it holds in a perturbative calculation, where special care is needed to identify the lattice prediction. Finally we present a proof of the uniqueness of the matrix elements obtained from Minkowski and Euclidean correlation functions to all order in perturbation theory.
Briceno, Raul A.; Hansen, Maxwell T.; Monahan, Christopher J.
2017-07-11
Lattice quantum chromodynamics (QCD) provides the only known systematic, nonperturbative method for first-principles calculations of nucleon structure. However, for quantities such as light-front parton distribution functions (PDFs) and generalized parton distributions (GPDs), the restriction to Euclidean time prevents direct calculation of the desired observable. Recently, progress has been made in relating these quantities to matrix elements of spatially nonlocal, zero-time operators, referred to as quasidistributions. Still, even for these time-independent matrix elements, potential subtleties have been identified in the role of the Euclidean signature. In this work, we investigate the analytic behavior of spatially nonlocal correlation functions and demonstrate thatmore » the matrix elements obtained from Euclidean lattice QCD are identical to those obtained using the Lehmann-Symanzik-Zimmermann reduction formula in Minkowski space. After arguing the equivalence on general grounds, we also show that it holds in a perturbative calculation, where special care is needed to identify the lattice prediction. Lastly, we present a proof of the uniqueness of the matrix elements obtained from Minkowski and Euclidean correlation functions to all order in perturbation theory.« less
On the Feynman-Hellmann theorem in quantum field theory and the calculation of matrix elements
NASA Astrophysics Data System (ADS)
Bouchard, Chris; Chang, Chia Cheng; Kurth, Thorsten; Orginos, Kostas; Walker-Loud, André
2017-07-01
The Feynman-Hellmann theorem can be derived from the long Euclidean-time limit of correlation functions determined with functional derivatives of the partition function. Using this insight, we fully develop an improved method for computing matrix elements of external currents utilizing only two-point correlation functions. Our method applies to matrix elements of any external bilinear current, including nonzero momentum transfer, flavor-changing, and two or more current insertion matrix elements. The ability to identify and control all the systematic uncertainties in the analysis of the correlation functions stems from the unique time dependence of the ground-state matrix elements and the fact that all excited states and contact terms are Euclidean-time dependent. We demonstrate the utility of our method with a calculation of the nucleon axial charge using gradient-flowed domain-wall valence quarks on the Nf=2 +1 +1 MILC highly improved staggered quark ensemble with lattice spacing and pion mass of approximately 0.15 fm and 310 MeV respectively. We show full control over excited-state systematics with the new method and obtain a value of gA=1.213 (26 ) with a quark-mass-dependent renormalization coefficient.
On the Feynman-Hellmann theorem in quantum field theory and the calculation of matrix elements
Bouchard, Chris; Chang, Chia Cheng; Kurth, Thorsten; ...
2017-07-12
In this paper, the Feynman-Hellmann theorem can be derived from the long Euclidean-time limit of correlation functions determined with functional derivatives of the partition function. Using this insight, we fully develop an improved method for computing matrix elements of external currents utilizing only two-point correlation functions. Our method applies to matrix elements of any external bilinear current, including nonzero momentum transfer, flavor-changing, and two or more current insertion matrix elements. The ability to identify and control all the systematic uncertainties in the analysis of the correlation functions stems from the unique time dependence of the ground-state matrix elements and the fact that all excited states and contact terms are Euclidean-time dependent. We demonstrate the utility of our method with a calculation of the nucleon axial charge using gradient-flowed domain-wall valence quarks on themore » $$N_f=2+1+1$$ MILC highly improved staggered quark ensemble with lattice spacing and pion mass of approximately 0.15 fm and 310 MeV respectively. We show full control over excited-state systematics with the new method and obtain a value of $$g_A = 1.213(26)$$ with a quark-mass-dependent renormalization coefficient.« less
Potential-model calculation of an order-v2 nonrelativistic QCD matrix element
NASA Astrophysics Data System (ADS)
Bodwin, Geoffrey T.; Kang, Daekyoung; Lee, Jungil
2006-07-01
We present two methods for computing dimensionally regulated nonrelativistic QCD heavy-quarkonium matrix elements that are related to the second derivative of the heavy-quarkonium wave function at the origin. The first method makes use of a hard-cutoff regulator as an intermediate step and requires knowledge only of the heavy-quarkonium wave function. It involves a significant cancellation that is an obstacle to achieving high numerical accuracy. The second method is more direct and yields a result that is identical to the Gremm-Kapustin relation, but it is limited to use in potential models. It can be generalized to the computation of matrix elements of higher order in the heavy-quark velocity and can be used to resum the contributions to decay and production rates that are associated with those matrix elements. We apply these methods to the Cornell potential model and compute a matrix element for the J/ψ state that appears in the leading relativistic correction to the production and decay of that state through the color-singlet quark-antiquark channel.
Matrix elements and diquark correlations in quenched QCD with overlap fermions.
NASA Astrophysics Data System (ADS)
Rebbi, Claudio
2006-12-01
We present results for BK and selected matrix elements for beyond the standard model interactions obtained in quenched QCD with overlap fermions. We also illustrate results on baryon wave- functions and diquark correlations within baryons in the Coulomb and Landau gauge.
Czader, Arkadiusz; Bittner, Eric R
2008-01-21
Excited states of the double-stranded DNA model (A)12.(T)12 were calculated in the framework of the Frenkel exciton theory. The off-diagonal elements of the exciton matrix were calculated using the transition densities and ideal dipole approximation associated with the lowest energy pipi* excitations of the individual nucleobases as obtained from time-dependent density functional theory calculations. The values of the coupling calculated with the transition density cubes (TDC) and ideal dipole approximation (IDA) methods were found to be significantly different for the small interchromophore distances. It was shown that the IDA overestimates the coupling significantly. The effects of structural fluctuations of the DNA chain on the magnitude of dipolar coupling were also found to be very significant. The difference between the maximum and minimum values was as large as 1000 and 300 cm(-1) for the IDA and TDC methods, respectively. To account for these effects, the properties of the excited states were averaged over a large number of conformations obtained from the molecular dynamics simulations. Our calculations using the TDC method indicate that the absorption of the UV light creates exciton states carrying the majority of the oscillator strength that are delocalized over at least six DNA bases. Upon relaxation, the excitation states localize over at least four contiguous bases.
Effect of element density on the NASTRAN calculated mechanical and thermal stresses of a spar
NASA Technical Reports Server (NTRS)
Jenkins, J. M.
1979-01-01
A NASTRAN model of a spar was examined to determine the sensitivity of calculated axial thermal stresses and bending stresses to changes in element density of the model. The thermal stresses calculated with three different element densities resulted in drastically differing values. The position of the constraint also significantly affected the value of the calculated thermal stresses. Mechanical stresses calculated from an applied loading were insensitive to element density.
Wen, Xiaotong; Rangarajan, Govindan; Ding, Mingzhou
2013-08-28
Granger causality is increasingly being applied to multi-electrode neurophysiological and functional imaging data to characterize directional interactions between neurons and brain regions. For a multivariate dataset, one might be interested in different subsets of the recorded neurons or brain regions. According to the current estimation framework, for each subset, one conducts a separate autoregressive model fitting process, introducing the potential for unwanted variability and uncertainty. In this paper, we propose a multivariate framework for estimating Granger causality. It is based on spectral density matrix factorization and offers the advantage that the estimation of such a matrix needs to be done only once for the entire multivariate dataset. For any subset of recorded data, Granger causality can be calculated through factorizing the appropriate submatrix of the overall spectral density matrix.
Sensitivity of the NMR density matrix to pulse sequence parameters: a simplified analytic approach.
Momot, Konstantin I; Takegoshi, K
2012-08-01
We present a formalism for the analysis of sensitivity of nuclear magnetic resonance pulse sequences to variations of pulse sequence parameters, such as radiofrequency pulses, gradient pulses or evolution delays. The formalism enables the calculation of compact, analytic expressions for the derivatives of the density matrix and the observed signal with respect to the parameters varied. The analysis is based on two constructs computed in the course of modified density-matrix simulations: the error interrogation operators and error commutators. The approach presented is consequently named the Error Commutator Formalism (ECF). It is used to evaluate the sensitivity of the density matrix to parameter variation based on the simulations carried out for the ideal parameters, obviating the need for finite-difference calculations of signal errors. The ECF analysis therefore carries a computational cost comparable to a single density-matrix or product-operator simulation. Its application is illustrated using a number of examples from basic NMR spectroscopy. We show that the strength of the ECF is its ability to provide analytic insights into the propagation of errors through pulse sequences and the behaviour of signal errors under phase cycling. Furthermore, the approach is algorithmic and easily amenable to implementation in the form of a programming code. It is envisaged that it could be incorporated into standard NMR product-operator simulation packages.
Collagen Matrix Density Drives the Metabolic Shift in Breast Cancer Cells.
Morris, Brett A; Burkel, Brian; Ponik, Suzanne M; Fan, Jing; Condeelis, John S; Aguirre-Ghiso, Julio A; Castracane, James; Denu, John M; Keely, Patricia J
2016-11-01
Increased breast density attributed to collagen I deposition is associated with a 4-6 fold increased risk of developing breast cancer. Here, we assessed cellular metabolic reprogramming of mammary carcinoma cells in response to increased collagen matrix density using an in vitro 3D model. Our initial observations demonstrated changes in functional metabolism in both normal mammary epithelial cells and mammary carcinoma cells in response to changes in matrix density. Further, mammary carcinoma cells grown in high density collagen matrices displayed decreased oxygen consumption and glucose metabolism via the tricarboxylic acid (TCA) cycle compared to cells cultured in low density matrices. Despite decreased glucose entry into the TCA cycle, levels of glucose uptake, cell viability, and ROS were not different between high and low density matrices. Interestingly, under high density conditions the contribution of glutamine as a fuel source to drive the TCA cycle was significantly enhanced. These alterations in functional metabolism mirrored significant changes in the expression of metabolic genes involved in glycolysis, oxidative phosphorylation, and the serine synthesis pathway. This study highlights the broad importance of the collagen microenvironment to cellular expression profiles, and shows that changes in density of the collagen microenvironment can modulate metabolic shifts of cancer cells. Copyright Â© 2016 The Authors. Published by Elsevier B.V. All rights reserved.
NASA Astrophysics Data System (ADS)
Angeli, C.; Cimiraglia, R.
2013-02-01
A symbolic program performing the Formal Reduction of Density Operators (FRODO), formerly developed in the MuPAD computer algebra system with the purpose of evaluating the matrix elements of the electronic Hamiltonian between internally contracted functions in a complete active space (CAS) scheme, has been rewritten in Mathematica. New version : A program summaryProgram title: FRODO Catalogue identifier: ADV Y _v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVY_v2_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.: 3878 No. of bytes in distributed program, including test data, etc.: 170729 Distribution format: tar.gz Programming language: Mathematica Computer: Any computer on which the Mathematica computer algebra system can be installed Operating system: Linux Classification: 5 Catalogue identifier of previous version: ADV Y _v1_0 Journal reference of previous version: Comput. Phys. Comm. 171(2005)63 Does the new version supersede the previous version?: No Nature of problem. In order to improve on the CAS-SCF wavefunction one can resort to multireference perturbation theory or configuration interaction based on internally contracted functions (ICFs) which are obtained by application of the excitation operators to the reference CAS-SCF wavefunction. The previous formulation of such matrix elements in the MuPAD computer algebra system, has been rewritten using Mathematica. Solution method: The method adopted consists in successively eliminating all occurrences of inactive orbital indices (core and virtual) from the products of excitation operators which appear in the definition of the ICFs and in the electronic Hamiltonian expressed in the second quantization formalism. Reasons for new version: Some years ago we published in this journal a couple of papers [1, 2
Exact and approximate many-body dynamics with stochastic one-body density matrix evolution
Lacroix, Denis
2005-06-01
We show that the dynamics of interacting fermions can be exactly replaced by a quantum jump theory in the many-body density matrix space. In this theory, jumps occur between densities formed of pairs of Slater determinants, D{sub ab}= vertical bar {phi}{sub a}><{phi}{sub b} vertical bar, where each state evolves according to the stochastic Schroedinger equation given by O. Juillet and Ph. Chomaz [Phys. Rev. Lett. 88, 142503 (2002)]. A stochastic Liouville-von Neumann equation is derived as well as the associated. Bogolyubov-Born-Green-Kirwood-Yvon hierarchy. Due to the specific form of the many-body density along the path, the presented theory is equivalent to a stochastic theory in one-body density matrix space, in which each density matrix evolves according to its own mean-field augmented by a one-body noise. Guided by the exact reformulation, a stochastic mean-field dynamics valid in the weak coupling approximation is proposed. This theory leads to an approximate treatment of two-body effects similar to the extended time-dependent Hartree-Fock scheme. In this stochastic mean-field dynamics, statistical mixing can be directly considered and jumps occur on a coarse-grained time scale. Accordingly, numerical effort is expected to be significantly reduced for applications.
NASA Astrophysics Data System (ADS)
Alborzpour, Jonathan P.; Tew, David P.; Habershon, Scott
2016-11-01
Solution of the time-dependent Schrödinger equation using a linear combination of basis functions, such as Gaussian wavepackets (GWPs), requires costly evaluation of integrals over the entire potential energy surface (PES) of the system. The standard approach, motivated by computational tractability for direct dynamics, is to approximate the PES with a second order Taylor expansion, for example centred at each GWP. In this article, we propose an alternative method for approximating PES matrix elements based on PES interpolation using Gaussian process regression (GPR). Our GPR scheme requires only single-point evaluations of the PES at a limited number of configurations in each time-step; the necessity of performing often-expensive evaluations of the Hessian matrix is completely avoided. In applications to 2-, 5-, and 10-dimensional benchmark models describing a tunnelling coordinate coupled non-linearly to a set of harmonic oscillators, we find that our GPR method results in PES matrix elements for which the average error is, in the best case, two orders-of-magnitude smaller and, in the worst case, directly comparable to that determined by any other Taylor expansion method, without requiring additional PES evaluations or Hessian matrices. Given the computational simplicity of GPR, as well as the opportunities for further refinement of the procedure highlighted herein, we argue that our GPR methodology should replace methods for evaluating PES matrix elements using Taylor expansions in quantum dynamics simulations.
NASA Astrophysics Data System (ADS)
Reby Roy, K. E.; Mohammed, Jesna; Abhiroop, V. M.; Thekkethil, S. R.
2017-02-01
Cryogenic fluids have many applications in space, medicine, preservation etc. The chill-down of cryogenic fluid transfer line is a complicated phenomenon occurring in most of the cryogenic systems. The cryogenic fluid transfer line, which is initially at room temperature, has to be cooled to the temperature of the cryogen as fast as possible. When the cryogenic fluid at liquid state passes along the line, transient heat transfer between the cryogen and the transfer line causes voracious evaporation of the liquid. This paper makes a contribution to the two-phase flow along a rectangular flow passage consisting of an array of elliptically shaped matrix elements. A simplified 2D model is considered and the problem is solved using ANSYS FLUENT. The present analysis aims to study the influence of the slenderness ratio of matrix elements on the heat transfer rate and chill down time. For a comparative study, matrix elements of slenderness ratios 5 and 10 are considered. Liquid nitrogen at 74K flows through the matrix. The material of the transfer line is assumed to be aluminium which is initially at room temperature. The influence of Reynolds numbers from 800 to 3000 on chill-down is also investigated.
Matrix-Assisted Plasma Atomization Emission Spectrometry for Surface Sampling Elemental Analysis
Yuan, Xin; Zhan, Xuefang; Li, Xuemei; Zhao, Zhongjun; Duan, Yixiang
2016-01-01
An innovative technology has been developed involving a simple and sensitive optical spectrometric method termed matrix-assisted plasma atomization emission spectrometry (MAPAES) for surface sampling elemental analysis using a piece of filter paper (FP) for sample introduction. MAPAES was carried out by direct interaction of the plasma tail plume with the matrix surface. The FP absorbs energy from the plasma source and releases combustion heating to the analytes originally present on its surface, thus to promote the atomization and excitation process. The matrix-assisted plasma atomization excitation phenomenon was observed for multiple elements. The FP matrix served as the partial energy producer and also the sample substrate to adsorb sample solution. Qualitative and quantitative determinations of metal ions were achieved by atomic emission measurements for elements Ba, Cu, Eu, In, Mn, Ni, Rh and Y. The detection limits were down to pg level with linear correlation coefficients better than 0.99. The proposed MAPAES provides a new way for atomic spectrometry which offers advantages of fast analysis speed, little sample consumption, less sample pretreatment, small size, and cost-effective. PMID:26762972
Matrix-Assisted Plasma Atomization Emission Spectrometry for Surface Sampling Elemental Analysis.
Yuan, Xin; Zhan, Xuefang; Li, Xuemei; Zhao, Zhongjun; Duan, Yixiang
2016-01-14
An innovative technology has been developed involving a simple and sensitive optical spectrometric method termed matrix-assisted plasma atomization emission spectrometry (MAPAES) for surface sampling elemental analysis using a piece of filter paper (FP) for sample introduction. MAPAES was carried out by direct interaction of the plasma tail plume with the matrix surface. The FP absorbs energy from the plasma source and releases combustion heating to the analytes originally present on its surface, thus to promote the atomization and excitation process. The matrix-assisted plasma atomization excitation phenomenon was observed for multiple elements. The FP matrix served as the partial energy producer and also the sample substrate to adsorb sample solution. Qualitative and quantitative determinations of metal ions were achieved by atomic emission measurements for elements Ba, Cu, Eu, In, Mn, Ni, Rh and Y. The detection limits were down to pg level with linear correlation coefficients better than 0.99. The proposed MAPAES provides a new way for atomic spectrometry which offers advantages of fast analysis speed, little sample consumption, less sample pretreatment, small size, and cost-effective.
$B^0_{(s)}$-mixing matrix elements from lattice QCD for the Standard Model and beyond
Bazavov, A.; Bernard, C.; Bouchard, C. M.; Chang, C. C.; DeTar, C.; Du, Daping; El-Khadra, A. X.; Freeland, E. D.; Gamiz, E.; Gottlieb, Steven; Heller, U. M.; Kronfeld, A. S.; Laiho, J.; Mackenzie, P. B.; Neil, E. T.; Simone, J.; Sugar, R.; Toussaint, D.; Van de Water, R. S.; Zhou, Ran
2016-06-28
We calculate—for the first time in three-flavor lattice QCD—the hadronic matrix elements of all five local operators that contribute to neutral B^{0}- and B_{s}-meson mixing in and beyond the Standard Model. We present a complete error budget for each matrix element and also provide the full set of correlations among the matrix elements. We also present the corresponding bag parameters and their correlations, as well as specific combinations of the mixing matrix elements that enter the expression for the neutral B-meson width difference. We obtain the most precise determination to date of the SU(3)-breaking ratio ξ=1.206(18)(6), where the second error stems from the omission of charm-sea quarks, while the first encompasses all other uncertainties. The threefold reduction in total uncertainty, relative to the 2013 Flavor Lattice Averaging Group results, tightens the constraint from B mixing on the Cabibbo-Kobayashi-Maskawa (CKM) unitarity triangle. Our calculation employs gauge-field ensembles generated by the MILC Collaboration with four lattice spacings and pion masses close to the physical value. We use the asqtad-improved staggered action for the light-valence quarks and the Fermilab method for the bottom quark. We use heavy-light meson chiral perturbation theory modified to include lattice-spacing effects to extrapolate the five matrix elements to the physical point. We combine our results with experimental measurements of the neutral B-meson oscillation frequencies to determine the CKM matrix elements |V_{td}| = 8.00(34)(8)×10^{-3}, |V_{ts}| = 39.0(1.2)(0.4)×10^{-3}, and |V_{td}/V_{ts}| = 0.2052(31)(10), which differ from CKM-unitarity expectations by about 2σ. In addition, these results and others from flavor-changing-neutral currents point towards an emerging tension between weak processes that are mediated at the loop and tree levels.
$$B^0_{(s)}$$-mixing matrix elements from lattice QCD for the Standard Model and beyond
Bazavov, A.; Bernard, C.; Bouchard, C. M.; ...
2016-06-28
We calculate—for the first time in three-flavor lattice QCD—the hadronic matrix elements of all five local operators that contribute to neutral B0- and Bs-meson mixing in and beyond the Standard Model. We present a complete error budget for each matrix element and also provide the full set of correlations among the matrix elements. We also present the corresponding bag parameters and their correlations, as well as specific combinations of the mixing matrix elements that enter the expression for the neutral B-meson width difference. We obtain the most precise determination to date of the SU(3)-breaking ratio ξ=1.206(18)(6), where the second errormore » stems from the omission of charm-sea quarks, while the first encompasses all other uncertainties. The threefold reduction in total uncertainty, relative to the 2013 Flavor Lattice Averaging Group results, tightens the constraint from B mixing on the Cabibbo-Kobayashi-Maskawa (CKM) unitarity triangle. Our calculation employs gauge-field ensembles generated by the MILC Collaboration with four lattice spacings and pion masses close to the physical value. We use the asqtad-improved staggered action for the light-valence quarks and the Fermilab method for the bottom quark. We use heavy-light meson chiral perturbation theory modified to include lattice-spacing effects to extrapolate the five matrix elements to the physical point. We combine our results with experimental measurements of the neutral B-meson oscillation frequencies to determine the CKM matrix elements |Vtd| = 8.00(34)(8)×10-3, |Vts| = 39.0(1.2)(0.4)×10-3, and |Vtd/Vts| = 0.2052(31)(10), which differ from CKM-unitarity expectations by about 2σ. In addition, these results and others from flavor-changing-neutral currents point towards an emerging tension between weak processes that are mediated at the loop and tree levels.« less
$B^0_{(s)}$-mixing matrix elements from lattice QCD for the Standard Model and beyond
Bazavov, A.; Bernard, C.; Bouchard, C. M.; Chang, C. C.; DeTar, C.; Du, Daping; El-Khadra, A. X.; Freeland, E. D.; Gamiz, E.; Gottlieb, Steven; Heller, U. M.; Kronfeld, A. S.; Laiho, J.; Mackenzie, P. B.; Neil, E. T.; Simone, J.; Sugar, R.; Toussaint, D.; Van de Water, R. S.; Zhou, Ran
2016-06-28
We calculate—for the first time in three-flavor lattice QCD—the hadronic matrix elements of all five local operators that contribute to neutral B^{0}- and B_{s}-meson mixing in and beyond the Standard Model. We present a complete error budget for each matrix element and also provide the full set of correlations among the matrix elements. We also present the corresponding bag parameters and their correlations, as well as specific combinations of the mixing matrix elements that enter the expression for the neutral B-meson width difference. We obtain the most precise determination to date of the SU(3)-breaking ratio ξ=1.206(18)(6), where the second error stems from the omission of charm-sea quarks, while the first encompasses all other uncertainties. The threefold reduction in total uncertainty, relative to the 2013 Flavor Lattice Averaging Group results, tightens the constraint from B mixing on the Cabibbo-Kobayashi-Maskawa (CKM) unitarity triangle. Our calculation employs gauge-field ensembles generated by the MILC Collaboration with four lattice spacings and pion masses close to the physical value. We use the asqtad-improved staggered action for the light-valence quarks and the Fermilab method for the bottom quark. We use heavy-light meson chiral perturbation theory modified to include lattice-spacing effects to extrapolate the five matrix elements to the physical point. We combine our results with experimental measurements of the neutral B-meson oscillation frequencies to determine the CKM matrix elements |V_{td}| = 8.00(34)(8)×10^{-3}, |V_{ts}| = 39.0(1.2)(0.4)×10^{-3}, and |V_{td}/V_{ts}| = 0.2052(31)(10), which differ from CKM-unitarity expectations by about 2σ. In addition, these results and others from flavor-changing-neutral currents point towards an emerging tension between weak processes that are mediated at the loop and tree levels.
NASA Astrophysics Data System (ADS)
Möller, Thomas
2016-12-01
General expressions for the matrix elements of the tight-binding operator are presented using the Racah-Wigner algebra, where the wave functions are expressed as coupled multiplet wave functions within a given angular momentum coupling scheme. The knowledge of all possible Slater determinants is not necessary and the matrix elements can be written as compact expressions computable with arbitrary accuracy.
Saitow, Masaaki; Kurashige, Yuki; Yanai, Takeshi
2013-07-28
We report development of the multireference configuration interaction (MRCI) method that can use active space scalable to much larger size references than has previously been possible. The recent development of the density matrix renormalization group (DMRG) method in multireference quantum chemistry offers the ability to describe static correlation in a large active space. The present MRCI method provides a critical correction to the DMRG reference by including high-level dynamic correlation through the CI treatment. When the DMRG and MRCI theories are combined (DMRG-MRCI), the full internal contraction of the reference in the MRCI ansatz, including contraction of semi-internal states, plays a central role. However, it is thought to involve formidable complexity because of the presence of the five-particle rank reduced-density matrix (RDM) in the Hamiltonian matrix elements. To address this complexity, we express the Hamiltonian matrix using commutators, which allows the five-particle rank RDM to be canceled out without any approximation. Then we introduce an approximation to the four-particle rank RDM by using a cumulant reconstruction from lower-particle rank RDMs. A computer-aided approach is employed to derive the exceedingly complex equations of the MRCI in tensor-contracted form and to implement them into an efficient parallel computer code. This approach extends to the size-consistency-corrected variants of MRCI, such as the MRCI+Q, MR-ACPF, and MR-AQCC methods. We demonstrate the capability of the DMRG-MRCI method in several benchmark applications, including the evaluation of single-triplet gap of free-base porphyrin using 24 active orbitals.
NASA Astrophysics Data System (ADS)
Roemelt, Michael
2015-07-01
Spin Orbit Coupling (SOC) is introduced to molecular ab initio density matrix renormalization group (DMRG) calculations. In the presented scheme, one first approximates the electronic ground state and a number of excited states of the Born-Oppenheimer (BO) Hamiltonian with the aid of the DMRG algorithm. Owing to the spin-adaptation of the algorithm, the total spin S is a good quantum number for these states. After the non-relativistic DMRG calculation is finished, all magnetic sublevels of the calculated states are constructed explicitly, and the SOC operator is expanded in the resulting basis. To this end, spin orbit coupled energies and wavefunctions are obtained as eigenvalues and eigenfunctions of the full Hamiltonian matrix which is composed of the SOC operator matrix and the BO Hamiltonian matrix. This treatment corresponds to a quasi-degenerate perturbation theory approach and can be regarded as the molecular equivalent to atomic Russell-Saunders coupling. For the evaluation of SOC matrix elements, the full Breit-Pauli SOC Hamiltonian is approximated by the widely used spin-orbit mean field operator. This operator allows for an efficient use of the second quantized triplet replacement operators that are readily generated during the non-relativistic DMRG algorithm, together with the Wigner-Eckart theorem. With a set of spin-orbit coupled wavefunctions at hand, the molecular g-tensors are calculated following the scheme proposed by Gerloch and McMeeking. It interprets the effective molecular g-values as the slope of the energy difference between the lowest Kramers pair with respect to the strength of the applied magnetic field. Test calculations on a chemically relevant Mo complex demonstrate the capabilities of the presented method.
Roemelt, Michael
2015-07-28
Spin Orbit Coupling (SOC) is introduced to molecular ab initio density matrix renormalization group (DMRG) calculations. In the presented scheme, one first approximates the electronic ground state and a number of excited states of the Born-Oppenheimer (BO) Hamiltonian with the aid of the DMRG algorithm. Owing to the spin-adaptation of the algorithm, the total spin S is a good quantum number for these states. After the non-relativistic DMRG calculation is finished, all magnetic sublevels of the calculated states are constructed explicitly, and the SOC operator is expanded in the resulting basis. To this end, spin orbit coupled energies and wavefunctions are obtained as eigenvalues and eigenfunctions of the full Hamiltonian matrix which is composed of the SOC operator matrix and the BO Hamiltonian matrix. This treatment corresponds to a quasi-degenerate perturbation theory approach and can be regarded as the molecular equivalent to atomic Russell-Saunders coupling. For the evaluation of SOC matrix elements, the full Breit-Pauli SOC Hamiltonian is approximated by the widely used spin-orbit mean field operator. This operator allows for an efficient use of the second quantized triplet replacement operators that are readily generated during the non-relativistic DMRG algorithm, together with the Wigner-Eckart theorem. With a set of spin-orbit coupled wavefunctions at hand, the molecular g-tensors are calculated following the scheme proposed by Gerloch and McMeeking. It interprets the effective molecular g-values as the slope of the energy difference between the lowest Kramers pair with respect to the strength of the applied magnetic field. Test calculations on a chemically relevant Mo complex demonstrate the capabilities of the presented method.
A novel FPGA-programmable switch matrix interconnection element in quantum-dot cellular automata
NASA Astrophysics Data System (ADS)
Hashemi, Sara; Rahimi Azghadi, Mostafa; Zakerolhosseini, Ali; Navi, Keivan
2015-04-01
The Quantum-dot cellular automata (QCA) is a novel nanotechnology, promising extra low-power, extremely dense and very high-speed structure for the construction of logical circuits at a nanoscale. In this paper, initially previous works on QCA-based FPGA's routing elements are investigated, and then an efficient, symmetric and reliable QCA programmable switch matrix (PSM) interconnection element is introduced. This element has a simple structure and offers a complete routing capability. It is implemented using a bottom-up design approach that starts from a dense and high-speed 2:1 multiplexer and utilise it to build the target PSM interconnection element. In this study, simulations of the proposed circuits are carried out using QCAdesigner, a layout and simulation tool for QCA circuits. The results demonstrate high efficiency of the proposed designs in QCA-based FPGA routing.
NASA Technical Reports Server (NTRS)
Buehler, Martin G. (Inventor)
1988-01-01
A set of addressable test structures, each of which uses addressing schemes to access individual elements of the structure in a matrix, is used to test the quality of a wafer before integrated circuits produced thereon are diced, packaged and subjected to final testing. The electrical characteristic of each element is checked and compared to the electrical characteristic of all other like elements in the matrix. The effectiveness of the addressable test matrix is in readily analyzing the electrical characteristics of the test elements and in providing diagnostic information.
NASA Astrophysics Data System (ADS)
Alamanos, N.; Pakou, A.; Lagoyannis, A.; Musumarra, A.
1999-12-01
The determination of ratio of neutron over proton matrix elements by inelastic proton scattering, for 0 +→2 + transitions, is investigated via the comparison between experimental data and theoretical calculations. Calculations into the context of a macroscopic and a microscopic description are performed for a wide mass range nuclei: 18O, 30Si, 32,34S, 48Ca, 88Sr, for which these ratios were determined previously with an independent technique. At that point the choice of the theoretical model may be very critical. It is thus the purpose of this investigation to point out the most suitable model. It is found that in general both theoretical models can be employed for the reliable determination of neutron over proton matrix element ratios.
Banik, Subrata; Pal, Sourav; Prasad, M Durga
2010-10-12
An effective operator approach based on the coupled cluster method is described and applied to calculate vibrational expectation values and absolute transition matrix elements. Coupled cluster linear response theory (CCLRT) is used to calculate excited states. The convergence pattern of these properties with the rank of the excitation operator is studied. The method is applied to a water molecule. Arponen-type double similarity transformation in extended coupled cluster (ECCM) framework is also used to generate an effective operator, and the convergence pattern of these properties is compared to the normal coupled cluster (NCCM) approach. It is found that the coupled cluster method provides an accurate description of these quantities for low lying vibrational excited states. The ECCM provides a significant improvement for the calculation of the transition matrix elements.
Short-distance matrix elements for $D$-meson mixing for 2+1 lattice QCD
Chang, Chia Cheng
2015-01-01
We study the short-distance hadronic matrix elements for D-meson mixing with partially quenched N_{f} = 2+1 lattice QCD. We use a large set of the MIMD Lattice Computation Collaboration's gauge configurations with a^{2} tadpole-improved staggered sea quarks and tadpole-improved Lüscher-Weisz gluons. We use the a^{2} tadpole-improved action for valence light quarks and the Sheikoleslami-Wohlert action with the Fermilab interpretation for the valence charm quark. Our calculation covers the complete set of five operators needed to constrain new physics models for D-meson mixing. We match our matrix elements to the MS-NDR scheme evaluated at 3 GeV. We report values for the Beneke-Buchalla-Greub-Lenz-Nierste choice of evanescent operators.
Kinetic-energy matrix elements for atomic Hylleraas-CI wave functions.
Harris, Frank E
2016-05-28
Hylleraas-CI is a superposition-of-configurations method in which each configuration is constructed from a Slater-type orbital (STO) product to which is appended (linearly) at most one interelectron distance rij. Computations of the kinetic energy for atoms by this method have been difficult due to the lack of formulas expressing these matrix elements for general angular momentum in terms of overlap and potential-energy integrals. It is shown here that a strategic application of angular-momentum theory, including the use of vector spherical harmonics, enables the reduction of all atomic kinetic-energy integrals to overlap and potential-energy matrix elements. The new formulas are validated by showing that they yield correct results for a large number of integrals published by other investigators.
NASA Technical Reports Server (NTRS)
Caruso, J. J.; Trowbridge, D.; Chamis, C. C.
1989-01-01
The mechanics of materials approach (definition of E, G, Nu, and Alpha) and the finite element method are used to explore the effects of partial bonding and fiber fracture on the behavior of high temperature metal matrix composites. Composite ply properties are calculated for various degrees of disbonding to evaluate the sensitivity of these properties to the presence of fiber/matrix disbonding and fiber fracture. The mechanics of materials approach allows for the determination of the basic ply material properties needed for design/analysis of composites. The finite element method provides the necessary structural response (forces and displacements) for the mechanics of materials equations. Results show that disbonding of fractured fibers affect only E sub (111) and alpha sub (111) significantly.
Nuclear matrix elements of the double beta decay for mass around 80
NASA Astrophysics Data System (ADS)
Yoshinaga, Naotaka; Higashiyama, Koji; Teruya, Eri
2014-09-01
In nature there are 30 kinds of nuclei which are expected to have double beta decays. Among them ten nuclei are actually observed for the neutrino double beta decays. Still no observation is made for the neutrinoless double beta decays (0 νββ) . The 0 νββ decay is expected to occur only when neutrinos have masses and they are Majorana particles. In that respect observation of 0 νββ is to determine whether neutrinos are Majorana particles or not. In theoretical side in order to estimate the half life of 0 νββ determination of the nuclear matrix elements are essential. They were calculated in many theoretical frameworks, but the results are not consistent in various models. In this study we carry out shell model calculations for 82Se and 82Kr nuclei. After obtaining the wavefunctions, we calculate the nuclear matrix elements. For comparison we make pair truncated shell model calculations.
Charge-independent trend of isoscalar matrix elements along the N˜Z line
NASA Astrophysics Data System (ADS)
Orce, J. N.; Velázquez, V.
2006-01-01
Shell model calculations have been carried out using the m-scheme numerical code ANTOINE in order to elucidate the particular trend of the isoscalar matrix elements, M, for A=4n+2 isobaric triplets ranging from A=18 to A=42. The 21+(T=1)→01+(T=1) transition energies, reduced transition probabilities and isoscalar matrix elements are predicted to a high degree of accuracy. The general agreement of M between those from mirror pairs and those from T=0 nuclides support our shell model calculations. The predicted results tie together recent experimental data, and the trend of M strength along the sd and beginning of the fp shells is interpreted in terms of the dynamic shell structure. Certain discrepancies arise at A=18 and A=38 isobaric triplets, which might be explained in terms of core polarization effects and the low occupancy of the orbits at the extremes of the sd shell.
Study of matrix crack-tilted fiber bundle interaction using caustics and finite element method.
Hao, Wenfeng; Zhu, Jianguo; Zhu, Qi; Yuan, Yanan
2016-02-01
In this work, the interaction between the matrix crack and a tilted fiber bundle was investigated via caustics and the finite element method (FEM). First, the caustic patterns at the crack tip with different distances from the tilted fiber were obtained and the stress intensity factors were extracted from the geometry of the caustic patterns. Subsequently, the shielding effect of the fiber bundle in front of the crack tip was analyzed. Furthermore, the interaction between the matrix crack and the broken fiber bundle was discussed. Finally, a finite element simulation was carried out using ABAQUS to verify the experimental results. The results demonstrate that the stress intensity factors extracted from caustic experiments are in excellent agreement with the data calculated by FEM.
NASA Astrophysics Data System (ADS)
Nemes, Csaba; Barcza, Gergely; Nagy, Zoltán; Legeza, Örs; Szolgay, Péter
2014-06-01
In the numerical analysis of strongly correlated quantum lattice models one of the leading algorithms developed to balance the size of the effective Hilbert space and the accuracy of the simulation is the density matrix renormalization group (DMRG) algorithm, in which the run-time is dominated by the iterative diagonalization of the Hamilton operator. As the most time-dominant step of the diagonalization can be expressed as a list of dense matrix operations, the DMRG is an appealing candidate to fully utilize the computing power residing in novel kilo-processor architectures. In the paper a smart hybrid CPU-GPU implementation is presented, which exploits the power of both CPU and GPU and tolerates problems exceeding the GPU memory size. Furthermore, a new CUDA kernel has been designed for asymmetric matrix-vector multiplication to accelerate the rest of the diagonalization. Besides the evaluation of the GPU implementation, the practical limits of an FPGA implementation are also discussed.
NASA Astrophysics Data System (ADS)
Sarkadi, L.
2017-03-01
The program MTRDCOUL [1] calculates the matrix elements of the Coulomb interaction between a charged particle and an atomic electron, ∫ ψf∗ (r) ∣ R - r∣-1ψi(r) d r. Bound-free transitions are considered, and relativistic hydrogenic wave functions are used. In this revised version a bug discovered in the F3Y CPC Program Library subprogram [2] is fixed.
Determination of electric-dipole matrix elements in K and Rb from Stark shift measurements
Arora, Bindiya; Safronova, M. S.; Clark, Charles W.
2007-11-15
Stark shifts of potassium and rubidium D1 lines have been measured with high precision by Miller et al. [Phys. Rev. A 49, 5128 (1994)]. In this work, we combine these measurements with our all-order calculations to determine the values of the electric-dipole matrix elements for the 4p{sub j}-3d{sub j{sup '}} transitions in K and the 5p{sub j}-4d{sub j{sup '}} transitions in Rb to high precision. The 4p{sub 1/2}-3d{sub 3/2} and 5p{sub 1/2}-4d{sub 3/2} transitions contribute on the order of 90% to the respective polarizabilities of the np{sub 1/2} states in K and Rb, and the remaining 10% can be accurately calculated using the relativistic all-order method. Therefore, the combination of the experimental data and theoretical calculations allows us to determine the np-(n-1)d matrix elements and their uncertainties. We compare these values with our all-order calculations of the np-(n-1)d matrix elements in K and Rb for a benchmark test of the accuracy of the all-order method for transitions involving nd states. Such matrix elements are of special interest for many applications, such as determination of ''magic'' wavelengths in alkali-metal atoms for state-insensitive cooling and trapping, and determination of blackbody radiation shifts in optical frequency standards with ions.
NASA Astrophysics Data System (ADS)
Ablinger, J.; Blümlein, J.; De Freitas, A.; Hasselhuhn, A.; Schneider, C.; Wißbrock, F.
2017-08-01
Starting at 3-loop order, the massive Wilson coefficients for deep-inelastic scattering and the massive operator matrix elements describing the variable flavor number scheme receive contributions of Feynman diagrams carrying quark lines with two different masses. In the case of the charm and bottom quarks, the usual decoupling of one heavy mass at a time no longer holds, since the ratio of the respective masses, η = mc2/mb2 ∼ 1 / 10, is not small enough. Therefore, the usual variable flavor number scheme (VFNS) has to be generalized. The renormalization procedure in the two-mass case is different from the single mass case derived in [1]. We present the moments N = 2 , 4 and 6 for all contributing operator matrix elements, expanding in the ratio η. We calculate the analytic results for general values of the Mellin variable N in the flavor non-singlet case, as well as for transversity and the matrix element Agq(3). We also calculate the two-mass scalar integrals of all topologies contributing to the gluonic operator matrix element Agg. As it turns out, the expansion in η is usually inapplicable for general values of N. We therefore derive the result for general values of the mass ratio. From the single pole terms we derive, now in a two-mass calculation, the corresponding contributions to the 3-loop anomalous dimensions. We introduce a new general class of iterated integrals and study their relations and present special values. The corresponding functions are implemented in computer-algebraic form.
Nuclear Matrix Elements for two-neutrino DBD in Te isotopes
Bes, D. R.; Civitarese, O.
2009-11-09
Theoretical matrix elements, for the ground-state to ground-state two-neutrino double-beta-decay mode of {sup 128,130}Te isotopes, are calculated within a formalism which describes interactions between neutrons in a superfluid phase and protons in a normal phase. The model is basically a parameter-free one, since all relevant parameters are fixed from phenomenology. A comparison with the available experimental data is presented.
Measuring the CKM matrix element V{sub tb} at D-zero and CDF
Heinson, A.P.
1997-07-01
I present measurements by the CDF collaboration of the Standard Model three generation CKM matrix element V{sub tb} and of a special case extension with additional assumptions, using current Tevatron t{anti t} data. I then show how we can significantly improve the precision on V{sub tb} and at the same time extend the measurement so it is not constrained by Standard Model assumptions, using single top production at the upgraded Tevatron.
D'Ariano, G M; Lo Presti, P
2001-05-07
Quantum operations describe any state change allowed in quantum mechanics, including the evolution of an open system or the state change due to a measurement. We present a general method based on quantum tomography for measuring experimentally the matrix elements of an arbitrary quantum operation. As input the method needs only a single entangled state. The feasibility of the technique for the electromagnetic field is shown, and the experimental setup is illustrated based on homodyne tomography of a twin beam.
An improved method for extracting matrix elements from lattice three-point functions
C. Aubin, K. Orginos
2011-12-01
The extraction of matrix elements from baryon three-point functions is complicated by the fact that the signal-to-noise drops rapidly as a function of time. Using a previously discussed method to improve the signal-to-noise for lattice two-point functions, we use this technique to do so for lattice three-point functions, using electromagnetic form factors for the nucleon and Delta as an example.
Useful extremum principle for the variational calculation of matrix elements. II
NASA Technical Reports Server (NTRS)
Gerjuoy, E.; Rosenberg, L.; Spruch, L.
1975-01-01
Recent work (Gerjuoy et al., 1974) on variational principles for diagonal bound state matrix elements of arbitrary Hermitian operators is extended. In particular, it is shown that the previously derived minimum principle for the trial auxiliary function appearing in such variational principles can be constructed using a modified Hamiltonian possessing not heretofore recognized positive definite properties. Thus there is at least one alternative to the particular modified Hamiltonian on which the results of Gerjuoy et al. (1974) originally were based.
Useful extremum principle for the variational calculation of matrix elements. II
NASA Technical Reports Server (NTRS)
Gerjuoy, E.; Rosenberg, L.; Spruch, L.
1975-01-01
Recent work (Gerjuoy et al., 1974) on variational principles for diagonal bound state matrix elements of arbitrary Hermitian operators is extended. In particular, it is shown that the previously derived minimum principle for the trial auxiliary function appearing in such variational principles can be constructed using a modified Hamiltonian possessing not heretofore recognized positive definite properties. Thus there is at least one alternative to the particular modified Hamiltonian on which the results of Gerjuoy et al. (1974) originally were based.
NASA Astrophysics Data System (ADS)
Liang, Wenkel; Isborn, Christine M.; Li, Xiaosong
2009-11-01
The calculation of doubly excited states is one of the major problems plaguing the modern day excited state workhorse methodology of linear response time dependent Hartree-Fock (TDHF) and density function theory (TDDFT). We have previously shown that the use of a resonantly tuned field within real-time TDHF and TDDFT is able to simultaneously excite both the α and β electrons to achieve the two-electron excited states of minimal basis H2 and HeH+ [C. M. Isborn and X. Li, J. Chem. Phys. 129, 204107 (2008)]. We now extend this method to many electron systems with the use of our Car-Parrinello density matrix search (CP-DMS) with a first-principles fictitious mass method for wave function optimization [X. Li, C. L. Moss, W. Liang, and Y. Feng, J. Chem. Phys. 130, 234115 (2009)]. Real-time TDHF/TDDFT is used during the application of the laser field perturbation, driving the electron density toward the doubly excited state. The CP-DMS method then converges the density to the nearest stationary state. We present these stationary state doubly excited state energies and properties at the HF and DFT levels for H2, HeH+, lithium hydride, ethylene, and butadiene.
NASA Astrophysics Data System (ADS)
Günay, E.
2017-02-01
This study defined as micromechanical finite element (FE) approach examining the stress transfer mechanism in single-walled carbon nanotube (SWCN) reinforced composites. In the modeling, 3D unit-cell method was evaluated. Carbon nanotube reinforced composites were modeled as three layers which comprises CNT, interface and matrix material. Firstly; matrix, fiber and interfacial materials all together considered as three layered cylindrical nanocomposite. Secondly, the cylindrical matrix material was assumed to be isotropic and also considered as a continuous medium. Then, fiber material was represented with zigzag type SWCNs. Finally, SWCN was combined with the elastic medium by using springs with different constants. In the FE modeling of SWCN reinforced composite model springs were modeled by using ANSYS spring damper element COMBIN14. The developed interfacial van der Waals interaction effects between the continuous matrix layer and the carbon nanotube fiber layer were simulated by applying these various spring stiffness values. In this study, the layered composite cylindrical FE model was presented as the equivalent mechanical properties of SWCN structures in terms of Young's modulus. The obtained results and literature values were presented and discussed. Figures, 16, 17, and 18 of the original article PDF file, as supplied to AIP Publishing, were affected by a PDF-processing error. Consequently, a solid diamond symbol appeared instead of a Greek tau on the y axis labels for these three figures. This article was updated on 17 March 2017 to correct the PDF-processing error, with the scientific content remaining unchanged.
Adaptive Finite Element Method for Solving the Exact Kohn-Sham Equation of Density Functional Theory
Bylaska, Eric J.; Holst, Michael; Weare, John H.
2009-04-14
Results of the application of an adaptive finite element (FE) based solution using the FETK library of M. Holst to Density Functional Theory (DFT) approximation to the electronic structure of atoms and molecules are reported. The severe problem associated with the rapid variation of the electronic wave functions in the near singular regions of the atomic centers is treated by implementing completely unstructured simplex meshes that resolve these features around atomic nuclei. This concentrates the computational work in the regions in which the shortest length scales are necessary and provides for low resolution in regions for which there is no electron density. The accuracy of the solutions significantly improved when adaptive mesh refinement was applied, and it was found that the essential difficulties of the Kohn-Sham eigenvalues equation were the result of the singular behavior of the atomic potentials. Even though the matrix representations of the discrete Hamiltonian operator in the adaptive finite element basis are always sparse with a linear complexity in the number of discretization points, the overall memory and computational requirements for the solver implemented were found to be quite high. The number of mesh vertices per atom as a function of the atomic number Z and the required accuracy e (in atomic units) was esitmated to be v (e;Z) = 122:37 * Z2:2346 /1:1173 , and the number of floating point operations per minimization step for a system of NA atoms was found to be 0(N3A*v(e,Z0) (e.g. Z=26, e=0.0015 au, and NA=100, the memory requirement and computational cost would be ~0.2 terabytes and ~25 petaflops). It was found that the high cost of the method could be reduced somewhat by using a geometric based refinement strategy to fix the error near the singularities.
The "JK-only" approximation in density matrix functional and wave function theory.
Kollmar, Christian
2004-12-15
Various energy functionals applying the "JK-only" approximation which leads to two-index two-electron integrals instead of four-index two-electron integrals in the electron-electron interaction term of the electronic energy are presented. Numerical results of multiconfiguration self-consistent field calculations for the best possible "JK-only" wave function are compared to those obtained from the pair excitation multiconfiguration self-consistent (PEMCSCF) method and two versions of density matrix functional theory. One of these is derived making explicit use of some necessary conditions for N representability of the second-order density matrix. It is shown that this method models the energy functional based on the best possible "JK-only" wave function with good accuracy. The calculations also indicate that only a minor fraction of the total correlation energy is incorporated by "JK-only" approaches for larger molecules.
NASA Astrophysics Data System (ADS)
Yanai, Takeshi; Kurashige, Yuki; Neuscamman, Eric; Chan, Garnet Kin-Lic
2010-01-01
We describe the joint application of the density matrix renormalization group and canonical transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the canonical transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, (i) total correlation energies in long polyenes and (ii) the isomerization curve of the [Cu2O2]2+ core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a (24e,24o) active space and 268 atomic orbitals in the polyenes and a (28e,32o) active space and 278 atomic orbitals in [Cu2O2]2+.
NASA Astrophysics Data System (ADS)
Kanazawa, Takuya; Wettig, Tilo
2014-10-01
We generalize QCD at asymptotically large isospin chemical potential to an arbitrary even number of flavors. We also allow for small quark chemical potentials, which stress the coincident Fermi surfaces of the paired quarks and lead to a sign problem in Monte Carlo simulations. We derive the corresponding low-energy effective theory in both p- and ɛ-expansion and quantify the severity of the sign problem. We construct the random matrix theory describing our physical situation and show that it can be mapped to a known random matrix theory at low baryon density so that new insights can be gained without additional calculations. In particular, we explain the Silver Blaze phenomenon at high isospin density. We also introduce stressed singular values of the Dirac operator and relate them to the pionic condensate. Finally we comment on extensions of our work to two-color QCD.
Matrix effects for elemental fractionation within ICPMS: applications for U-Th-Pb geochronology
NASA Astrophysics Data System (ADS)
Chen, W.
2016-12-01
Recent development in instruments provides significant technical supports for daily, quick, money saving geochemical analyses. Laser ablation ICPMS stands out due to these reasons, especially for the U-Th-Pb isotopic dating. Matrix-matched external standardization is by far the most common approach used in U-Th-Pb dating via LA-ICPMS. However, matrix-effects between standard and sample for in-situ dating have shown to be both significant and insignificant. It remains mysterious whether a well matrix-matched standard is needed for U-Th-Pb dating by LA-ICPMS. This study provides an experimental framework for the understanding of matrix effects induced elemental fractionation for U-Th-Pb associated with ICPMS. A preliminary study on the influence of varied U, Th and Pb amounts on their fractionations has been carried out. Experimental data show that different U, Th and Pb contents result in varied 238U/206Pb and 232Th/208Pb ratios. The fractionations of U/Pb and Th/Pb increase with the increasing contents (1 ppb to 100 ppb) with a strong positive anomaly at 10 ppb. Matrixes representing minerals frequently used in dating have been investigated for the influences on U/Pb and Th/Pb fractionations, which suggest a complicated effect. Little fractionations observed between mineral pairs (e.g., monazite and apatite; zircon and perovskite; rutile and perovskite; xenotime and baddeleyite), whereas large fractionations identified for other minerals (e.g., zircon and baddeleyite; monazite and sphene; rutile and baddeleyite). Single element matrix (i.e., Si, P, Ca, Zr, Ti) has been studied to identify their effects on the fractionations. U/Pb ratio increases with the increasing Si and P contents, whereas it decreases for Zr, Ca and Ti. Th/Pb ratio increases with increasing Si contents, decreases for P and Zr, and increases first then decreases for Ca and Ti. Above all, different matrix and U, Th and Pb amounts show distinct U/Pb and Th/Pb fractionations within ICPMS. The
MOON for neutrino-less ββ decays and ββ nuclear matrix elements
NASA Astrophysics Data System (ADS)
Ejiri, H.
2009-11-01
The MOON project aims at spectroscopic 0vββ studies with the v-mass sensitivity of 100-30 meV by measuring two beta rays from 100Mo and/or 82Se. The detector is a compact super-module of multi-layer PL scintillator plates. R&D works made by the pro to-type MOON-1 and the small PL plate show the possible energy resolution of around σ~2.2%, as required for the mass sensitivity. Nuclear matrix elements M2v for 2vββ are shown to be given by the sum ΣLMk of the 2vββ matrix elements Mk through intermediate quasi-particle states in the Fermi-surface, where Mi is obtained experimentally by using the GT(Jπ = 1+) matrix elements of Mi(k) and Mf(k) for the successive single-β transitions through the k-th intermediate state.
Matrix element method at next-to-leading order for arbitrary jet algorithms
NASA Astrophysics Data System (ADS)
Baumeister, Robin; Weinzierl, Stefan
2017-02-01
The matrix element method usually employs leading-order matrix elements. We discuss the generalization towards higher orders in perturbation theory and show how the matrix element method can be used at next-to-leading order for arbitrary infrared-safe jet algorithms. We discuss three variants at next-to-leading order. The first two variants work at the level of the jet momenta. The first variant adheres to strict fixed order in perturbation theory. We present a method for the required integration over the radiation phase space. The second variant is inspired by the POWHEG method and works as the first variant at the level of the jet momenta. The third variant is a more exclusive POWHEG version. Here we resolve exactly one jet into two subjets. If the two subjets are resolved above a scale p⊥min, the likelihood is computed from the POWHEG-modified real emission part, otherwise it is given by the POWHEG-modified virtual part.
MOON for neutrino-less {beta}{beta} decays and {beta}{beta} nuclear matrix elements
Ejiri, H.
2009-11-09
The MOON project aims at spectroscopic 0v{beta}{beta} studies with the v-mass sensitivity of 100-30 meV by measuring two beta rays from {sup 100}Mo and/or {sup 82}Se. The detector is a compact super-module of multi-layer PL scintillator plates. R and D works made by the pro to-type MOON-1 and the small PL plate show the possible energy resolution of around {sigma}{approx}2.2%, as required for the mass sensitivity. Nuclear matrix elements M{sup 2v} for 2v{beta}{beta} are shown to be given by the sum {sigma}{sub L}M{sub k} of the 2v{beta}{beta} matrix elements M{sub k} through intermediate quasi-particle states in the Fermi-surface, where Mi is obtained experimentally by using the GT(J{sup {pi}} = 1{sup +}) matrix elements of M{sub i}(k) and M{sub f}(k) for the successive single-{beta} transitions through the k-th intermediate state.
van der Spoel, D; Berendsen, H J
1996-01-01
In this work we give an overview of the methodologies required to compute the rate of proton transfer in hydrogen bonded systems in solution. Using ab initio or density functional methods we determine proton potentials of a truncated system as a function of proton-donor proton-acceptor distance as well as nonbonding parameters. By classical molecular dynamics we evaluate a swarm of proton potentials with the proton fixed in the reactant well. The rate of proton transfer is calculated perturbatively using the Density Matrix Evolution (DME) method, going beyond the Born Oppenheimer approximation. The method is illustrated by two examples: hydrogen malonate and the active center of HIV-1 protease.
Testing the density matrix expansion against ab initio calculations of trapped neutron drops
Bogner, S. K.; Hergert, H.; Furnstahl, R. J.; Kortelainen, Erno M; Stoitsov, M. V.; Maris, Pieter; Vary, J. P.
2011-01-01
Microscopic input to a universal nuclear energy density functional can be provided through the density matrix expansion (DME), which has recently been revived and improved. Several DME implementation strategies are tested for neutron drop systems in harmonic traps by comparing to Hartree-Fock (HF) and ab initio no-core full configuration (NCFC) calculations with a model interaction (Minnesota potential). The new DME with exact treatment of Hartree contributions is found to best reproduce HF results and supplementing the functional with fit Skyrme-like contact terms shows systematic improvement toward the full NCFC results.
Derivation of the density matrix of a single photon produced in parametric down-conversion
Kolenderski, Piotr; Wasilewski, Wojciech
2009-07-15
We discuss an effective numerical method of density matrix determination of fiber coupled single photon generated in process of spontaneous parametric down conversion in type I noncollinear configuration. The presented theory has been successfully applied in case of source utilized to demonstrate the experimental characterization of spectral state of single photon, what was reported in Wasilewski, Kolenderski, and Frankowski [Phys. Rev. Lett. 99, 123601 (2007)].
Matrix density effects on the mechanical properties of SiC/RBSN composites
NASA Technical Reports Server (NTRS)
Bhatt, Ramakrishna T.; Kiser, James D.
1990-01-01
The room temperature mechanical properties were measured for SiC fiber reinforced reaction-bonded silicon nitride composites (SiC/RBSN) of different densities. The composites consisted of approx. 30 vol percent uniaxially aligned 142 micron diameter SiC fibers (Textron SCS-6) in a reaction-bonded Si3N4 matrix. The composite density was varied by changing the consolidation pressure during RBSN processing and by hot isostatically pressing the SiC/RBSN composites. Results indicate that as the consolidation pressure was increased from 27 to 138 MPa, the average pore size of the nitrided composites decreased from 0.04 to 0.02 microns and the composite density increased from 2.07 to 2.45 gm/cc. Nonetheless, these improvements resulted in only small increases in the first matrix cracking stress, primary elastic modulus, and ultimate tensile strength values of the composites. In contrast, HIP consolidation of SiC/RBSN resulted in a fully dense material whose first matrix cracking stress and elastic modulus were approx. 15 and 50 percent higher, respectively, and ultimate tensile strength values were approx. 40 percent lower than those for unHIPed SiC/RBSN composites. The modulus behavior for all specimens can be explained by simple rule-of-mixture theory. Also, the loss in ultimate strength for the HIPed composites appears to be related to a degradation in fiber strength at the HIP temperature. However, the density effect on matrix fracture strength was much less than would be expected based on typical monolithic Si3N4 behavior, suggesting that composite theory is indeed operating. Possible practical implications of these observations are discussed.
Density-matrix method applied to mode coupling in lenslike fibers
NASA Astrophysics Data System (ADS)
Maeda, K.; Hamasaki, J.
1980-04-01
Mode conversion due to random refractive-index fluctuations of a lossless multimode waveguide is considered. An equation of motion for an average density matrix, which describes wave phenomena in statistically identical waveguides is derived. This equation includes the coupled power equation given by Marcuse, and also describes evolution of correlations between propagating modes. Using this equation, mode-conversion characteristics among degenerate modes in a lenslike fiber are obtained for several correlation lengths and variances of the refractive-index fluctuations.
Huo, Pengfei; Coker, David F
2012-12-14
Powerful approximate methods for propagating the density matrix of complex systems that are conveniently described in terms of electronic subsystem states and nuclear degrees of freedom have recently been developed that involve linearizing the density matrix propagator in the difference between the forward and backward paths of the nuclear degrees of freedom while keeping the interference effects between the different forward and backward paths of the electronic subsystem described in terms of the mapping Hamiltonian formalism and semi-classical mechanics. Here we demonstrate that different approaches to developing the linearized approximation to the density matrix propagator can yield a mean-field like approximate propagator in which the nuclear variables evolve classically subject to Ehrenfest-like forces that involve an average over quantum subsystem states, and by adopting an alternative approach to linearizing we obtain an algorithm that involves classical like nuclear dynamics influenced by a quantum subsystem state dependent force reminiscent of trajectory surface hopping methods. We show how these different short time approximations can be implemented iteratively to achieve accurate, stable long time propagation and explore their implementation in different representations. The merits of the different approximate quantum dynamics methods that are thus consistently derived from the density matrix propagator starting point and different partial linearization approximations are explored in various model system studies of multi-state scattering problems and dissipative non-adiabatic relaxation in condensed phase environments that demonstrate the capabilities of these different types of approximations for treating non-adiabatic electronic relaxation, bifurcation of nuclear distributions, and the passage from nonequilibrium coherent dynamics at short times to long time thermal equilibration in the presence of a model dissipative environment.
NASA Astrophysics Data System (ADS)
Thorvaldsen, Andreas J.; Ruud, Kenneth; Kristensen, Kasper; Jørgensen, Poul; Coriani, Sonia
2008-12-01
A general method is presented for the calculation of molecular properties to arbitrary order at the Kohn-Sham density functional level of theory. The quasienergy and Lagrangian formalisms are combined to derive response functions and their residues by straightforward differentiation of the quasienergy derivative Lagrangian using the elements of the density matrix in the atomic orbital representation as variational parameters. Response functions and response equations are expressed in the atomic orbital basis, allowing recent advances in the field of linear-scaling methodology to be used. Time-dependent and static perturbations are treated on an equal footing, and atomic basis sets that depend on the applied frequency-dependent perturbations may be used, e.g., frequency-dependent London atomic orbitals. The 2n+1 rule may be applied if computationally favorable, but alternative formulations using higher-order perturbed density matrices are also derived. These may be advantageous in order to minimize the number of response equations that needs to be solved, for instance, when one of the perturbations has many components, as is the case for the first-order geometrical derivative of the hyperpolarizability.
Effective field theory during inflation: Reduced density matrix and its quantum master equation
NASA Astrophysics Data System (ADS)
Boyanovsky, D.
2015-07-01
We study the power spectrum of super-Hubble fluctuations of an inflatonlike scalar field, the "system," coupled to another scalar field, the "environment" during de Sitter inflation. We obtain the reduced density matrix for the inflaton fluctuations by integrating out the environmental degrees of freedom. These are considered to be massless and conformally coupled to gravity as a proxy to describe degrees of freedom that remain sub-Hubble all throughout inflation. The time evolution of the density matrix is described by a quantum master equation, which describes the decay of the vacuum state, the production of particles and correlated pairs and quantum entanglement between super and sub-Hubble degrees of freedom. The quantum master equation provides a nonperturbative resummation of secular terms from self-energy (loop) corrections to the inflaton fluctuations. In the case studied here these are Sudakov-type double logarithms which result in the decay of the power spectrum of inflaton fluctuations upon horizon crossing with a concomitant violation of scale invariance. The reduced density matrix and its quantum master equation furnish a powerful nonperturbative framework to study the effective field theory of long wavelength fluctuations by tracing short wavelength degrees of freedom.
NASA Astrophysics Data System (ADS)
Saini, Anshul; Stojkovic, Dejan
2016-09-01
We study time-dependent Hawking-like radiation as seen by an infalling observer during gravitational collapse of a thin shell. We calculate the occupation number of particles of which the frequencies are measured in the proper time of an infalling observer in Eddington-Finkelstein coordinates. We solve the equations for the whole process from the beginning of the collapse till the moment when the collapsing shell reaches zero radius. The radiation distribution is not thermal in the whole frequency regime, but it is approximately thermal for the wavelengths of the order of the Schwarzschild radius of the collapsing shell. After the Schwarzschild radius is crossed, the temperature increases without limits as the singularity is approached. We also calculate the density matrix associated with this radiation. It turns out that the off-diagonal correlation terms to the diagonal Hawking leading-order terms are very important. While the trace of the diagonal (Hawking) density matrix squared decreases during the evolution, the trace of the total density matrix squared remains unity at all times and all frequencies.
Urinary stones as a novel matrix for human biomonitoring of toxic and essential elements.
Kuta, J; Smetanová, S; Benová, D; Kořistková, T; Machát, J
2016-02-01
Monitoring of body burden of toxic elements is usually based on analysis of concentration of particular elements in blood, urine and/or hair. Analysis of these matrices, however, predominantly reflects short- or medium-term exposure to trace elements or pollutants. In this work, urinary stones were investigated as a matrix for monitoring long-term exposure to toxic and essential elements. A total of 431 samples of urinary calculi were subjected to mineralogical and elemental analysis by infrared spectroscopy and inductively coupled plasma mass spectrometry. The effect of mineralogical composition of the stones and other parameters such as sex, age and geographical location on contents of trace and minor elements is presented. Our results demonstrate the applicability of such approach and confirm that the analysis of urinary calculi can be helpful in providing complementary information on human exposure to trace metals and their excretion. Analysis of whewellite stones (calcium oxalate monohydrate) with content of phosphorus <0.6 % has been proved to be a promising tool for biomonitoring of trace and minor elements.
Stoitsov, M. V.; Kortelainen, Erno M; Bogner, S. K.; Duguet, T.; Furnstahl, R. J.; Gebremariam, B.; Schunck, N.
2010-01-01
In a recent series of papers, Gebremariam, Bogner, and Duguet derived a microscopically-based nuclear energy density functional by applying the Density Matrix Expansion (DME) to the Hartree-Fock energy obtained from chiral effective field theory (EFT) two- and three-nucleon interactions. Due to the structure of the chiral interactions, each coupling in the DME functional is given as the sum of a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the finite-range pion exchanges. Since the contact contributions have essentially the same structure as those entering empirical Skyrme functionals, a microscopically guided Skyrme phenomenology has been suggested in which the contact terms in the DME functional are released for optimization to finite-density observables to capture short-range correlation energy contributions from beyond Hartree-Fock. The present paper is the first attempt to assess the ability of the newly suggested DME functional, which has a much richer set of density dependencies than traditional Skyrme functionals, to generate sensible and stable results for nuclear applications. The results of the first proof-of-principle calculations are given, and numerous practical issues related to the implementation of the new functional in existing Skyrme codes are discussed. Using a restricted singular value decomposition (SVD) optimization procedure, it is found that the new DME functional gives numerically stable results and exhibits a small but systematic reduction in {chi}^{2} compared to standard Skyrme functionals, thus justifying its suitability for future global optimizations and large-scale calculations.
Stoitsov, M.; Kortelainen, M.; Schunck, N.; Bogner, S. K.; Gebremariam, B.; Duguet, T.
2010-11-15
In a recent series of articles, Gebremariam, Bogner, and Duguet derived a microscopically based nuclear energy density functional by applying the density matrix expansion (DME) to the Hartree-Fock energy obtained from chiral effective field theory two- and three-nucleon interactions. Owing to the structure of the chiral interactions, each coupling in the DME functional is given as the sum of a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the finite-range pion exchanges. Because the contact contributions have essentially the same structure as those entering empirical Skyrme functionals, a microscopically guided Skyrme phenomenology has been suggested in which the contact terms in the DME functional are released for optimization to finite-density observables to capture short-range correlation energy contributions from beyond Hartree-Fock. The present article is the first attempt to assess the ability of the newly suggested DME functional, which has a much richer set of density dependencies than traditional Skyrme functionals, to generate sensible and stable results for nuclear applications. The results of the first proof-of-principle calculations are given, and numerous practical issues related to the implementation of the new functional in existing Skyrme codes are discussed. Using a restricted singular value decomposition optimization procedure, it is found that the new DME functional gives numerically stable results and exhibits a small but systematic reduction of our test {chi}{sup 2} function compared to standard Skyrme functionals, thus justifying its suitability for future global optimizations and large-scale calculations.
A Data Matrix Method for Improving the Quantification of Element Percentages of SEM/EDX Analysis
NASA Technical Reports Server (NTRS)
Lane, John
2009-01-01
A simple 2D M N matrix involving sample preparation enables the microanalyst to peer below the noise floor of element percentages reported by the SEM/EDX (scanning electron microscopy/ energy dispersive x-ray) analysis, thus yielding more meaningful data. Using the example of a 2 3 sample set, there are M = 2 concentration levels of the original mix under test: 10 percent ilmenite (90 percent silica) and 20 percent ilmenite (80 percent silica). For each of these M samples, N = 3 separate SEM/EDX samples were drawn. In this test, ilmenite is the element of interest. By plotting the linear trend of the M sample s known concentration versus the average of the N samples, a much higher resolution of elemental analysis can be performed. The resulting trend also shows how the noise is affecting the data, and at what point (of smaller concentrations) is it impractical to try to extract any further useful data.
Two functions of the density matrix and their relation to the chemical bond
NASA Astrophysics Data System (ADS)
Schmider, Hartmut L.; Becke, Axel D.
2002-02-01
We examine and compare two previously introduced functions of the one-particle density matrix that are suitable to represent its off-diagonal structure in a condensed form and that have illustrative connections to the nature of the chemical bond. One of them, the Localized-Orbital Locator (LOL) [J. Molec. Struct. (THEOCHEM) 527, 51 (2000)], is based only on the noninteracting kinetic-energy density τ and the charge density ρ at a point, and gives an intuitive measure of the relative speed of electrons in its vicinity. Alternatively, LOL focuses on regions that are dominated by single localized orbitals. The other one, the Parity Function P [J. Chem. Phys. 105, 11134 (1996)], is a section through the Wigner phase-space function at zero momentum, and contains information about the phase of the interference of atomiclike orbital contributions from bound centers. In this paper, we discuss the way in which these functions condense information in the density matrix, and illustrate on a variety of examples of unusual chemical bonds how they can help to understand the nature of "covalence."
Yordanov, D. Lishev, St.; Shivarova, A.
2016-02-15
Combining measurements of the extracted currents with probe and laser-photodetachment diagnostics, the study is an extension of recent tests of factors and gas-discharge conditions stimulating the extraction of volume produced negative ions. The experiment is in a single element of a rf source with the design of a matrix of small-radius inductively driven discharges. The results are for the electron and negative-ion densities, for the plasma potential and for the electronegativity in the vicinity of the plasma electrode as well as for the currents of the extracted negative ions and electrons. The plasma-electrode bias and the rf power have been varied. Necessity of a high bias to the plasma electrode and stable linear increase of the extracted currents with the rf power are the main conclusions.
Evaluation of Solid Modeling Software for Finite Element Analysis of Woven Ceramic Matrix Composites
NASA Technical Reports Server (NTRS)
Nemeth, Noel N.; Mital, Subodh; Lang, Jerry
2010-01-01
Three computer programs, used for the purpose of generating 3-D finite element models of the Repeating Unit Cell (RUC) of a textile, were examined for suitability to model woven Ceramic Matrix Composites (CMCs). The programs evaluated were the open-source available TexGen, the commercially available WiseTex, and the proprietary Composite Material Evaluator (COMATE). A five-harness-satin (5HS) weave for a melt-infiltrated (MI) silicon carbide matrix and silicon carbide fiber was selected as an example problem and the programs were tested for their ability to generate a finite element model of the RUC. The programs were also evaluated for ease-of-use and capability, particularly for the capability to introduce various defect types such as porosity, ply shifting, and nesting of a laminate. Overall, it was found that TexGen and WiseTex were useful for generating solid models of the tow geometry; however, there was a lack of consistency in generating well-conditioned finite element meshes of the tows and matrix. TexGen and WiseTex were both capable of allowing collective and individual shifting of tows within a ply and WiseTex also had a ply nesting capability. TexGen and WiseTex were sufficiently userfriendly and both included a Graphical User Interface (GUI). COMATE was satisfactory in generating a 5HS finite element mesh of an idealized weave geometry but COMATE lacked a GUI and was limited to only 5HS and 8HS weaves compared to the larger amount of weave selections available with TexGen and WiseTex.
Analysis of the segmented contraction of basis functions using density matrix theory.
Custodio, Rogério; Gomes, André Severo Pereira; Sensato, Fabrício Ronil; Trevas, Júlio Murilo Dos Santos
2006-11-30
A particular formulation based on density matrix (DM) theory at the Hartree-Fock level of theory and the description of the atomic orbitals as integral transforms is introduced. This formulation leads to a continuous representation of the density matrices as functions of a generator coordinate and to the possibility of plotting either the continuous or discrete density matrices as functions of the exponents of primitive Gaussian basis functions. The analysis of these diagrams provides useful information allowing: (a) the determination of the most important primitives for a given orbital, (b) the core-valence separation, and (c) support for the development of contracted basis sets by the segmented method. Copyright 2006 Wiley Periodicals, Inc.
Density hysteresis of heavy water confined in a nanoporous silica matrix
Zhang, Yang; Faraone, Antonio; Kamitakahara, William; Liu, Kao-Hsiang; Mou, Chung-Yuan; Leao, Juscelino B; Chang, Sung C; Chen, Sow-hsin H
2011-01-01
A neutron scattering technique was developed to measure the density of heavy water confined in a nanoporous silica matrix in a temperature-pressure range, from 300 to 130 K and from 1 to 2,900 bars, where bulk water will crystalize. We observed a prominent hysteresis phenomenon in the measured density profiles between warming and cooling scans above 1,000 bars. We inter- pret this hysteresis phenomenon as support (although not a proof) of the hypothetical existence of a first-order liquid liquid phase transition of water that would exist in the macroscopic system if crystallization could be avoided in the relevant phase region. Moreover, the density data we obtained for the confined heavy water under these conditions are valuable to large communities in biology and earth and planetary sciences interested in phenomena in which nanometer-sized water layers are involved.
Density hysteresis of heavy water confined in a nanoporous silica matrix
Zhang, Yang; Faraone, Antonio; Kamitakahara, William A.; Liu, Kao-Hsiang; Mou, Chung-Yuan; Leão, Juscelino B.; Chang, Sung; Chen, Sow-Hsin
2011-01-01
A neutron scattering technique was developed to measure the density of heavy water confined in a nanoporous silica matrix in a temperature-pressure range, from 300 to 130 K and from 1 to 2,900 bars, where bulk water will crystalize. We observed a prominent hysteresis phenomenon in the measured density profiles between warming and cooling scans above 1,000 bars. We interpret this hysteresis phenomenon as support (although not a proof) of the hypothetical existence of a first-order liquid–liquid phase transition of water that would exist in the macroscopic system if crystallization could be avoided in the relevant phase region. Moreover, the density data we obtained for the confined heavy water under these conditions are valuable to large communities in biology and earth and planetary sciences interested in phenomena in which nanometer-sized water layers are involved. PMID:21746898
Gamberg, L. P.; Mukherjee, A.; Mulders, P. J.
2011-04-01
Gluonic pole matrix elements explain the appearance of single spin asymmetries (SSA) in high-energy scattering processes. They involve a combination of operators which are odd under time reversal (T-odd). Such matrix elements appear in principle both for parton distribution functions and parton fragmentation functions. We show that for parton fragmentation functions, these gluonic pole matrix elements vanish as a consequence of the analytic structure of scattering amplitudes in quantum chromodynamics. This result is important in the study of the universality of transverse-momentum-dependent (TMD) fragmentation functions.
X-ray microanalysis of elements present in the matrix of cnidarian nematocysts.
Tardent, P; Zierold, K; Klug, M; Weber, J
1990-01-01
The composition and concentration of elements, in particular those of metallic cations, present in the intracapsular matrix and the wall of nematocysts of various cnidarian species have been recorded by means of X-ray microanalysis performed on 100nm thick cryosections. The predominant cation detected in the nematocyst matrix of the hydrozoan Podocoryne carnea (medusa), the scyphozoan Aurelia aurita (scyphopolyp) and the anthozoan Calliactis parasitica (tentacles and acontia) is K(+). Mg(2+) prevails in tentacular cysts of Anthopleura elegantissima, Actinia equina and Anemonia viridis, whereas, the acrorhagial cysts of A. elegantissima and A. equina contain Ca(2+) instead of Mg(2+). The acrorhagial cysts of A. viridis contain Mg(2+) like those of the tentacles. In the tentacular nematocysts of Podocoryne carnea polyps (Hydrozoa) on the other hand ambiguous element contents were found indicating that the cysts of this species has no preference for a particular cation. The high values of sulfur recorded in the matrix and particularly the wall of all the cysts are reflecting the presence of numerous protein disulfide bonds within the structural components (wall, shaft, tubule) of the nematocysts.
Extending the range of real time density matrix renormalization group simulations
NASA Astrophysics Data System (ADS)
Kennes, D. M.; Karrasch, C.
2016-03-01
We discuss a few simple modifications to time-dependent density matrix renormalization group (DMRG) algorithms which allow to access larger time scales. We specifically aim at beginners and present practical aspects of how to implement these modifications within any standard matrix product state (MPS) based formulation of the method. Most importantly, we show how to 'combine' the Schrödinger and Heisenberg time evolutions of arbitrary pure states | ψ > and operators A in the evaluation of ψ(t) = < ψ | A(t) | ψ > . This includes quantum quenches. The generalization to (non-)thermal mixed state dynamics ρ(t) =Tr [ ρA(t) ] induced by an initial density matrix ρ is straightforward. In the context of linear response (ground state or finite temperature T > 0) correlation functions, one can extend the simulation time by a factor of two by 'exploiting time translation invariance', which is efficiently implementable within MPS DMRG. We present a simple analytic argument for why a recently-introduced disentangler succeeds in reducing the effort of time-dependent simulations at T > 0. Finally, we advocate the python programming language as an elegant option for beginners to set up a DMRG code.
Controlled-surface-wettability-based fabrication of hydrogel substrates with matrix tethering density variations
NASA Astrophysics Data System (ADS)
Rahman, Md. Mahmudur; Lee, Donghee; Bhagirath, Divya; Zhao, Xiangshan; Band, Vimla; Ryu, Sangjin
2014-03-01
It is widely accepted that cells behave differently responding to the stiffness of extracellular matrix (ECM). Such observations were made by culturing cells on hydrogel substrates of tunable stiffness. However, it was recently proposed that cells actually sense how strongly they are tethered to ECM, not the local stiffness of ECM. To investigate the hypothesis, we develop constant-stiffness hydrogel substrates with varying matrix tethering density (the number of anchoring sites between the gel and the ECM protein molecules). We fabricate polyacrylamide gel of static stiffness and conjugate ECM proteins to the gel using a cross-linker. When treating the gel with the cross-linker, we control positioning of cross-linker solutions with different concentrations using superhydrophobic barriers on glass, functionalize the gel by pressing it to the aligned cross-linker solutions, and conjugate an ECM protein of constant concentration to the gel. We expect that the gel will be functionalized to different degrees depending on the concentration distribution of the cross-linker and thus the gel will have variations of matrix tethering density even with constant ECM protein concentration. We acknowledge support from Bioengineering for Human Health grant of UNL-UNMC.
Effect of bone graft density on in vitro cell behavior with enamel matrix derivative.
Miron, Richard J; Caluseru, Oana M; Guillemette, Vincent; Zhang, Yufeng; Buser, Daniel; Chandad, Fatiha; Sculean, Anton
2015-09-01
Bone replacement grafting materials play an important role in regenerative dentistry. Despite a large array of tested bone-grafting materials, little information is available comparing the effects of bone graft density on in vitro cell behavior. Therefore, the aim of the present study is to compare the effects of cells seeded on bone grafts at low and high density in vitro for osteoblast adhesion, proliferation, and differentiation. The response of osteoblasts to the presence of a growth factor (enamel matrix derivative, (EMD)) in combination with low (8 mg per well) or high (100 mg per well) bone grafts (BG; natural bone mineral, Bio-Oss®) density, was studied and compared for osteoblast cell adhesion, proliferation, and differentiation as assessed by real-time PCR. Standard tissue culture plastic was used as a control with and without EMD. The present study demonstrates that in vitro testing of bone-grafting materials is largely influenced by bone graft seeding density. Osteoblast adhesion was up to 50 % lower when cells were seeded on high-density BG when compared to low-density BG and control tissue culture plastic. Furthermore, proliferation was affected in a similar manner whereby cell proliferation on high-density BG (100 mg/well) was significantly increased when compared to that on low-density BG (8 mg/well). In contrast, cell differentiation was significantly increased on high-density BG as assessed by real-time PCR for markers collagen 1 (Col 1), alkaline phosphatase (ALP), and osteocalcin (OC) as well as alizarin red staining. The effects of EMD on osteoblast adhesion, proliferation, and differentiation further demonstrated that the bone graft seeding density largely controls in vitro results. EMD significantly increased cell attachment only on high-density BG, whereas EMD was able to further stimulate cell proliferation and differentiation of osteoblasts on control culture plastic and low-density BG when compared to high-density BG. The results
NASA Astrophysics Data System (ADS)
Micha, David A.
This contribution deals with two approaches for localized phenomena in excited many-atom systems. The first approach develops a quantum quasi-classical treatment for the density operator, including all atoms. It is based on a partial Wigner representation and is illustrated with applications to photodissociation of NaI, and to light emission of excited Li interacting with a He cluster. This second application describes the direct dynamics with a time-dependent electronic density matrix, expanded in a basis set of atomic functions. It shows that such an approach can deal with electronically excited many-atom systems involving tens of quantum states and hundreds of classical variables. The second approach makes use of the reduced density operator description for a system in a medium. This allows for dissipative dynamics, which can be instantaneous or delayed. An application is presented for femtosecond photodesorption using a Markovian dissipation and construction of the density operator from density amplitudes, for CO/Cu(001). A second application of a reduced density operator has been made to vibrational relaxation of adsorbates, solving integrodifferential equations to compare delayed, instantaneous, and Markovian dissipation. It is concluded that delayed dissipation is needed at short times and that a Markovian treatment is suitable for the interpretation of cross-sectional measurements that involve long-term dynamics.
Mniszewski, S M; Cawkwell, M J; Wall, M E; Mohd-Yusof, J; Bock, N; Germann, T C; Niklasson, A M N
2015-10-13
We present an algorithm for the calculation of the density matrix that for insulators scales linearly with system size and parallelizes efficiently on multicore, shared memory platforms with small and controllable numerical errors. The algorithm is based on an implementation of the second-order spectral projection (SP2) algorithm [ Niklasson, A. M. N. Phys. Rev. B 2002 , 66 , 155115 ] in sparse matrix algebra with the ELLPACK-R data format. We illustrate the performance of the algorithm within self-consistent tight binding theory by total energy calculations of gas phase poly(ethylene) molecules and periodic liquid water systems containing up to 15,000 atoms on up to 16 CPU cores. We consider algorithm-specific performance aspects, such as local vs nonlocal memory access and the degree of matrix sparsity. Comparisons to sparse matrix algebra implementations using off-the-shelf libraries on multicore CPUs, graphics processing units (GPUs), and the Intel many integrated core (MIC) architecture are also presented. The accuracy and stability of the algorithm are illustrated with long duration Born-Oppenheimer molecular dynamics simulations of 1000 water molecules and a 303 atom Trp cage protein solvated by 2682 water molecules.
Adiabatic approximation in time-dependent reduced-density-matrix functional theory
Requist, Ryan; Pankratov, Oleg
2010-04-15
With the aim of describing real-time electron dynamics, we introduce an adiabatic approximation for the equation of motion of the one-body reduced density matrix (one-matrix). The eigenvalues of the one-matrix, which represent the occupation numbers of single-particle orbitals, are obtained from the constrained minimization of the instantaneous ground-state energy functional rather than from their dynamical equations. The performance of the approximation vis-a-vis nonadiabatic effects is assessed in real-time simulations of a two-site Hubbard model. Due to Landau-Zener-type transitions, the system evolves into a nonstationary state with persistent oscillations in the observables. The amplitude of the oscillations displays a strongly nonmonotonic dependence on the strength of the electron-electron interaction and the rate of variation of the external potential. We interpret an associated resonance behavior in the phase of the oscillations in terms of 'scattering' with spectator energy levels. To clarify the motivation for the minimization condition, we derive a sequence of energy functionals E{sub v}{sup (n)}, for which the corresponding sequence of minimizing one-matrices is asymptotic to the exact one-matrix in the adiabatic limit.
Density of states features in some anomalous melting elements.
Schulze, R K; Wallace, D C; Lashley, J C
2013-11-20
Valence band photoemission measurements have been made on crystalline and supercooled liquid gallium, and across the liquid and solid phases of bismuth and indium. Measurements are angle integrated and made using photon excitations of 21.21 and 40.81 eV. In all cases the Bloch states are destroyed upon melting and the free electron gas is constrained by a charge-neutral liquid. The spectra of indium show little change upon solidification, indicating a common electronic structure for crystalline and liquid phases. In contrast, the energy distribution curves for supercooled gallium and bismuth show large changes in the electronic structure from solid to liquid phases, giving rise to the formation of pseudogaps in the density of states at the Fermi energy, EF. Observations of this kind enable us to distinguish normal or anomalous melting from photoemission measurements.
Cawkwell, M J; Wood, M A; Niklasson, Anders M N; Mniszewski, S M
2014-12-09
The algorithm developed in Cawkwell, M. J. et al. J. Chem. Theory Comput. 2012 , 8 , 4094 for the computation of the density matrix in electronic structure theory on a graphics processing unit (GPU) using the second-order spectral projection (SP2) method [ Niklasson, A. M. N. Phys. Rev. B 2002 , 66 , 155115 ] has been efficiently parallelized over multiple GPUs on a single compute node. The parallel implementation provides significant speed-ups with respect to the single GPU version with no loss of accuracy. The performance and accuracy of the parallel GPU-based algorithm is compared with the performance of the SP2 algorithm and traditional matrix diagonalization methods on a multicore central processing unit (CPU).
Random matrix model of QCD at finite density and the nature of the quenched limit
Stephanov, M.A.
1996-06-01
We use a random matrix model to study chiral symmetry breaking in QCD at finite chemical potential {mu}. We solve the model and compute the eigenvalue density of the Dirac matrix on a complex plane. A naive {open_quote}{open_quote}replica trick{close_quote}{close_quote} fails for {mu}{ne}0; we find that quenched QCD is not a simple {ital n}{r_arrow}0 limit of QCD with {ital n} quarks. It is the limit of a theory with 2{ital n} quarks: {ital n} quarks with original action and {ital n} quarks with conjugate action. The results agree with earlier studies of lattice QCD at {mu}{ne}0 and provide a simple analytical explanation of a long-standing puzzle. {copyright} {ital 1996 The American Physical Society.}
Second-Order Self-Consistent-Field Density-Matrix Renormalization Group.
Ma, Yingjin; Knecht, Stefan; Keller, Sebastian; Reiher, Markus
2017-06-13
We present a matrix-product state (MPS)-based quadratically convergent density-matrix renormalization group self-consistent-field (DMRG-SCF) approach. Following a proposal by Werner and Knowles (J. Chem. Phys. 1985, 82, 5053), our DMRG-SCF algorithm is based on a direct minimization of an energy expression which is correct to second order with respect to changes in the molecular orbital basis. We exploit a simultaneous optimization of the MPS wave function and molecular orbitals in order to achieve quadratic convergence. In contrast to previously reported (augmented Hessian) Newton-Raphson and superconfiguration-interaction algorithms for DMRG-SCF, energy convergence beyond a quadratic scaling is possible in our ansatz. Discarding the set of redundant active-active orbital rotations, the DMRG-SCF energy converges typically within two to four cycles of the self-consistent procedure.
Performance of the density matrix functional theory in the quantum theory of atoms in molecules.
García-Revilla, Marco; Francisco, E; Costales, A; Martín Pendás, A
2012-02-02
The generalization to arbitrary molecular geometries of the energetic partitioning provided by the atomic virial theorem of the quantum theory of atoms in molecules (QTAIM) leads to an exact and chemically intuitive energy partitioning scheme, the interacting quantum atoms (IQA) approach, that depends on the availability of second-order reduced density matrices (2-RDMs). This work explores the performance of this approach in particular and of the QTAIM in general with approximate 2-RDMs obtained from the density matrix functional theory (DMFT), which rests on the natural expansion (natural orbitals and their corresponding occupation numbers) of the first-order reduced density matrix (1-RDM). A number of these functionals have been implemented in the promolden code and used to perform QTAIM and IQA analyses on several representative molecules and model chemical reactions. Total energies, covalent intra- and interbasin exchange-correlation interactions, as well as localization and delocalization indices have been determined with these functionals from 1-RDMs obtained at different levels of theory. Results are compared to the values computed from the exact 2-RDMs, whenever possible.
Determination of element affinities by density fractionation of bulk coal samples
Querol, X.; Klika, Z.; Weiss, Z.; Finkelman, R.B.; Alastuey, A.; Juan, R.; Lopez-Soler, A.; Plana, F.; Kolker, A.; Chenery, S.R.N.
2001-01-01
A review has been made of the various methods of determining major and trace element affinities for different phases, both mineral and organic in coals, citing their various strengths and weaknesses. These include mathematical deconvolution of chemical analyses, direct microanalysis, sequential extraction procedures and density fractionation. A new methodology combining density fractionation with mathematical deconvolution of chemical analyses of whole coals and their density fractions has been evaluated. These coals formed part of the IEA-Coal Research project on the Modes of Occurrence of Trace Elements in Coal. Results were compared to a previously reported sequential extraction methodology and showed good agreement for most elements. For particular elements (Be, Mo, Cu, Se and REEs) in specific coals where disagreement was found, it was concluded that the occurrence of rare trace element bearing phases may account for the discrepancy, and modifications to the general procedure must be made to account for these.
Study of color-octet matrix elements through J/ψ production in e+e- annihilation
NASA Astrophysics Data System (ADS)
Li, Yi-Jie; Xu, Guang-Zhi; Zhang, Pan-Pan; Zhang, Yu-Jie; Liu, Kui-Yong
2017-09-01
In this paper, the color-octet long distance matrix elements are studied through the inclusive J/ψ production in e+e- annihilation within the framework of non-relativistic QCD factorization. The calculations are up-to next-to-leading order with the radiative and relativistic corrections in the energy region of the B-factory and the near-threshold region of 4.6{-}5.6 GeV. A constraint of the long distance matrix elements (< ^1S_08> , < ^3P_08> ) is obtained. Through our estimation, the P-wave color-octet matrix element (< 0|^3P^8_0|0> ) should be of the order of 0.008m_c^2 GeV^3 or less. The constrained region is not compatible with the values of the long distance matrix elements fitted at hadron colliders.
Nucleon matrix elements with Nf=2+1+1 maximally twisted fermions
Simon Dinter, Constantia Alexandrou, Martha Constantinou, Vincent Drach, Karl Jansen, Dru Renner
2010-06-01
We present the first lattice calculation of nucleon matrix elements using four dynamical flavors. We use the Nf=2+1+1 maximally twisted mass formulation. The renormalization is performed non-perturbatively in the RI'-MOM scheme and results are given for the vector and axial vector operators with up to one-derivative. Our calculation of the average momentum of the unpolarized non-singlet parton distribution is presented and compared to our previous results obtained from the Nf=2 case.
Using the modified matrix element method to constrain Lμ-Lτ interactions
NASA Astrophysics Data System (ADS)
Elahi, Fatemeh; Martin, Adam
2017-07-01
In this paper, we explore the discriminatory power of the matrix element method (MEM) in constraining the Lμ-Lτ model at the LHC. The Z' boson associated with the spontaneously broken U (1 )Lμ-Lτ symmetry only interacts with the second and third generation of leptons at tree level, and is thus difficult to produce at the LHC. We argue that the best channels for discovering this Z' are in Z →4 μ and 2 μ + ET. Both these channels have a large number of kinematic observables, which strongly motivates the usage of a multivariate technique. The MEM is a multivariate analysis that uses the squared matrix element |M |2 to quantify the likelihood of the testing hypotheses. As the computation of the |M |2 requires knowing the initial and final state momenta and the model parameters, it is not commonly used in new physics searches. Conventionally, new parameters are estimated by maximizing the likelihood of the signal with respect to the background, and we outline scenarios in which this procedure is (in)effective. We illustrate that the new parameters can also be estimated by studying the |M |2 distributions, and, even if our parameter estimation is off, we can gain better sensitivity than cut-and-count methods. Additionally, unlike the conventional MEM, where one integrates over all unknown momenta in processes with ET, we show an example scenario where these momenta can be estimated using the process topology. This procedure, which we refer to as the "modified squared matrix element," is computationally much faster than the canonical matrix element method and maintains signal-background discrimination. Bringing the MEM and the aforementioned modifications to bear on the Lμ-Lτ model, we find that with 300 fb-1 of integrated luminosity, we are sensitive to the couplings of gZ'≳0.002 g1 and MZ'<20 GeV , and gZ'≳0.005 g1 and 20 GeV
Many-body correlations of QRPA in nuclear matrix elements of double-beta decay
Terasaki, J.
2015-10-28
We present two new ideas on the quasiparticle random-phase approximation (QRPA) approach for calculating nuclear matrix elements of double-beta decay. First, it is necessary to calculate overlaps of the QRPA states obtained on the basis of the ground states of different nuclei. We calculate this overlap using quasiboson vacua as the QRPA ground states. Second, we show that two-particle transfer paths are possible to use for the calculation under the closure approximation. A calculation is shown for {sup 150}Nd→{sup 150}Sm using these two new ideas, and their implication is discussed.
NASA Astrophysics Data System (ADS)
Sarkadi, L.
2017-03-01
The program MTRXCOUL [1] calculates the matrix elements of the Coulomb interaction between a charged particle and an atomic electron, ∫ψf∗ (r) | R - r | - 1ψi(r) d r. Bound-free transitions are considered, and non-relativistic hydrogenic wave functions are used. In this revised version a bug discovered in the F3Y CPC Program Library (PL) subprogram [2] is fixed. Furthermore, the COULCC CPC PL subprogram [3] applied for the calculations of the radial wave functions of the free states and the Bessel functions is replaced by the CPC PL subprogram DCOUL [4].
Closed formula for the matrix elements of the volume operator in canonical quantum gravity
NASA Astrophysics Data System (ADS)
Thiemann, T.
1998-06-01
We derive a closed formula for the matrix elements of the volume operator for canonical Lorentzian quantum gravity in four space-time dimensions in the continuum in a spin-network basis. We also display a new technique of regularization which is state dependent but we are forced to it in order to maintain diffeomorphism covariance and in that sense it is natural. We arrive naturally at the expression for the volume operator as defined by Ashtekar and Lewandowski up to a state-independent factor.
Electron-H2 Collisions Studied Using the Finite Element Z-Matrix Method
NASA Technical Reports Server (NTRS)
Huo, Winifred M.; Brown, David; Langhoff, Stephen R. (Technical Monitor)
1997-01-01
We have applied the Z-matrix method, using a mixed basis of finite elements and Gaussians, to study e-H2 elastic and inelastic collisions. Special attention is paid to the quality of the basis set and the treatment of electron correlation. The calculated cross sections are invariant, to machine accuracy, with respect to the choice of parameters a, b, d, e as long as they satisfy Equation (3). However, the log derivative approach, i.e., the choice a = -e = 1, b = d = 0 appears to converge slightly faster than other choices. The cross sections agree well with previous theoretical results. Comparison will be made with available experimental data.
Nuclear matrix elements from direct lifetime or cross-section measurements
Werner, V.; Cooper, N.; Hinton, M.; Ilie, G.; Radeck, D.
2012-11-20
The method of simultaneous lifetime and g factor measurements using a plunger device and the RDDS and TDRIV techniques is introduced. Results on lifetimes and hyperfine-interaction parameters for 2{sup +}{sub 1} states in {sup 104-108}Pd, {sup 96,98,104}Ru, and {sup 92,94}Zr, using a plunger device. Another method to obtain electromagnetic matrix elements is direct cross section measurements using NRF. The method is outlined, and some recent results on {sup 76}Se are shown.
Stochastic method with low mode substitution for nucleon isovector matrix elements
NASA Astrophysics Data System (ADS)
Yang, Yi-Bo; Alexandru, Andrei; Draper, Terrence; Gong, Ming; Liu, Keh-Fei; χ QCD Collaboration
2016-02-01
We introduce a stochastic method with low-mode substitution to evaluate the connected three-point functions. The isovector matrix elements of the nucleon for the axial-vector coupling gA3, scalar couplings gS3 and the quark momentum fraction ⟨x ⟩u -d are calculated with overlap fermion on 2 +1 flavor domain-wall configurations on a 243×64 lattice at mπ=330 MeV with lattice spacing a =0.114 fm .
Number-conserving random phase approximation with analytically integrated matrix elements
Kyotoku, M. ); Schmid, K.W. ); Gruemmer, F. ); Faessler, A. )
1990-01-01
In the present paper a number conserving random phase approximation is derived as a special case of the recently developed random phase approximation in general symmetry projected quasiparticle mean fields. All the occurring integrals induced by the number projection are performed analytically after writing the various overlap and energy matrices in the random phase approximation equation as polynomials in the gauge angle. In the limit of a large number of particles the well-known pairing vibration matrix elements are recovered. We also present a new analytically number projected variational equation for the number conserving pairing problem.
Reduced matrix elements of spin-spin interactions for the atomic f-electron configurations
NASA Astrophysics Data System (ADS)
Yeung, Y. Y.
2014-03-01
A re-examination of some major references on the intra-atomic magnetic interactions over the last six decades reveals that there exist some gaps or puzzles concerning the previous studies of the spin-spin interactions for the atomic f-shell electrons. Hence, tables are provided for the relevant reduced matrix elements of the four double-tensor operators zr (r=1,2,3, and 4) of rank 2 in both the orbital and spin spaces. The range of the tables covers all states of the configurations from f4 to f7.
Quantum correlations in different density-matrix representations of spin-1/2 open chain
NASA Astrophysics Data System (ADS)
Fel'dman, E. B.; Zenchuk, A. I.
2012-07-01
We consider quantum correlations in a spin-1/2 open chain of N nodes with the XY Hamiltonian using different bases for the density-matrix representation and the initial state with a single polarized node. These bases of our choice are the following: (i) the basis of eigenvectors of the fermion operators which appears naturally through the Jordan-Wigner transformation (this representation of the density matrix is referred to as the β representation); (ii) its Fourier representation (c representation of the density matrix); and (iii) the basis of eigenvectors of the operators Ijz (the z projection of the jth spin, j=1,⋯,N). Although for the short chains (a few nodes) the qualitative behavior of the entanglement and the discord are very similar (the difference is quantitative), this is not valid for longer chains (N≳10). In this case, there are qualitative and quantitative distinctions between the entanglement and the discord in all three cases. We underline the three most important features: (i) the quantum discord is static in the β representation, where the entanglement is identical to zero; (ii) in the c representation, the concurrence may be nonzero only between the nearest neighbors (with a single exception), while the discord is nonzero between any two nodes; and (iii) there is so-called “echo” in the evolution of the discord, which is not observed in the evolution of the concurrence. Using different bases, we may choose the preferable behavior of quantum correlations which allows a given quantum system to be more flexible in applications.
Eigenvalue density of linear stochastic dynamical systems: A random matrix approach
NASA Astrophysics Data System (ADS)
Adhikari, S.; Pastur, L.; Lytova, A.; Du Bois, J.
2012-02-01
Eigenvalue problems play an important role in the dynamic analysis of engineering systems modeled using the theory of linear structural mechanics. When uncertainties are considered, the eigenvalue problem becomes a random eigenvalue problem. In this paper the density of the eigenvalues of a discretized continuous system with uncertainty is discussed by considering the model where the system matrices are the Wishart random matrices. An analytical expression involving the Stieltjes transform is derived for the density of the eigenvalues when the dimension of the corresponding random matrix becomes asymptotically large. The mean matrices and the dispersion parameters associated with the mass and stiffness matrices are necessary to obtain the density of the eigenvalues in the frameworks of the proposed approach. The applicability of a simple eigenvalue density function, known as the Marenko-Pastur (MP) density, is investigated. The analytical results are demonstrated by numerical examples involving a plate and the tail boom of a helicopter with uncertain properties. The new results are validated using an experiment on a vibrating plate with randomly attached spring-mass oscillators where 100 nominally identical samples are physically created and individually tested within a laboratory framework.
Parker, Shane M.; Shiozaki, Toru
2014-12-07
We extend the active space decomposition method, recently developed by us, to more than two active sites using the density matrix renormalization group algorithm. The fragment wave functions are described by complete or restricted active-space wave functions. Numerical results are shown on a benzene pentamer and a perylene diimide trimer. It is found that the truncation errors in our method decrease almost exponentially with respect to the number of renormalization states M, allowing for numerically exact calculations (to a few μE{sub h} or less) with M = 128 in both cases. This rapid convergence is because the renormalization steps are used only for the interfragment electron correlation.
Applying the density matrix expansion with coordinate-space chiral interactions
NASA Astrophysics Data System (ADS)
Dyhdalo, A.; Bogner, S. K.; Furnstahl, R. J.
2017-05-01
We apply the density matrix expansion (DME) at Hartree-Fock level with long-range chiral effective field theory interactions defined in coordinate space up to next-to-next-to-leading order. We consider chiral potentials both with and without explicit Δ isobars. The challenging algebra associated with applying the DME to three-nucleon forces is tamed using a new organization scheme, which will also facilitate generalizations. We include local regulators on the interactions to mitigate the effects of singular potentials on the DME couplings and simplify the optimization of generalized Skyrme-like functionals.
Analysis of NMR self-diffusion measurements by a density matrix calculation
NASA Astrophysics Data System (ADS)
Stepišnik, J.
1981-04-01
The density matrix formalism with the Magnus expansion of the time evolution operator is used to study the nmr response in a pulsed magnetic field gradient (mfg) spin-echo experiment. The results show that the spin-echo cannot only measure the self-diffusion coefficient but can determine the spectrum of the single-particle velocity autocorrelation function as well. The proper combination of rf and mfg pulse sequences are proposed for measuring self-diffusion in spin systems with strong dipolar coupling where the classical method fails.
NASA Astrophysics Data System (ADS)
Mendoza-Arenas, J. J.; Franco, R.; Silva-Valencia, J.
2010-01-01
We analyze the one-dimensional Kondo necklace model, at zero temperature, with an anisotropy parameter η in the interaction of the conduction chain, by means of the density matrix renormalization group. We calculate the energy gap and estimate the quantum critical points that separate a Kondo singlet state from an antiferromagnetic state, assuming a Kosterlitz-Thouless tendency. We also observe the correlation functions and the structure factors that support our critical points. The resulting phase diagram is presented and compared to that reported previously using Lanczos calculations. It is shown that the quantum critical points vary very slowly with η , but when η approaches zero, they drop abruptly.
NASA Astrophysics Data System (ADS)
Schmider, Hartmut; Smith, Vedene H., Jr.; Weyrich, Wolf
1992-06-01
For the beryllium atom, it is demonstrated that coherent form factors F(k) can be insufficient for inferring the one-particle reduced density matrix (ODM). The description in terms of reciprocal form factors B(s) as the complementary momentum-space property is compared with the results for a least-squares fit to F(k) data. A virtually complete description of the true ODM may be obtained by using a combined data set, as can be shown by representing the ODM in spherically averaged form.
Density-matrix-power functional: Performance for finite systems and the homogeneous electron gas
NASA Astrophysics Data System (ADS)
Lathiotakis, N. N.; Sharma, S.; Dewhurst, J. K.; Eich, F. G.; Marques, M. A. L.; Gross, E. K. U.
2009-04-01
An exchange-correlation energy functional involving fractional power of the one-body reduced density matrix [S. Sharma, J. K. Dewhurst, N. N. Lathiotakis, and E. K. U. Gross, Phys. Rev. B 78, 201103(R) (2008)] is applied to finite systems and to the homogeneous electron gas. The performance of the functional is assessed for the correlation and atomization energies of a large set of molecules and for the correlation energy of the homogeneous electron gas. High accuracy is found for these two very different types of systems.
Highly linear high-density vector quantiser and vector-matrix multiplier
NASA Astrophysics Data System (ADS)
Pedroni, V. A.
1994-06-01
Simplicity is a key factor in the development of high-density systems. The authors discuss a balanced, four-quadrant, fully-analogue vector-matrix multiplier (VMM) and a vector quantiser (VQ) which require very small silicon area for their implementations, while presenting high linearity, a totally flexible input dynamic range, a symmetric power consumption behaviour, and are inherently suitable for parallel operation. The circuits require only four transistors per synapse in the VMM and two in the VQ, plus two (small) refresh transistors.
Implementation and testing of a frozen density matrix-divide and conquer algorithm
Ermolaeva, M.D.; Vaart, A. van der; Merz, K.M. Jr.
1999-03-25
The authors have implemented and tested a frozen density matrix (FDM) approximation to the basic divide and conquer (DC) semiempirical algorithm. Molecular dynamics and Monte Carlo simulations were performed to estimate the advantages of the method. Results were compared to those obtained from the original DC method and the combined quantum mechanical/molecular mechanical (WM/MM) method. The authors found that the FDM approximation speeds DC calculations up significantly, while only introducing small errors. They also found that the FDM DC scheme performs better than the standard QM/MM approach in terms of defining the electronic and structural properties of the systems studied herein.
Block product density matrix embedding theory for strongly correlated spin systems
NASA Astrophysics Data System (ADS)
Gunst, Klaas; Wouters, Sebastian; De Baerdemacker, Stijn; Van Neck, Dimitri
2017-05-01
Density matrix embedding theory (DMET) is a relatively new technique for the calculation of strongly correlated systems. Recently, block product DMET (BPDMET) was introduced for the study of spin systems such as the antiferromagnetic J1-J2 model on the square lattice. In this paper, we extend the variational Ansatz of BPDMET using spin-state optimization, yielding improved results. We apply the same techniques to the Kitaev-Heisenberg model on the honeycomb lattice, comparing the results when using several types of clusters. Energy profiles and correlation functions are investigated. A diagonalization in the tangent space of the variational approach yields information on the excited states and the corresponding spectral functions.
A practical guide to density matrix embedding theory in quantum chemistry
Wouters, Sebastian; Jimenez-Hoyos, Carlos A.; Sun, Qiming; ...
2016-05-09
Density matrix embedding theory (DMET) (Knizia, G.; Chan, G. K.-L. Phys. Rev. Lett. 2012, 109, 186404) provides a theoretical framework to treat finite fragments in the presence of a surrounding molecular or bulk environment, even when there is significant correlation or entanglement between the two. In this work, we give a practically oriented and explicit description of the numerical and theoretical formulation of DMET. Here, we also describe in detail how to perform self-consistent DMET optimizations. We explore different embedding strategies with and without a self-consistency condition in hydrogen rings, beryllium rings, and a sample SN2 reaction.
Application of Löwdin projectors to evaluate density matrix evolutions
NASA Astrophysics Data System (ADS)
Chandrakumar, N.
Projection operators are employed to evaluate functions of operators. In particular, this formalism is used to find polynomial expressions for exponential operators and thence to solve density matrix evolutions in closed analytical form. Problems explicitly treated include pulse rotation of spin-I and spin - {3}/{2} systems, spin tickling and spin interferometry on a system of two coupled spin- {1}/{2} nuclei, isotropic mixing in systems of two coupled nuclei (both spins- {1}/{2} or spins-1), and dipolar evolution in a two-spin- {1}/{2} system. The method is compared to the BCH approach for operator evolutions.
Parker, Shane M; Shiozaki, Toru
2014-12-07
We extend the active space decomposition method, recently developed by us, to more than two active sites using the density matrix renormalization group algorithm. The fragment wave functions are described by complete or restricted active-space wave functions. Numerical results are shown on a benzene pentamer and a perylene diimide trimer. It is found that the truncation errors in our method decrease almost exponentially with respect to the number of renormalization states M, allowing for numerically exact calculations (to a few μE(h) or less) with M = 128 in both cases. This rapid convergence is because the renormalization steps are used only for the interfragment electron correlation.
NASA Astrophysics Data System (ADS)
Chen, GuanHua; Su, ZhongMin; Shen, ZhenWen; Yan, YiJing
1998-08-01
A new variation method is proposed to determine the effective Hamiltonians for conjugated π-electron systems. This method is based on the minimization of the difference between the ground state reduced single electron density matrix calculated from the effective Hamiltonian and its ab initio counterpart under a set of well-defined constraints. Applications are made to various oligomers of polymethineimine (PMI), polyazine (PAZ) and polyazoethene (PAE) at the Hartree-Fock level. Calculated are also the optical gaps of these oligomers. The effective Hamiltonians contain electron-electron Coulomb interactions and are suitable for the study of excited state dynamic processes such as nonlinear optical properties in π-conjugated systems.
Alwall, J.; Hoche, S.; Krauss, F.; Lavesson, N.; Lonnblad, L.; Maltoni, F.; Mangano, M.L.; Moretti, M.; Papadopoulos, C.G.; Piccinini, F.; Schumann, S.; Treccani, M.; Winter, J.; Worek, M.; /SLAC /Durham U., IPPP /Lund U. /Louvain U. /CERN /Ferrara U. /INFN, Ferrara /Athens U. /INFN, Pavia /Dresden, Tech. U. /Karlsruhe U., TP /Silesia U.
2007-06-27
We compare different procedures for combining fixed-order tree-level matrix-element generators with parton showers. We use the case of W-production at the Tevatron and the LHC to compare different implementations of the so-called CKKW and MLM schemes using different matrix-element generators and different parton cascades. We find that although similar results are obtained in all cases, there are important differences.
NASA Astrophysics Data System (ADS)
Kanungo, Bikash; Gavini, Vikram
2017-01-01
We present a computationally efficient approach to perform large-scale all-electron density functional theory calculations by enriching the classical finite element basis with compactly supported atom-centered numerical basis functions that are constructed from the solution of the Kohn-Sham (KS) problem for single atoms. We term these numerical basis functions as enrichment functions, and the resultant basis as the enriched finite element basis. The compact support for the enrichment functions is obtained by using smooth cutoff functions, which enhances the conditioning and maintains the locality of the enriched finite element basis. The integrals involved in the evaluation of the discrete KS Hamiltonian and overlap matrix in the enriched finite element basis are computed using an adaptive quadrature grid that is constructed based on the characteristics of enrichment functions. Further, we propose an efficient scheme to invert the overlap matrix by using a blockwise matrix inversion in conjunction with special reduced-order quadrature rules, which is required to transform the discrete Kohn-Sham problem to a standard eigenvalue problem. Finally, we solve the resulting standard eigenvalue problem, in each self-consistent field iteration, by using a Chebyshev polynomial based filtering technique to compute the relevant eigenspectrum. We demonstrate the accuracy, efficiency, and parallel scalability of the proposed method on semiconducting and heavy-metallic systems of various sizes, with the largest system containing 8694 electrons. We obtain accuracies in the ground-state energies that are ˜1 mHa with reference ground-state energies employing classical finite element as well as Gaussian basis sets. Using the proposed formulation based on enriched finite element basis, for accuracies commensurate with chemical accuracy, we observe a staggering 50 -300 -fold reduction in the overall computational time when compared to classical finite element basis. Further, we find a
NASA Astrophysics Data System (ADS)
Silvi, Pietro; Calarco, Tommaso; Morigi, Giovanna; Montangero, Simone
2014-03-01
Ions of the same charge inside confining potentials can form crystalline structures which can be controlled by means of the ion density and of the external trap parameters. In particular, a linear chain of trapped ions exhibits a transition to a zigzag equilibrium configuration, which is controlled by the strength of the transverse confinement. Studying this phase transition in the quantum regime is a challenging problem, even when employing numerical methods to simulate microscopically quantum many-body systems. Here we present a compact analytical treatment to map the original long-range problem into a short-range quantum field theory on a lattice. We provide a complete numerical architecture, based on the density matrix renormalization group, to address the effective quantum ϕ4 model. This technique is instrumental in giving a complete characterization of the phase diagram, as well as pinpointing the universality class of the criticality.
Density matrix theory of transport and gain in quantum cascade lasers in a magnetic field
NASA Astrophysics Data System (ADS)
Savić, Ivana; Vukmirović, Nenad; Ikonić, Zoran; Indjin, Dragan; Kelsall, Robert W.; Harrison, Paul; Milanović, Vitomir
2007-10-01
A density matrix theory of electron transport and optical gain in quantum cascade lasers in an external magnetic field is formulated. Starting from a general quantum kinetic treatment, we describe the intraperiod and interperiod electron dynamics at the non-Markovian, Markovian, and Boltzmann approximation levels. Interactions of electrons with longitudinal optical phonons and classical light fields are included in the present description. The non-Markovian calculation for a prototype structure reveals a significantly different gain spectra in terms of linewidth and additional polaronic features in comparison to the Markovian and Boltzmann ones. Despite strongly controversial interpretations of the origin of the transport processes in the non-Markovian or Markovian and the Boltzmann approaches, they yield comparable values of the current densities.
Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions.
Changlani, Hitesh J; Zheng, Huihuo; Wagner, Lucas K
2015-09-14
We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding. For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard U(∗)/t to be 1.3 ± 0.2, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large-scale calculations using techniques designed for lattice models.
Measurement of single top quark production at D0 using a matrix element method
Mitrevski, Jovan Pavle
2007-01-01
Until now, the top quark has only been observed produced in pairs, by the strong force. According to the standard model, it can also be produced singly, via an electroweak interaction. Top quarks produced this way provide powerful ways to test the charged-current electroweak interactions of the top quark, to measure |V_{tb}|, and to search for physics beyond the standard model. This thesis describes the application of the matrix element analysis technique to the search for single top quark production with the D0 detector using 0.9 fb^{-1} of Run II data. From a comparison of the matrix element discriminants between data and the background model, assuming a Standard Model s-channel to t-channel cross section ratio of σ_{s}/σ_{t} = 0.44, we measure the single top quark production cross section: σ(p$\\bar{p}$ → tb + X, tqb + X) = 4.8$-1.4\\atop{+1.6}$ pb. This result has a p-value of 0.08%, corresponding to a 3.2 standard deviation Gaussian equivalent significance.
Top quark mass measurement from dilepton events at CDF II with the matrix-element method
Abulencia, A.; Acosta, D.; Adelman, Jahred A.; Affolder, T.; Akimoto, T.; Albrow, M.G.; Ambrose, D.; Amerio, S.; Amidei, D.; Anastassov, A.; Anikeev, K.; /Taiwan, Inst. Phys. /Argonne /Barcelona, IFAE /Baylor U. /INFN, Bologna /Bologna U. /Brandeis U. /UC, Davis /UCLA /UC, San Diego /UC, Santa Barbara
2006-05-01
We describe a measurement of the top quark mass using events with two charged leptons collected by the CDF II detector from p{bar p} collisions with {radical}s = 1.96 TeV at the Fermilab Tevatron. The likelihood in top mass is calculated for each event by convoluting the leading order matrix element describing q{bar q} {yields} t{bar t} {yields} b{ell}{nu}{sub {ell}}{bar b}{ell}{prime} {nu}{sub {ell}}, with detector resolution functions. The presence of background events in the data sample is modeled using similar calculations involving the matrix elements for major background processes. In a data sample with integrated luminosity of 340 pb{sup -1}, we observe 33 candidate events and measure M{sub top} = 165.2 {+-} 6.1(stat.) {+-} 3.4(syst.) GeV/c{sup 2}. This measurement represents the first application of this method to events with two charged leptons and is the most precise single measurement of the top quark mass in this channel.
Precision Measurement of the Neutron Twist-3 Matrix Element dn2: Probing Color Forces
Posik, Matthew; Flay, David; Parno, Diana; Allada, Kalyan; Armstrong, Whitney; Averett, Todd; Benmokhtar, Fatiha; Bertozzi, William; Camsonne, Alexandre; Canan, Mustafa; Cates, Gordon; Chen, Chunhua; Chen, Jian-Ping; Choi, Seonho; Chudakov, Eugene; Cusanno, Francesco; Dalton, Mark; Deconinck, Wouter; De Jager, Cornelis; Deng, Xiaoyan; Deur, Alexandre; Dutta, Chiranjib; El Fassi, Lamiaa; Franklin, Gregg; Friend, Megan; Gao, Haiyan; Garibaldi, Franco; Gilad, Shalev; Gilman, Ronald; Glamazdin, Oleksandr; Golge, Serkan; Gomez, Javier; Guo, Lei; Hansen, Jens-Ole; Higinbotham, Douglas; Holmstrom, Timothy; Huang, J; Hyde, Charles; Ibrahim Abdalla, Hassan; Jiang, Xiaodong; Jin, Ge; Katich, Joseph; Kelleher, Aidan; Kolarkar, Ameya; Korsch, Wolfgang; Kumbartzki, Gerfried; LeRose, John; Lindgren, Richard; Liyanage, Nilanga; Long, Elena; Lukhanin, Oleksandr; Mamyan, Vahe; McNulty, Dustin; Meziani, Zein-Eddine; Michaels, Robert; Mihovilovic, Miha; Moffit, Bryan; Muangma, Navaphon; Nanda, Sirish; Narayan, Amrendra; Nelyubin, Vladimir; Norum, Blaine; Nuruzzaman, nfn; Oh, Yongseok; Peng, Jen-chieh; Qian, Xin; Qiang, Yi; Rakhman, Abdurahim; Riordan, Seamus; Saha, Arunava; Sawatzky, Bradley; Hashemi Shabestari, Mitra; Shahinyan, Albert; Sirca, Simon; Solvignon-Slifer, Patricia; Subedi, Ramesh; Sulkosky, Vincent; Tobias, William; Troth, Wolfgang; Wang, Diancheng; Wang, Y; Wojtsekhowski, Bogdan; Yan, X; Yao, Huan; Ye, Yunxiu; Ye, Zhihong; Yuan, Lulin; Zhan, X; Zhang, Y; Zhang, Y -W; Zhao, Bo; Zheng, Xiaochao
2014-07-01
Double-spin asymmetries and absolute cross sections were measured at large Bjorken x (0.25 lte x lte 0.90), in both the deep-inelastic and resonance regions, by scattering longitudinally polarized electrons at beam energies of 4.7 and 5.9 GeV from a transversely and longitudinally polarized 3He target. In this dedicated experiment, the spin structure function g2 on 3He was determined with precision at large x, and the neutron twist-three matrix element dn2 was measured at ?Q2? of 3.21 and 4.32 GeV2/c2, with an absolute precision of about 10?5. Our results are found to be in agreement with lattice QCD calculations and resolve the disagreement found with previous data at ?Q2?= 5 GeV2/c2. Combining dn2 and a newly extracted twist-four matrix element, fn2, the average neutron color electric and magnetic forces were extracted and found to be of opposite sign and about 60 MeV/fm in magnitude.
NASA Astrophysics Data System (ADS)
Komninos, Yannis; Mercouris, Theodoros; Nicolaides, Cleanthes A.
2017-01-01
The present study examines the mathematical properties of the free-free ( f - f) matrix elements of the full electric field operator, O E (κ, r̅), of the multipolar Hamiltonian. κ is the photon wavenumber. Special methods are developed and applied for their computation, for the general case where the scattering wavefunctions are calculated numerically in the potential of the term-dependent ( N - 1) electron core, and are energy-normalized. It is found that, on the energy axis, the f - f matrix elements of O E (κ, r̅) have singularities of first order, i.e., as ɛ' → ɛ, they behave as ( ɛ - ɛ')-1. The numerical applications are for f - f transitions in hydrogen and neon, obeying electric dipole and quadrupole selection rules. In the limit κ = 0, O E (κ, r̅) reduces to the length form of the electric dipole approximation (EDA). It is found that the results for the EDA agree with those of O E (κ, r̅), with the exception of a wave-number region k' = k ± κ about the point k' = k.
NASA Astrophysics Data System (ADS)
Monthus, Cécile
2016-07-01
For short-ranged disordered quantum models in one dimension, the many-body-localization is analyzed via the adaptation to the many-body context (Serbyn et al 2015 Phys. Rev. X 5 041047) of the Thouless point of view on the Anderson transition: the question is whether a local interaction between two long chains is able to reshuffle completely the eigenstates (delocalized phase with a volume-law entanglement) or whether the hybridization between tensor states remains limited (many-body-localized phase with an area-law entanglement). The central object is thus the level of hybridization induced by the matrix elements of local operators, as compared with the difference of diagonal energies. The multifractal analysis of these matrix elements of local operators is used to analyze the corresponding statistics of resonances. Our main conclusion is that the critical point is characterized by the strong-multifractality spectrum f(0≤slant α ≤slant 2)=\\fracα{2} , well known in the context of Anderson localization in spaces of effective infinite dimensionality, where the size of the Hilbert space grows exponentially with the volume. Finally, the possibility of a delocalized non-ergodic phase near criticality is discussed.
Symbolic algorithms for the computation of Moshinsky brackets and nuclear matrix elements
NASA Astrophysics Data System (ADS)
Ursescu, D.; Tomaselli, M.; Kuehl, T.; Fritzsche, S.
2005-12-01
To facilitate the use of the extended nuclear shell model (NSM), a FERMI module for calculating some of its basic quantities in the framework of MAPLE is provided. The Moshinsky brackets, the matrix elements for several central and non-central interactions between nuclear two-particle states as well as their expansion in terms of Talmi integrals are easily given within a symbolic formulation. All of these quantities are available for interactive work. Program summaryTitle of program:Fermi Catalogue identifier:ADVO Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVO Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:None Computer for which the program is designed and others on which is has been tested:All computers with a licence for the computer algebra package MAPLE [Maple is a registered trademark of Waterloo Maple Inc., produced by MapleSoft division of Waterloo Maple Inc.] Instalations:GSI-Darmstadt; University of Kassel (Germany) Operating systems or monitors under which the program has beentested: WindowsXP, Linux 2.4 Programming language used:MAPLE 8 and 9.5 from MapleSoft division of Waterloo Maple Inc. Memory required to execute with typical data:30 MB No. of lines in distributed program including test data etc.:5742 No. of bytes in distributed program including test data etc.:288 939 Distribution program:tar.gz Nature of the physical problem:In order to perform calculations within the nuclear shell model (NSM), a quick and reliable access to the nuclear matrix elements is required. These matrix elements, which arise from various types of forces among the nucleons, can be calculated using Moshinsky's transformation brackets between relative and center-of-mass coordinates [T.A. Brody, M. Moshinsky, Tables of Transformation Brackets, Monografias del Instituto de Fisica, Universidad Nacional Autonoma de Mexico, 1960] and by the proper use of the nuclear states in different coupling notations
Charge-exchange reactions and nuclear matrix elements for {beta}{beta} decay
Frekers, D.
2009-11-09
Charge-exchange reactions of (n, p) and (p, n) type at intermediate energies are a powerful tool for the study of nuclear matrix element in {beta}{beta} decay. The present paper reviews some of the most recent experiments in this context. Here, the (n, p) type reactions are realized through (d, {sup 2}He), where {sup 2}He refers to two protons in a singlet {sup 1}S{sub 0} state and where both of these are momentum analyzed and detected by the same spectrometer and detector. These reactions have been developed and performed exclusively at KVI, Groningen (NL), using an incident deuteron energy of 183 MeV. Final state resolutions of about 100 keV have routinely been available. On the other hand, the ({sup 3}He, t) reaction is of (p, n) type and was developed at the RCNP facility in Osaka (JP). Measurements with an unprecedented high resolution of 30 keV at incident energies of 420 MeV are now readily possible. Using both reaction types one can extract the Gamow-Teller transition strengths B(GT{sup +}) and B(GT{sup -}), which define the two ''legs'' of the {beta}{beta} decay matrix elements for the 2v{beta}{beta} decay The high resolution available in both reactions allows a detailed insight into the excitations of the intermediate odd-odd nuclei and, as will be shown, some unexpected features are being unveiled.
Top Quark Mass Measurement in the Lepton plus Jets Channel Using a Modified Matrix Element Method
Aaltonen, T.; Adelman, J.; Akimoto, T.; Alvarez Gonzalez, B.; Amerio, S.; Amidei, D.; Anastassov, A.; Annovi, A.; Antos, J.; Apollinari, G.; Apresyan, A.; /Purdue U. /Waseda U.
2008-12-01
The authors report a measurement of the top quark mass, m{sub t}, obtained from p{bar p} collisions at {radical}s = 1.96 TeV at the Fermilab Tevatron using the CDF II detector. They analyze a sample corresponding to an integrated luminosity of 1.9 rfb{sup -1}. They select events with an electron or muon, large missing transverse energy, and exactly four high-energy jets in the central region of the detector, at least one of which is tagged as coming from a b quark. They calculate a signal likelihood using a matrix element integration method, where the matrix element is modified by using effective propagators to take into account assumptions on event kinematics. The event likelihood is a function of m{sub t} and a parameter JES that determines in situ the calibration of the jet energies. They use a neural network discriminant to distinguish signal from background events. They also apply a cut on the peak value of each event likelihood curve to reduce the contribution of background and badly reconstructed events. Using the 318 events that pass all selection criteria, they find m{sub t} = 172.7 {+-} 1.8 (stat. + JES) {+-} 1.2(syst.) GeV/c{sup 2}.
Determination of color-octet matrix elements from e+e- processes at low energies
NASA Astrophysics Data System (ADS)
Yuan, Feng; Qiao, Cong-Feng; Chao, Kuang-Ta
1997-08-01
We present an analysis of the preliminary experimental data of direct J/ψ production in e+e- processes at low energies. We find that the color-octet contributions are crucially important to the cross section in this energy region, and their inclusion produces a good description of the data. By fitting to the data, we extract the individual values of two color-octet matrix elements:
The Sp(3, R) Sympletic Model: a comparison of exact and approximate matrix elements
NASA Astrophysics Data System (ADS)
McCoy, Anna; Caprio, Mark; Rowe, David
2014-03-01
The Sp(3, R) symplectic model has a close physical connection to both the microscopic shell model and the collective deformation and rotational degrees of freedom, and it is a natural extension of the Elliot SU(3) model from single-shell to multi-shell dynamics. The Sp(3, R) Lie algebra--which contains the angular momentum operators, the quadrupole and vibrational momentum operators and the quadrupole flow tensor operators--is the smallest algebra containing both the shell model Hamiltonian and the rotor algebra. In the limit of large number of oscillator quanta, the Sp(3, R) algebra contracts to the U(3) boson algebra. For large values of the Casimir operator of the SU(3) subalgebra, the sp(3, R) algebra further contracts to the algebra of the collective coupled rotor-vibrator model. The exact Sp(3, R) matrix elements, calculated using the vector coherent state method, are compared with approximate matrix elements calculated in the U(3) boson limit. Science Advancement under a Cottrell Scholar Award and by the US DOE under grant DE-FG02-95ER-40934.
Coulomb and spin-orbit interaction matrix elements in the ? configuration
NASA Astrophysics Data System (ADS)
Lo, Edwin
1998-11-01
The 0953-4075/31/21/006/img2 configuration is analysed in group-theoretical terms. Starting from the table given by Condon and Odabasi for the configuration 0953-4075/31/21/006/img2, we determine a set of convenient group-theoretical basis states, and rewrite the Coulomb matrix elements in terms of this new basis. Linear combinations from the different parts of the Coulomb operators are formed such that they have simple group transformation properties in our scheme. The sequence of groups that we use is 0953-4075/31/21/006/img4, where T denotes the isospin of Simonis et al, in which electrons with the same angular momentum l but different principal quantum numbers n are accommodated by introducing the eigenvalue 0953-4075/31/21/006/img5 of 0953-4075/31/21/006/img6. Using the Wigner-Eckart theorem and selection rules on the higher symmetry groups, the tables of the Coulomb and spin-orbit matrix elements for the reconstituted operators (with simple group transformation properties) are much simplified in terms of these basis states.
Top quark mass measurement in the lepton plus jets channel using a modified matrix element method
NASA Astrophysics Data System (ADS)
Aaltonen, T.; Adelman, J.; Akimoto, T.; González, B. Álvarez; Amerio, S.; Amidei, D.; Anastassov, A.; Annovi, A.; Antos, J.; Apollinari, G.; Apresyan, A.; Arisawa, T.; Artikov, A.; Ashmanskas, W.; Attal, A.; Aurisano, A.; Azfar, F.; Azzurri, P.; Badgett, W.; Barbaro-Galtieri, A.; Barnes, V. E.; Barnett, B. A.; Bartsch, V.; Bauer, G.; Beauchemin, P.-H.; Bedeschi, F.; Beecher, D.; Behari, S.; Bellettini, G.; Bellinger, J.; Benjamin, D.; Beretvas, A.; Beringer, J.; Bhatti, A.; Binkley, M.; Bisello, D.; Bizjak, I.; Blair, R. E.; Blocker, C.; Blumenfeld, B.; Bocci, A.; Bodek, A.; Boisvert, V.; Bolla, G.; Bortoletto, D.; Boudreau, J.; Boveia, A.; Brau, B.; Bridgeman, A.; Brigliadori, L.; Bromberg, C.; Brubaker, E.; Budagov, J.; Budd, H. S.; Budd, S.; Burke, S.; Burkett, K.; Busetto, G.; Bussey, P.; Buzatu, A.; Byrum, K. L.; Cabrera, S.; Calancha, C.; Campanelli, M.; Campbell, M.; Canelli, F.; Canepa, A.; Carls, B.; Carlsmith, D.; Carosi, R.; Carrillo, S.; Carron, S.; Casal, B.; Casarsa, M.; Castro, A.; Catastini, P.; Cauz, D.; Cavaliere, V.; Cavalli-Sforza, M.; Cerri, A.; Cerrito, L.; Chang, S. H.; Chen, Y. C.; Chertok, M.; Chiarelli, G.; Chlachidze, G.; Chlebana, F.; Cho, K.; Chokheli, D.; Chou, J. P.; Choudalakis, G.; Chuang, S. H.; Chung, K.; Chung, W. H.; Chung, Y. S.; Chwalek, T.; Ciobanu, C. I.; Ciocci, M. A.; Clark, A.; Clark, D.; Compostella, G.; Convery, M. E.; Conway, J.; Cordelli, M.; Cortiana, G.; Cox, C. A.; Cox, D. J.; Crescioli, F.; Almenar, C. Cuenca; Cuevas, J.; Culbertson, R.; Cully, J. C.; Dagenhart, D.; Datta, M.; Davies, T.; de Barbaro, P.; de Cecco, S.; Deisher, A.; de Lorenzo, G.; Dell'Orso, M.; Deluca, C.; Demortier, L.; Deng, J.; Deninno, M.; Derwent, P. F.; di Giovanni, G. P.; Dionisi, C.; di Ruzza, B.; Dittmann, J. R.; D'Onofrio, M.; Donati, S.; Dong, P.; Donini, J.; Dorigo, T.; Dube, S.; Efron, J.; Elagin, A.; Erbacher, R.; Errede, D.; Errede, S.; Eusebi, R.; Fang, H. C.; Farrington, S.; Fedorko, W. T.; Feild, R. G.; Feindt, M.; Fernandez, J. P.; Ferrazza, C.; Field, R.; Flanagan, G.; Forrest, R.; Frank, M. J.; Franklin, M.; Freeman, J. C.; Furic, I.; Gallinaro, M.; Galyardt, J.; Garberson, F.; Garcia, J. E.; Garfinkel, A. F.; Genser, K.; Gerberich, H.; Gerdes, D.; Gessler, A.; Giagu, S.; Giakoumopoulou, V.; Giannetti, P.; Gibson, K.; Gimmell, J. L.; Ginsburg, C. M.; Giokaris, N.; Giordani, M.; Giromini, P.; Giunta, M.; Giurgiu, G.; Glagolev, V.; Glenzinski, D.; Gold, M.; Goldschmidt, N.; Golossanov, A.; Gomez, G.; Gomez-Ceballos, G.; Goncharov, M.; González, O.; Gorelov, I.; Goshaw, A. T.; Goulianos, K.; Gresele, A.; Grinstein, S.; Grosso-Pilcher, C.; Group, R. C.; Grundler, U.; da Costa, J. Guimaraes; Gunay-Unalan, Z.; Haber, C.; Hahn, K.; Hahn, S. R.; Halkiadakis, E.; Han, B.-Y.; Han, J. Y.; Happacher, F.; Hara, K.; Hare, D.; Hare, M.; Harper, S.; Harr, R. F.; Harris, R. M.; Hartz, M.; Hatakeyama, K.; Hays, C.; Heck, M.; Heijboer, A.; Heinrich, J.; Henderson, C.; Herndon, M.; Heuser, J.; Hewamanage, S.; Hidas, D.; Hill, C. S.; Hirschbuehl, D.; Hocker, A.; Hou, S.; Houlden, M.; Hsu, S.-C.; Huffman, B. T.; Hughes, R. E.; Husemann, U.; Hussein, M.; Huston, J.; Incandela, J.; Introzzi, G.; Iori, M.; Ivanov, A.; James, E.; Jang, D.; Jayatilaka, B.; Jeon, E. J.; Jha, M. K.; Jindariani, S.; Johnson, W.; Jones, M.; Joo, K. K.; Jun, S. Y.; Jung, J. E.; Junk, T. R.; Kamon, T.; Kar, D.; Karchin, P. E.; Kato, Y.; Kephart, R.; Keung, J.; Khotilovich, V.; Kilminster, B.; Kim, D. H.; Kim, H. S.; Kim, H. W.; Kim, J. E.; Kim, M. J.; Kim, S. B.; Kim, S. H.; Kim, Y. K.; Kimura, N.; Kirsch, L.; Klimenko, S.; Knuteson, B.; Ko, B. R.; Kondo, K.; Kong, D. J.; Konigsberg, J.; Korytov, A.; Kotwal, A. V.; Kreps, M.; Kroll, J.; Krop, D.; Krumnack, N.; Kruse, M.; Krutelyov, V.; Kubo, T.; Kuhr, T.; Kulkarni, N. P.; Kurata, M.; Kwang, S.; Laasanen, A. T.; Lami, S.; Lammel, S.; Lancaster, M.; Lander, R. L.; Lannon, K.; Lath, A.; Latino, G.; Lazzizzera, I.; Lecompte, T.; Lee, E.; Lee, H. S.; Lee, S. W.; Leone, S.; Lewis, J. D.; Lin, C.-S.; Linacre, J.; Lindgren, M.; Lipeles, E.; Lister, A.; Litvintsev, D. O.; Liu, C.; Liu, T.; Lockyer, N. S.; Loginov, A.; Loreti, M.; Lovas, L.; Lucchesi, D.; Luci, C.; Lueck, J.; Lujan, P.; Lukens, P.; Lungu, G.; Lyons, L.; Lys, J.; Lysak, R.; MacQueen, D.; Madrak, R.; Maeshima, K.; Makhoul, K.; Maki, T.; Maksimovic, P.; Malde, S.; Malik, S.; Manca, G.; Manousakis-Katsikakis, A.; Margaroli, F.; Marino, C.; Marino, C. P.; Martin, A.; Martin, V.; Martínez, M.; Martínez-Ballarín, R.; Maruyama, T.; Mastrandrea, P.; Masubuchi, T.; Mathis, M.; Mattson, M. E.; Mazzanti, P.; McFarland, K. S.; McIntyre, P.; McNulty, R.; Mehta, A.; Mehtala, P.; Menzione, A.; Merkel, P.; Mesropian, C.; Miao, T.; Miladinovic, N.; Miller, R.; Mills, C.; Milnik, M.; Mitra, A.; Mitselmakher, G.; Miyake, H.; Moggi, N.; Moon, C. S.; Moore, R.; Morello, M. J.; Morlock, J.; Fernandez, P. Movilla; Mülmenstädt, J.; Mukherjee, A.; Muller, Th.; Mumford, R.; Murat, P.; Mussini, M.; Nachtman, J.; Nagai, Y.; Nagano, A.; Naganoma, J.; Nakamura, K.; Nakano, I.; Napier, A.; Necula, V.; Nett, J.; Neu, C.; Neubauer, M. S.; Neubauer, S.; Nielsen, J.; Nodulman, L.; Norman, M.; Norniella, O.; Nurse, E.; Oakes, L.; Oh, S. H.; Oh, Y. D.; Oksuzian, I.; Okusawa, T.; Orava, R.; Osterberg, K.; Griso, S. Pagan; Palencia, E.; Papadimitriou, V.; Papaikonomou, A.; Paramonov, A. A.; Parks, B.; Pashapour, S.; Patrick, J.; Pauletta, G.; Paulini, M.; Paus, C.; Peiffer, T.; Pellett, D. E.; Penzo, A.; Phillips, T. J.; Piacentino, G.; Pianori, E.; Pinera, L.; Pitts, K.; Plager, C.; Pondrom, L.; Poukhov, O.; Pounder, N.; Prakoshyn, F.; Pronko, A.; Proudfoot, J.; Ptohos, F.; Pueschel, E.; Punzi, G.; Pursley, J.; Rademacker, J.; Rahaman, A.; Ramakrishnan, V.; Ranjan, N.; Redondo, I.; Renton, P.; Renz, M.; Rescigno, M.; Richter, S.; Rimondi, F.; Ristori, L.; Robson, A.; Rodrigo, T.; Rodriguez, T.; Rogers, E.; Rolli, S.; Roser, R.; Rossi, M.; Rossin, R.; Roy, P.; Ruiz, A.; Russ, J.; Rusu, V.; Saarikko, H.; Safonov, A.; Sakumoto, W. K.; Saltó, O.; Santi, L.; Sarkar, S.; Sartori, L.; Sato, K.; Savoy-Navarro, A.; Schlabach, P.; Schmidt, A.; Schmidt, E. E.; Schmidt, M. A.; Schmidt, M. P.; Schmitt, M.; Schwarz, T.; Scodellaro, L.; Scribano, A.; Scuri, F.; Sedov, A.; Seidel, S.; Seiya, Y.; Semenov, A.; Sexton-Kennedy, L.; Sforza, F.; Sfyrla, A.; Shalhout, S. Z.; Shears, T.; Shepard, P. F.; Shimojima, M.; Shiraishi, S.; Shochet, M.; Shon, Y.; Shreyber, I.; Sidoti, A.; Siegrist, J.; Sinervo, P.; Sisakyan, A.; Slaughter, A. J.; Slaunwhite, J.; Sliwa, K.; Smith, J. R.; Snider, F. D.; Snihur, R.; Soha, A.; Somalwar, S.; Sorin, V.; Spalding, J.; Spreitzer, T.; Squillacioti, P.; Stanitzki, M.; St. Denis, R.; Stelzer, B.; Stelzer-Chilton, O.; Stentz, D.; Strologas, J.; Strycker, G. L.; Stuart, D.; Suh, J. S.; Sukhanov, A.; Suslov, I.; Suzuki, T.; Taffard, A.; Takashima, R.; Takeuchi, Y.; Tanaka, R.; Tecchio, M.; Teng, P. K.; Terashi, K.; Thom, J.; Thompson, A. S.; Thompson, G. A.; Thomson, E.; Tipton, P.; Ttito-Guzmán, P.; Tkaczyk, S.; Toback, D.; Tokar, S.; Tollefson, K.; Tomura, T.; Tonelli, D.; Torre, S.; Torretta, D.; Totaro, P.; Tourneur, S.; Trovato, M.; Tsai, S.-Y.; Tu, Y.; Turini, N.; Ukegawa, F.; Vallecorsa, S.; van Remortel, N.; Varganov, A.; Vataga, E.; Vázquez, F.; Velev, G.; Vellidis, C.; Vidal, M.; Vidal, R.; Vila, I.; Vilar, R.; Vine, T.; Vogel, M.; Volobouev, I.; Volpi, G.; Wagner, P.; Wagner, R. G.; Wagner, R. L.; Wagner, W.; Wagner-Kuhr, J.; Wakisaka, T.; Wallny, R.; Wang, S. M.; Warburton, A.; Waters, D.; Weinberger, M.; Weinelt, J.; Wester, W. C., III; Whitehouse, B.; Whiteson, D.; Wicklund, A. B.; Wicklund, E.; Wilbur, S.; Williams, G.; Williams, H. H.; Wilson, P.; Winer, B. L.; Wittich, P.; Wolbers, S.; Wolfe, C.; Wright, T.; Wu, X.; Würthwein, F.; Xie, S.; Yagil, A.; Yamamoto, K.; Yamaoka, J.; Yang, U. K.; Yang, Y. C.; Yao, W. M.; Yeh, G. P.; Yoh, J.; Yorita, K.; Yoshida, T.; Yu, G. B.; Yu, I.; Yu, S. S.; Yun, J. C.; Zanello, L.; Zanetti, A.; Zhang, X.; Zheng, Y.; Zucchelli, S.
2009-04-01
We report a measurement of the top quark mass, mt, obtained from p pmacr collisions at s=1.96TeV at the Fermilab Tevatron using the CDF II detector. We analyze a sample corresponding to an integrated luminosity of 1.9fb-1. We select events with an electron or muon, large missing transverse energy, and exactly four high-energy jets in the central region of the detector, at least one of which is tagged as coming from a b quark. We calculate a signal likelihood using a matrix element integration method, where the matrix element is modified by using effective propagators to take into account assumptions on event kinematics. Our event likelihood is a function of mt and a parameter JES (jet energy scale) that determines in situ the calibration of the jet energies. We use a neural network discriminant to distinguish signal from background events. We also apply a cut on the peak value of each event likelihood curve to reduce the contribution of background and badly reconstructed events. Using the 318 events that pass all selection criteria, we find mt=172.7±1.8(stat+JES)±1.2(syst)GeV/c2.
Quantum Monte Carlo with density matrix: potential energy curve derived properties.
Bonfim, Víctor S; Borges, Nádia M; Martins, João B L; Gargano, Ricardo; Politi, José Roberto Dos S
2017-04-01
In this work, we used diffusion quantum Monte Carlo with density matrix (d-DMC) and variational quantum Monte Carlo (d-VMC) to determine the potential energy curve (PEC) and obtain the spectroscopic constants of H2 molecule in the ground state, in order to evaluate the capability of these methods to provide an accurate PEC description. These quantum Monte Carlo methods build with density matrix are new approaches to conventional quantum Monte Carlo methods based on wave function formed by product of α and β determinants. To investigate the robustness of d-DMC, we performed calculations with two different basis sets and analyzed the influence of the size of these sets on results. To the best of our knowledge, this is the first study that shows the dissociation energy and rotational constant obtained from d-QMC. We found that the quality of PEC described by the d-DMC is essentially coincident with the most accurate results available in the literature, regardless of the complexity of basis set employed.
Leptogenesis with heavy neutrino flavours: from density matrix to Boltzmann equations
Blanchet, Steve; Bari, Pasquale Di; Jones, David A.; Marzola, Luca E-mail: pdb1d08@soton.ac.uk E-mail: daj1g08@soton.ac.uk
2013-01-01
Leptogenesis with heavy neutrino flavours is discussed within a density matrix formalism. We write the density matrix equation, describing the generation of the matter-antimatter asymmetry, for an arbitrary choice of the right-handed (RH) neutrino masses. For hierarchical RH neutrino masses lying in the fully flavoured regimes, this reduces to multiple-stage Boltzmann equations. In this case we recover and extend results previously derived within a quantum state collapse description. We confirm the generic existence of phantom terms. However, taking into account the effect of gauge interactions, we show that they are washed out at the production with a wash-out rate that is halved compared to that one acting on the total asymmetry. In the N{sub 1}-dominated scenario they cancel without contributing to the final baryon asymmetry. In other scenarios they do not in general and they have to be taken into account. We also confirm that there is a (orthogonal) component in the asymmetry produced by the heavier RH neutrinos which completely escapes the washout from the lighter RH neutrinos and show that phantom terms additionally contribute to it. The other (parallel) component is washed out with the usual exponential factor, even for weak washout. Finally, as an illustration, we study the two RH neutrino model in the light of the above findings, showing that phantom terms can contribute to the final asymmetry also in this case.
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.
Effects of Extracellular Matrix Density and Mesenchymal Stem Cells on Neovascularization In Vivo
Kniazeva, Ekaterina; Kachgal, Suraj
2011-01-01
Aberrant angiogenesis is common to a variety of diseases in which alterations in tissue mechanical properties also occur. A fundamental understanding of the interdependence of angiogenesis and tissue structural properties may enhance the development of therapeutic strategies. We previously established that increasing extracellular matrix density inhibits capillary morphogenesis in three-dimensional tissues in vitro, and that addition of human mesenchymal stem cells (MSCs) partially rescues a healthy angiogenic phenotype. This study's goal was to investigate if these effects can be recapitulated in vivo. Human umbilical vein endothelial cells, MSCs, or a mixture of both was suspended in fibrin gel precursor solutions of 5, 10, and 15 mg/mL concentrations and injected subcutaneously into SCID mice. Neovascularization was assessed in tissue constructs retrieved at 3, 7, and 21 days by quantifying vessel numbers, perfusion, thickness, maturity, and perivascular collagen deposition. The data show that changing extracellular matrix density inhibits capillary morphogenesis in vivo in a manner consistent with that observed in vitro. Delivery of both human umbilical vein endothelial cells and MSCs produced more robust and mature vessels than delivery of either cell type alone in all tissue concentrations. PMID:20979533
The reduced density matrix method and the role of three-index representability conditions
NASA Astrophysics Data System (ADS)
Braams, Bastiaan J.; Zhao, Zhengji; Fukuda, Mituhiro; Overton, Michael L.; Percus, Jerome K.
2004-03-01
The variational approach for electronic structure based on the two-body reduced density matrix is studied, incorporating two representability conditions beyond the previously used P, Q and G conditions. The additional conditions (called T1 and T2 here) are implicit in work of R. M. Erdahl and extend the well-known three-index diagonal conditions also known as the Weinhold-Wilson inequalities. Calculations of the ground state energy and the dipole moment are reported for 47 different systems, in each case using an STO-6G basis set and comparing with Hartree-Fock, SDCI, BD(T), CCSD(T) and full CI calculations [2]. It is found that the use of the T1 and T2 conditions gives a significant improvement over just the P, Q and G conditions, and provides in all cases that we have studied more accurate results than the other mentioned approximations. [1] R. M. Erdahl, Int. J. Quantum Chem. 13, 697--718 (1978). [2] Zhengji Zhao, Bastiaan J. Braams, Mituhiro Fukuda, Michael L. Overton and Jerome K. Percus: "The reduced density matrix method and the role of three-index representability conditions". Accepted for publication in Journal of Chemical Physics.
Low excitations of 16O using generalized density matrix random phase approximation GDRPA
NASA Astrophysics Data System (ADS)
Taqi, Ali H.; Radhi, R. A.; Hussein, Adil M.
2014-07-01
The random phase approximation (RPA) equations based on the generalized density matrix (GDM), the so-called GDRPA are reformulated in a more compact matrix form, which renders the method especially suitable for realistic nuclear structure calculations. The GDRPA Hamiltonian is expressed in terms of the one-body particle-particle (pp) and hole-hole (hh) density matrices, and the nuclear force contributes not only in the particle-hole (ph) channel, as in normal ph-RPA, but also in the pp and hh channels. The Hamiltonian is diagonalized iteratively starting from initial guess values and the iterating process is carried out until self-consistency is achieved. The calculation in the model space 1p, 1d and 2s using Warburton and Brown interaction WBP is performed for 16O. The GDRPA in the ph shell model calculations is tested, by comparing the energy eigenvalues and the electron scattering form factors with the results of the normal RPA and with the available experimental data.
Leptogenesis with heavy neutrino flavours: from density matrix to Boltzmann equations
NASA Astrophysics Data System (ADS)
Blanchet, Steve; Di Bari, Pasquale; Jones, David A.; Marzola, Luca
2013-01-01
Leptogenesis with heavy neutrino flavours is discussed within a density matrix formalism. We write the density matrix equation, describing the generation of the matter-antimatter asymmetry, for an arbitrary choice of the right-handed (RH) neutrino masses. For hierarchical RH neutrino masses lying in the fully flavoured regimes, this reduces to multiple-stage Boltzmann equations. In this case we recover and extend results previously derived within a quantum state collapse description. We confirm the generic existence of phantom terms. However, taking into account the effect of gauge interactions, we show that they are washed out at the production with a wash-out rate that is halved compared to that one acting on the total asymmetry. In the N1-dominated scenario they cancel without contributing to the final baryon asymmetry. In other scenarios they do not in general and they have to be taken into account. We also confirm that there is a (orthogonal) component in the asymmetry produced by the heavier RH neutrinos which completely escapes the washout from the lighter RH neutrinos and show that phantom terms additionally contribute to it. The other (parallel) component is washed out with the usual exponential factor, even for weak washout. Finally, as an illustration, we study the two RH neutrino model in the light of the above findings, showing that phantom terms can contribute to the final asymmetry also in this case.
A state interaction spin-orbit coupling density matrix renormalization group method.
Sayfutyarova, Elvira R; Chan, Garnet Kin-Lic
2016-06-21
We describe a state interaction spin-orbit (SISO) coupling method using density matrix renormalization group (DMRG) wavefunctions and the spin-orbit mean-field (SOMF) operator. We implement our DMRG-SISO scheme using a spin-adapted algorithm that computes transition density matrices between arbitrary matrix product states. To demonstrate the potential of the DMRG-SISO scheme we present accurate benchmark calculations for the zero-field splitting of the copper and gold atoms, comparing to earlier complete active space self-consistent-field and second-order complete active space perturbation theory results in the same basis. We also compute the effects of spin-orbit coupling on the spin-ladder of the iron-sulfur dimer complex [Fe2S2(SCH3)4](3-), determining the splitting of the lowest quartet and sextet states. We find that the magnitude of the zero-field splitting for the higher quartet and sextet states approaches a significant fraction of the Heisenberg exchange parameter.
Metal-insulator transition in disordered systems from the one-body density matrix
NASA Astrophysics Data System (ADS)
Olsen, Thomas; Resta, Raffaele; Souza, Ivo
2017-01-01
The insulating state of matter can be probed by means of a ground state geometrical marker, which is closely related to the modern theory of polarization (based on a Berry phase). In the present work we show that this marker can be applied to determine the metal-insulator transition in disordered systems. In particular, for noninteracting systems the geometrical marker can be obtained from the configurational average of the norm-squared one-body density matrix, which can be calculated within open as well as periodic boundary conditions. This is in sharp contrast to a classification based on the static conductivity, which is only sensible within periodic boundary conditions. We exemplify the method by considering a simple lattice model, known to have a metal-insulator transition as a function of the disorder strength, and demonstrate that the transition point can be obtained accurately from the one-body density matrix. The approach has a general ab initio formulation and could in principle be applied to realistic disordered materials by standard electronic structure methods.
Measurement of the top quark mass in the dilepton final state using the matrix element method
Grohsjean, Alexander
2008-12-15
The top quark, discovered in 1995 by the CDF and D0 experiments at the Fermilab Tevatron Collider, is the heaviest known fundamental particle. The precise knowledge of its mass yields important constraints on the mass of the yet-unobserved Higgs boson and allows to probe for physics beyond the Standard Model. The first measurement of the top quark mass in the dilepton channel with the Matrix Element method at the D0 experiment is presented. After a short description of the experimental environment and the reconstruction chain from hits in the detector to physical objects, a detailed review of the Matrix Element method is given. The Matrix Element method is based on the likelihood to observe a given event under the assumption of the quantity to be measured, e.g. the mass of the top quark. The method has undergone significant modifications and improvements compared to previous measurements in the lepton+jets channel: the two undetected neutrinos require a new reconstruction scheme for the four-momenta of the final state particles, the small event sample demands the modeling of additional jets in the signal likelihood, and a new likelihood is designed to account for the main source of background containing tauonic Z decay. The Matrix Element method is validated on Monte Carlo simulated events at the generator level. For the measurement, calibration curves are derived from events that are run through the full D0 detector simulation. The analysis makes use of the Run II data set recorded between April 2002 and May 2008 corresponding to an integrated luminosity of 2.8 fb^{-1}. A total of 107 t$\\bar{t}$ candidate events with one electron and one muon in the final state are selected. Applying the Matrix Element method to this data set, the top quark mass is measured to be m_{top}^{Run IIa} = 170.6 ± 6.1(stat.)_{-1.5}^{+2.1}(syst.)GeV; m_{top}^{Run IIb} = 174.1 ± 4.4(stat.)_{-1.8}^{+2.5}(syst.)GeV; m
Shamloo, Amir; Mohammadaliha, Negar; Heilshorn, Sarah C; Bauer, Amy L
2016-04-01
A thorough understanding of determining factors in angiogenesis is a necessary step to control the development of new blood vessels. Extracellular matrix density is known to have a significant influence on cellular behaviors and consequently can regulate vessel formation. The utilization of experimental platforms in combination with numerical models can be a powerful method to explore the mechanisms of new capillary sprout formation. In this study, using an integrative method, the interplay between the matrix density and angiogenesis was investigated. Owing the fact that the extracellular matrix density is a global parameter that can affect other parameters such as pore size, stiffness, cell-matrix adhesion and cross-linking, deeper understanding of the most important biomechanical or biochemical properties of the ECM causing changes in sprout morphogenesis is crucial. Here, we implemented both computational and experimental methods to analyze the mechanisms responsible for the influence of ECM density on the sprout formation that is difficult to be investigated comprehensively using each of these single methods. For this purpose, we first utilized an innovative approach to quantify the correspondence of the simulated collagen fibril density to the collagen density in the experimental part. Comparing the results of the experimental study and computational model led to some considerable achievements. First, we verified the results of the computational model using the experimental results. Then, we reported parameters such as the ratio of proliferating cells to migrating cells that was difficult to obtain from experimental study. Finally, this integrative system led to gain an understanding of the possible mechanisms responsible for the effect of ECM density on angiogenesis. The results showed that stable and long sprouts were observed at an intermediate collagen matrix density of 1.2 and 1.9 mg/ml due to a balance between the number of migrating and proliferating
Lehtovaara, Lauri; Havu, Ville; Puska, Martti
2009-08-07
We present for static density functional theory and time-dependent density functional theory calculations an all-electron method which employs high-order hierarchical finite-element bases. Our mesh generation scheme, in which structured atomic meshes are merged to an unstructured molecular mesh, allows a highly nonuniform discretization of the space. Thus it is possible to represent the core and valence states using the same discretization scheme, i.e., no pseudopotentials or similar treatments are required. The nonuniform discretization also allows the use of large simulation cells, and therefore avoids any boundary effects.
ERIC Educational Resources Information Center
Arnold, Randy J.; Arndt, Brett; Blaser, Emilia; Blosser, Chris; Caulton, Dana; Chung, Won Sog; Fiorenza, Garrett; Heath, Wyatt; Jacobs, Alex; Kahng, Eunice; Koh, Eun; Le, Thao; Mandla, Kyle; McCory, Chelsey; Newman, Laura; Pithadia, Amit; Reckelhoff, Anna; Rheinhardt, Joseph; Skljarevski, Sonja; Stuart, Jordyn; Taylor, Cassie; Thomas, Scott; Tse, Kyle; Wall, Rachel; Warkentien, Chad
2011-01-01
A multivitamin tablet and liquid are analyzed for the elements calcium, magnesium, iron, zinc, copper, and manganese using atomic absorption spectrometry. Linear calibration and standard addition are used for all elements except calcium, allowing for an estimate of the matrix effects encountered for this complex sample. Sample preparation using…
ERIC Educational Resources Information Center
Arnold, Randy J.; Arndt, Brett; Blaser, Emilia; Blosser, Chris; Caulton, Dana; Chung, Won Sog; Fiorenza, Garrett; Heath, Wyatt; Jacobs, Alex; Kahng, Eunice; Koh, Eun; Le, Thao; Mandla, Kyle; McCory, Chelsey; Newman, Laura; Pithadia, Amit; Reckelhoff, Anna; Rheinhardt, Joseph; Skljarevski, Sonja; Stuart, Jordyn; Taylor, Cassie; Thomas, Scott; Tse, Kyle; Wall, Rachel; Warkentien, Chad
2011-01-01
A multivitamin tablet and liquid are analyzed for the elements calcium, magnesium, iron, zinc, copper, and manganese using atomic absorption spectrometry. Linear calibration and standard addition are used for all elements except calcium, allowing for an estimate of the matrix effects encountered for this complex sample. Sample preparation using…
Kajzer-Bonk, Joanna; Skórka, Piotr; Nowicki, Piotr; Bonk, Maciej; Król, Wiesław; Szpiłyk, Damian; Woyciechowski, Michal
2016-01-01
The type of matrix, the landscape surrounding habitat patches, may determine the distribution and function of local populations. However, the matrix is often heterogeneous, and its various components may differentially contribute to metapopulation processes at different spatial scales, a phenomenon that has rarely been investigated. The aim of this study was to estimate the relative importance of matrix composition and spatial scale, habitat quality, and management intensity on the occurrence and density of local populations of two endangered large blue butterflies: Phengaris teleius and P. nausithous. Presence and abundance data were assessed over two years, 2011-12, in 100 local patches within two heterogeneous regions (near Kraków and Tarnów, southern Poland). The matrix composition was analyzed at eight spatial scales. We observed high occupancy rates in both species, regions and years. With the exception of area and isolation, almost all of the matrix components contributed to Phengaris sp. densities. The different matrix components acted at different spatial scales (grassland cover within 4 and 3 km, field cover within 0.4 and 0.3 km and water cover within 4 km radii for P. teleius and P. nausithous, respectively) and provided the highest independent contribution to the butterfly densities. Additionally, the effects of a 0.4 km radius of forest cover and a food plant cover on P. teleius, and a 1 km radius of settlement cover and management intensity on P. nausithous densities were observed. Contrary to former studies we conclude that the matrix heterogeneity and spatial scale rather than general matrix type are of relevance for densities of butterflies. Conservation strategies for these umbrella species should concentrate on maintaining habitat quality and managing matrix composition at the most appropriate spatial scales.
Skórka, Piotr; Nowicki, Piotr; Bonk, Maciej; Król, Wiesław; Szpiłyk, Damian; Woyciechowski, Michal
2016-01-01
The type of matrix, the landscape surrounding habitat patches, may determine the distribution and function of local populations. However, the matrix is often heterogeneous, and its various components may differentially contribute to metapopulation processes at different spatial scales, a phenomenon that has rarely been investigated. The aim of this study was to estimate the relative importance of matrix composition and spatial scale, habitat quality, and management intensity on the occurrence and density of local populations of two endangered large blue butterflies: Phengaris teleius and P. nausithous. Presence and abundance data were assessed over two years, 2011–12, in 100 local patches within two heterogeneous regions (near Kraków and Tarnów, southern Poland). The matrix composition was analyzed at eight spatial scales. We observed high occupancy rates in both species, regions and years. With the exception of area and isolation, almost all of the matrix components contributed to Phengaris sp. densities. The different matrix components acted at different spatial scales (grassland cover within 4 and 3 km, field cover within 0.4 and 0.3 km and water cover within 4 km radii for P. teleius and P. nausithous, respectively) and provided the highest independent contribution to the butterfly densities. Additionally, the effects of a 0.4 km radius of forest cover and a food plant cover on P. teleius, and a 1 km radius of settlement cover and management intensity on P. nausithous densities were observed. Contrary to former studies we conclude that the matrix heterogeneity and spatial scale rather than general matrix type are of relevance for densities of butterflies. Conservation strategies for these umbrella species should concentrate on maintaining habitat quality and managing matrix composition at the most appropriate spatial scales. PMID:28005942
Mabry, Karen, E.; Dreelin, Erin, A.; Barrett, Gary, W.
2003-01-01
Mabry, K.E., E.A. Dreelin, and G.W. Barrett. 2003. Influence of landscape elements on population densities and habitat use of three small-mammal species. J. Mammology. 84(1):20-25. Corridor effects on population densities and habitat use of 3 small mammal species were assessed in an experimentally fragmented landscape. Corridor presence did not have a statistically significant effect on population densities of cotton rats or cotton mice; however, a significant effect was observed for old-field mice. The results suggest that landscape fragmentation and habitat structure may have varying effects on population densities of different species.
Measurement of the RMS Parity Violating Matrix Element in URANIUM-239
NASA Astrophysics Data System (ADS)
Zhu, Xianzhou (Joe).
We report the first determination of the Root -Mean-Square (RMS) parity violating matrix element in a compound nucleus (CN) system, ^{239 }U. The experiment was performed using the intense pulsed epithermal neutron beam available at the Los Alamos Neutron Scattering Center (LANSCE). The helicity dependence of neutron transmission through a spin zero target (^{238}U) is measured for neutron energies from 6 eV to 300 eV. Parity violation is analyzed on 17 p-wave resonances among which five show 2sigma or larger effects. The largest is a 7sigma effect at the 63.5 eV resonance which shows a parity violating asymmetry of p = 2.6%. A likelihood analysis is performed on these 17 parity violating asymmetries, and the RMS parity violating matrix element is determined for the first time to be M = 0.59_sp{-0.25}{+0.50} meV which corresponds to a parity violating spreading width ofGamma^{PV} = (1.0 {+1.7atop -0.8} ) times 10^{-7} {rm eV}.Using statistical nuclear spectroscopy, we are able to relate M to the effective nucleon-nucleon (NN) interaction. The result is | alpha_{p}| ~ (4 {+4atop -2} ) times 10^{-7} where alpha_{p} is the ratio of the parity violating strength to the parity conserving strength in the effective NN interaction. This agrees qualitatively with the estimate of free NN interaction. The consistency of the experimental measurement with expectation suggests that the manifestation of parity violating NN interaction in CN is understood. It is a challenging problem for the theorists to relate the RMS matrix element in the CN to the underlying NN interaction, therefore providing alternative ways to determine the Desplanques -Donoghue-Holstein (DDH) parameters of the NN interaction. The success of the parity violation study also validates the proposed experiment of studying the time reversal symmetry violation utilizing the large enhancement in the CN.
Webster, Duncan; Schulte, Friederike A; Lambers, Floor M; Kuhn, Gisela; Müller, Ralph
2015-03-18
Huiskes et al. hypothesized that mechanical strains sensed by osteocytes residing in trabecular bone dictate the magnitude of load-induced bone formation. More recently, the mechanical environment in bone marrow has also been implicated in bone׳s response to mechanical stimulation. In this study, we hypothesize that trabecular load-induced bone formation can be predicted by mechanical signals derived from an integrative µFE model, incorporating a description of both the bone and marrow phase. Using the mouse tail loading model in combination with in vivo micro-computed tomography (µCT) we tracked load induced changes in the sixth caudal vertebrae of C57BL/6 mice to quantify the amount of newly mineralized and eroded bone volumes. To identify the mechanical signals responsible for adaptation, local morphometric changes were compared to micro-finite element (µFE) models of vertebrae prior to loading. The mechanical parameters calculated were strain energy density (SED) on trabeculae at bone forming and resorbing surfaces, SED in the marrow at the boundary between bone forming and resorbing surfaces, along with SED in the trabecular bone and marrow volumes. The gradients of each parameter were also calculated. Simple regression analysis showed mean SED gradients in the trabecular bone matrix to significantly correlate with newly mineralized and eroded bone volumes R(2)=0.57 and 0.41, respectively, p<0.001). Nevertheless, SED gradients in the marrow were shown to be the best predictor of osteoblastic and osteoclastic activity (R(2)=0.83 and 0.60, respectively, p<0.001). These data suggest that the mechanical environment of the bone marrow plays a significant role in determining osteoblast and osteoclast activity.
Johnson, Christopher D; Worrall, Fred
2007-06-01
This paper reports the preparation and properties of a new low density granular absorbent material based on a zeolite/vermiculite composite. The composite prepared addresses a number of important issues relating to the use of zeolites in environmental and waste management applications. The material prepared has large particle size due to binderless adhesion of zeolite crystals within the protective lamellar matrix provided by the vermiculite granule. Additionally, the porous nature of new material ensures that it outperforms natural zeolite grains in ion-exchange tests. The material was shown to have a low bulk density (0.75 g cm(-3)) adding the benefit that the majority of grains float on water for over 15 h. The conclusion of the study is that the use of composite matrices enable the preparation of materials which show the physical properties of the host, (e.g., granular and low density), whilst maintaining the powder-like properties (e.g., high ion-exchange and small crystal size) of the active component. The resulting material can be easily handled and separated from aqueous waste streams using either flotation or exploiting its granular nature.
NASA Astrophysics Data System (ADS)
Putaja, A.; Eich, F. G.; Baldsiefen, T.; Räsänen, E.
2016-03-01
Physically valid and numerically efficient approximations for the exchange and correlation energy are critical for reduced-density-matrix-functional theory to become a widely used method in electronic structure calculations. Here we examine the physical limits of power functionals of the form f (n ,n') =(nn')α for the scaling function in the exchange-correlation energy. To this end we obtain numerically the minimizing momentum distributions for the three- and two-dimensional homogeneous electron gas, respectively. In particular, we examine the limiting values for the power α to yield physically sound solutions that satisfy the Lieb-Oxford lower bound for the exchange-correlation energy and exclude pinned states with the condition n (k )<1 for all wave vectors k . The results refine the constraints previously obtained from trial momentum distributions. We also compute the values for α that yield the exact correlation energy and its kinetic part for both the three- and two-dimensional electron gas. In both systems, narrow regimes of validity and accuracy are found at α ≳0.6 and at rs≳10 for the density parameter, corresponding to relatively low densities.
[Atomic volume, packing density of the atoms, and chemical bonds in nonmetallic elements].
Trömel, M
2007-08-01
The atomic volume of crystalline elements is largely determined by the packing density of atoms in the respective modification. The determination of packing density is improved by assuming that the atomic distances depend on bond valences according to Pauling's equation. With the additional assumption of equal valence in different modifications, the experimental atomic volume of an element in any given structure is reduced to its volume in close-packed structures, e.g. f.c.c. The ratio of this reduced atomic volume and the experimental atomic volume is a measure of packing density. Reduced atomic volumes of C, Si, Ge, P, As, S and Se, as calculated from different modifications, correspond in most cases to within less than +/-1% for each element, even if calculated from extremely different structures like diamond and buckminsterfullerene in the case of carbon, or from numerous modifications of sulfur with annular molecules of different sizes. Exceptions (graphite, white phosphorus, tin and selenium) indicate deviating valences.
Cwik, T.; Jamnejad, V.; Zuffada, C.
1994-12-31
The usefulness of finite element modeling follows from the ability to accurately simulate the geometry and three-dimensional fields on the scale of a fraction of a wavelength. To make this modeling practical for engineering design, it is necessary to integrate the stages of geometry modeling and mesh generation, numerical solution of the fields-a stage heavily dependent on the efficient use of a sparse matrix equation solver, and display of field information. The stages of geometry modeling, mesh generation, and field display are commonly completed using commercially available software packages. Algorithms for the numerical solution of the fields need to be written for the specific class of problems considered. Interior problems, i.e. simulating fields in waveguides and cavities, have been successfully solved using finite element methods. Exterior problems, i.e. simulating fields scattered or radiated from structures, are more difficult to model because of the need to numerically truncate the finite element mesh. To practically compute a solution to exterior problems, the domain must be truncated at some finite surface where the Sommerfeld radiation condition is enforced, either approximately or exactly. Approximate methods attempt to truncate the mesh using only local field information at each grid point, whereas exact methods are global, needing information from the entire mesh boundary. In this work, a method that couples three-dimensional finite element (FE) solutions interior to the bounding surface, with an efficient integral equation (IE) solution that exactly enforces the Sommerfeld radiation condition is developed. The bounding surface is taken to be a surface of revolution (SOR) to greatly reduce computational expense in the IE portion of the modeling.
Influence of Pairing on the Nuclear Matrix Elements of the Neutrinoless {beta}{beta} Decays
Caurier, E.; Nowacki, F.
2008-02-08
We study in this Letter the neutrinoless double beta decay nuclear matrix elements (NME's) in the framework of the interacting shell model. We analyze them in terms of the total angular momentum of the decaying neutron pair and as a function of the seniority truncations in the nuclear wave functions. This point of view turns out to be very adequate to gauge the accuracy of the NME's predicted by different nuclear models. In addition, it gives back the protagonist role in this process to the pairing interaction, the one which is responsible for the very existence of double beta decay emitters. We show that low seniority approximations, comparable to those implicit in the quasiparticle RPA in a spherical basis, tend to overestimate the NME's in several decays.
Lattice QCD calculation of the proton decay matrix element in the continuum limit
Tsutsui, N.; Hashimoto, S.; Kaneko, T.; Kuramashi, Y.; Aoki, S.; Kanaya, K.; Taniguchi, Y.; Fukugita, M.; Ishikawa, K-I.; Okawa, M.; Ishizuka, N.; Iwasaki, Y.; Ukawa, A.; Yoshie, T.; Onogi, T.
2004-12-01
We present a quenched lattice QCD calculation of the {alpha} and {beta} parameters of the proton decay matrix element. The simulation is carried out using the Wilson quark action at three values of the lattice spacing in the range a{approx_equal}0.1-0.064 fm to study the scaling violation effect. We find only mild scaling violation when the lattice scale is determined by the nucleon mass. We obtain in the continuum limit, vertical bar {alpha}(NDR,2 GeV) vertical bar=0.0090(09)(+5-19) GeV{sup 3} and vertical bar{beta}(NDR,2 GeV)vertical bar=0.0096(09)(+6-20) GeV{sup 3} with {alpha} and {beta} in a relatively opposite sign, where the first error is statistical and the second is due to the uncertainty in the determination of the physical scale.
The Matrix Element Method at the LHC: status and prospects for Run II
NASA Astrophysics Data System (ADS)
Wertz, Sébastien
2016-10-01
The Matrix Element Method (MEM) is a powerful multivariate method allowing to maximally exploit the experimental and theoretical information available to an analysis. Applications of the MEM at LHC experiments are discussed, such as searches for rare processes and measurements of properties of the Standard Model Higgs boson. The MadWeight software, allowing for a fast and automated computation of MEM weights for any user- specified process, is briefly reviewed. A new implementation of the MEM in the C++ language, MoMEMta, is presented. Building on MadWeight's tricks to accelerate the calculations, it aims at a much improved modularity and maintainability. Examples of this modularity are discussed: the possibility to compute several weights in parallel (propagation of systematic uncertainties), the Differential MEM (DMEM), and a novel way to search for lion-resonant. New Physics.
Measurement of the top quark mass using the matrix element technique in dilepton final states
Abazov, V. M.; Abbott, B.; Acharya, B. S.; Adams, M.; Adams, T.; Agnew, J. P.; Alexeev, G. D.; Alkhazov, G.; Alton, A.; Askew, A.; Atkins, S.; Augsten, K.; Aushev, V.; Aushev, Y.; Avila, C.; Badaud, F.; Bagby, L.; Baldin, B.; Bandurin, D. V.; Banerjee, S.; Barberis, E.; Baringer, P.; Bartlett, J. F.; Bassler, U.; Bazterra, V.; Bean, A.; Begalli, M.; Bellantoni, L.; Beri, S. B.; Bernardi, G.; Bernhard, R.; Bertram, I.; Besançon, M.; Beuselinck, R.; Bhat, P. C.; Bhatia, S.; Bhatnagar, V.; Blazey, G.; Blessing, S.; Bloom, K.; Boehnlein, A.; Boline, D.; Boos, E. E.; Borissov, G.; Borysova, M.; Brandt, A.; Brandt, O.; Brochmann, M.; Brock, R.; Bross, A.; Brown, D.; Bu, X. B.; Buehler, M.; Buescher, V.; Bunichev, V.; Burdin, S.; Buszello, C. P.; Camacho-Pérez, E.; Casey, B. C. K.; Castilla-Valdez, H.; Caughron, S.; Chakrabarti, S.; Chan, K. M.; Chandra, A.; Chapon, E.; Chen, G.; Cho, S. W.; Choi, S.; Choudhary, B.; Cihangir, S.; Claes, D.; Clutter, J.; Cooke, M.; Cooper, W. E.; Corcoran, M.; Couderc, F.; Cousinou, M. -C.; Cuth, J.; Cutts, D.; Das, A.; Davies, G.; de Jong, S. J.; De La Cruz-Burelo, E.; Déliot, F.; Demina, R.; Denisov, D.; Denisov, S. P.; Desai, S.; Deterre, C.; DeVaughan, K.; Diehl, H. T.; Diesburg, M.; Ding, P. F.; Dominguez, A.; Dubey, A.; Dudko, L. V.; Duperrin, A.; Dutt, S.; Eads, M.; Edmunds, D.; Ellison, J.; Elvira, V. D.; Enari, Y.; Evans, H.; Evdokimov, A.; Evdokimov, V. N.; Fauré, A.; Feng, L.; Ferbel, T.; Fiedler, F.; Filthaut, F.; Fisher, W.; Fisk, H. E.; Fortner, M.; Fox, H.; Franc, J.; Fuess, S.; Garbincius, P. H.; Garcia-Bellido, A.; García-González, J. A.; Gavrilov, V.; Geng, W.; Gerber, C. E.; Gershtein, Y.; Ginther, G.; Gogota, O.; Golovanov, G.; Grannis, P. D.; Greder, S.; Greenlee, H.; Grenier, G.; Gris, Ph.; Grivaz, J. -F.; Grohsjean, A.; Grünendahl, S.; Grünewald, M. W.; Guillemin, T.; Gutierrez, G.; Gutierrez, P.; Haley, J.; Han, L.; Harder, K.; Harel, A.; Hauptman, J. M.; Hays, J.; Head, T.; Hebbeker, T.; Hedin, D.; Hegab, H.; Heinson, A. P.; Heintz, U.; Hensel, C.; Heredia-De La Cruz, I.; Herner, K.; Hesketh, G.; Hildreth, M. D.; Hirosky, R.; Hoang, T.; Hobbs, J. D.; Hoeneisen, B.; Hogan, J.; Hohlfeld, M.; Holzbauer, J. L.; Howley, I.; Hubacek, Z.; Hynek, V.; Iashvili, I.; Ilchenko, Y.; Illingworth, R.; Ito, A. S.; Jabeen, S.; Jaffré, M.; Jayasinghe, A.; Jeong, M. S.; Jesik, R.; Jiang, P.; Johns, K.; Johnson, E.; Johnson, M.; Jonckheere, A.; Jonsson, P.; Joshi, J.; Jung, A. W.; Juste, A.; Kajfasz, E.; Karmanov, D.; Katsanos, I.; Kaur, M.; Kehoe, R.; Kermiche, S.; Khalatyan, N.; Khanov, A.; Kharchilava, A.; Kharzheev, Y. N.; Kiselevich, I.; Kohli, J. M.; Kozelov, A. V.; Kraus, J.; Kumar, A.; Kupco, A.; Kurča, T.; Kuzmin, V. A.; Lammers, S.; Lebrun, P.; Lee, H. S.; Lee, S. W.; Lee, W. M.; Lei, X.; Lellouch, J.; Li, D.; Li, H.; Li, L.; Li, Q. Z.; Lim, J. K.; Lincoln, D.; Linnemann, J.; Lipaev, V. V.; Lipton, R.; Liu, H.; Liu, Y.; Lobodenko, A.; Lokajicek, M.; Lopes de Sa, R.; Luna-Garcia, R.; Lyon, A. L.; Maciel, A. K. A.; Madar, R.; Magaña-Villalba, R.; Malik, S.; Malyshev, V. L.; Mansour, J.; Martínez-Ortega, J.; McCarthy, R.; McGivern, C. L.; Meijer, M. M.; Melnitchouk, A.; Menezes, D.; Mercadante, P. G.; Merkin, M.; Meyer, A.; Meyer, J.; Miconi, F.; Mondal, N. K.; Mulhearn, M.; Nagy, E.; Narain, M.; Nayyar, R.; Neal, H. A.; Negret, J. P.; Neustroev, P.; Nguyen, H. T.; Nunnemann, T.; Orduna, J.; Osman, N.; Pal, A.; Parashar, N.; Parihar, V.; Park, S. K.; Partridge, R.; Parua, N.; Patwa, A.; Penning, B.; Perfilov, M.; Peters, Y.; Petridis, K.; Petrillo, G.; Pétroff, P.; Pleier, M. -A.; Podstavkov, V. M.; Popov, A. V.; Prewitt, M.; Price, D.; Prokopenko, N.; Qian, J.; Quadt, A.; Quinn, B.; Ratoff, P. N.; Razumov, I.; Ripp-Baudot, I.; Rizatdinova, F.; Rominsky, M.; Ross, A.; Royon, C.; Rubinov, P.; Ruchti, R.; Sajot, G.; Sánchez-Hernández, A.; Sanders, M. P.; Santos, A. S.; Savage, G.; Savitskyi, M.; Sawyer, L.; Scanlon, T.; Schamberger, R. D.; Scheglov, Y.; Schellman, H.; Schott, M.; Schwanenberger, C.; Schwienhorst, R.; Sekaric, J.; Severini, H.; Shabalina, E.; Shary, V.; Shaw, S.; Shchukin, A. A.; Simak, V.; Skubic, P.; Slattery, P.; Snow, G. R.; Snow, J.; Snyder, S.; Söldner-Rembold, S.; Sonnenschein, L.; Soustruznik, K.; Stark, J.; Stefaniuk, N.; Stoyanova, D. A.; Strauss, M.; Suter, L.; Svoisky, P.; Titov, M.; Tokmenin, V. V.; Tsai, Y. -T.; Tsybychev, D.; Tuchming, B.; Tully, C.; Uvarov, L.; Uvarov, S.; Uzunyan, S.; Van Kooten, R.; van Leeuwen, W. M.; Varelas, N.; Varnes, E. W.; Vasilyev, I. A.; Verkheev, A. Y.; Vertogradov, L. S.; Verzocchi, M.; Vesterinen, M.; Vilanova, D.; Vokac, P.; Wahl, H. D.; Wang, M. H. L. S.; Warchol, J.; Watts, G.; Wayne, M.; Weichert, J.; Welty-Rieger, L.; Williams, M. R. J.; Wilson, G. W.; Wobisch, M.; Wood, D. R.; Wyatt, T. R.; Xie, Y.; Yamada, R.; Yang, S.; Yasuda, T.; Yatsunenko, Y. A.; Ye, W.; Ye, Z.; Yin, H.; Yip, K.; Youn, S. W.; Yu, J. M.; Zennamo, J.; Zhao, T. G.; Zhou, B.; Zhu, J.; Zielinski, M.; Zieminska, D.; Zivkovic, L.
2016-08-18
Here, we present a measurement of the top quark mass in pp collisions at a center-of-mass energy of 1.96 TeV at the Fermilab Tevatron collider. The data were collected by the D0 experiment corresponding to an integrated luminosity of 9.7 fb^{-1}. The matrix element technique is applied to tt events in the final state containing leptons (electrons or muons) with high transverse momenta and at least two jets. The calibration of the jet energy scale determined in the lepton+jets final state of tt decays is applied to jet energies. This correction provides a substantial reduction in systematic uncertainties. We obtain a top quark mass of m_{t} = 173.93±1.84 GeV.
Measurement of the top quark mass using the matrix element technique in dilepton final states
Abazov, V. M.; Abbott, B.; Acharya, B. S.; ...
2016-08-18
Here, we present a measurement of the top quark mass in pp collisions at a center-of-mass energy of 1.96 TeV at the Fermilab Tevatron collider. The data were collected by the D0 experiment corresponding to an integrated luminosity of 9.7 fb-1. The matrix element technique is applied to tt events in the final state containing leptons (electrons or muons) with high transverse momenta and at least two jets. The calibration of the jet energy scale determined in the lepton+jets final state of tt decays is applied to jet energies. This correction provides a substantial reduction in systematic uncertainties. We obtain amore » top quark mass of mt = 173.93±1.84 GeV.« less
A modified Finite Element-Transfer Matrix for control design of space structures
NASA Technical Reports Server (NTRS)
Tan, T.-M.; Yousuff, A.; Bahar, L. Y.; Konstandinidis, M.
1990-01-01
The Finite Element-Transfer Matrix (FETM) method was developed for reducing the computational efforts involved in structural analysis. While being widely used by structural analysts, this method does, however, have certain limitations, particularly when used for the control design of large flexible structures. In this paper, a new formulation based on the FETM method is presented. The new method effectively overcomes the limitations in the original FETM method, and also allows an easy construction of reduced models that are tailored for the control design. Other advantages of this new method include the ability to extract open loop frequencies and mode shapes with less computation, and simplification of the design procedures for output feedback, constrained compensation, and decentralized control. The development of this new method and the procedures for generating reduced models using this method are described in detail and the role of the reduced models in control design is discussed through an illustrative example.
Grassmann integral and Balian-Brézin decomposition in Hartree-Fock-Bogoliubov matrix elements
NASA Astrophysics Data System (ADS)
Mizusaki, Takahiro; Oi, Makito; Chen, Fang-Qi; Sun, Yang
2013-08-01
We present a new formula to calculate matrix elements of a general unitary operator with respect to Hartree-Fock-Bogoliubov states allowing multiple quasi-particle excitations. The Balian-Brézin decomposition of the unitary operator [R. Balian, E. Brézin, Il Nuovo Cimento B 64 (1969) 37] is employed in the derivation. We found that this decomposition is extremely suitable for an application of Fermion coherent state and Grassmann integrals in the quasi-particle basis. The resultant formula is compactly expressed in terms of the Pfaffian, and shows the similar bipartite structure to the formula that we have previously derived in the bare-particles basis [T. Mizusaki, M. Oi, Phys. Lett. B 715 (2012) 219].
Top Quark Mass Measurement Using a Matrix Element Method with Quasi-Monte Carlo Integration
Lujan, Paul J.
2008-10-01
We report an updated measurement of the top quark mass obtained from ppbar collisions at sqrt(s) = 1.96 TeV at the Fermilab Tevatron using the CDF II detector. Our measurement uses a matrix element integration method to obtain a signal likelihood, with a neural network used to identify background events and a likelihood cut applied to reduce the effect of badly reconstructed events. We use a 2.7 fb{sup -1} sample and observe 422 events passing all of our cuts. We find m{sub t} = 172.2 +/- 1.0 (stat.) +/- 0.9 (JES) +/- 1.0 (syst.) GeV/c{sup 2}, or m{sub t} = 172.2 +/- 1.7 (total) GeV/c{sup 2}.
Measurement of the top quark mass using the matrix element technique in dilepton final states
NASA Astrophysics Data System (ADS)
Abazov, V. M.; Abbott, B.; Acharya, B. S.; Adams, M.; Adams, T.; Agnew, J. P.; Alexeev, G. D.; Alkhazov, G.; Alton, A.; Askew, A.; Atkins, S.; Augsten, K.; Aushev, V.; Aushev, Y.; Avila, C.; Badaud, F.; Bagby, L.; Baldin, B.; Bandurin, D. V.; Banerjee, S.; Barberis, E.; Baringer, P.; Bartlett, J. F.; Bassler, U.; Bazterra, V.; Bean, A.; Begalli, M.; Bellantoni, L.; Beri, S. B.; Bernardi, G.; Bernhard, R.; Bertram, I.; Besançon, M.; Beuselinck, R.; Bhat, P. C.; Bhatia, S.; Bhatnagar, V.; Blazey, G.; Blessing, S.; Bloom, K.; Boehnlein, A.; Boline, D.; Boos, E. E.; Borissov, G.; Borysova, M.; Brandt, A.; Brandt, O.; Brochmann, M.; Brock, R.; Bross, A.; Brown, D.; Bu, X. B.; Buehler, M.; Buescher, V.; Bunichev, V.; Burdin, S.; Buszello, C. P.; Camacho-Pérez, E.; Casey, B. C. K.; Castilla-Valdez, H.; Caughron, S.; Chakrabarti, S.; Chan, K. M.; Chandra, A.; Chapon, E.; Chen, G.; Cho, S. W.; Choi, S.; Choudhary, B.; Cihangir, S.; Claes, D.; Clutter, J.; Cooke, M.; Cooper, W. E.; Corcoran, M.; Couderc, F.; Cousinou, M.-C.; Cuth, J.; Cutts, D.; Das, A.; Davies, G.; de Jong, S. J.; De La Cruz-Burelo, E.; Déliot, F.; Demina, R.; Denisov, D.; Denisov, S. P.; Desai, S.; Deterre, C.; DeVaughan, K.; Diehl, H. T.; Diesburg, M.; Ding, P. F.; Dominguez, A.; Dubey, A.; Dudko, L. V.; Duperrin, A.; Dutt, S.; Eads, M.; Edmunds, D.; Ellison, J.; Elvira, V. D.; Enari, Y.; Evans, H.; Evdokimov, A.; Evdokimov, V. N.; Fauré, A.; Feng, L.; Ferbel, T.; Fiedler, F.; Filthaut, F.; Fisher, W.; Fisk, H. E.; Fortner, M.; Fox, H.; Franc, J.; Fuess, S.; Garbincius, P. H.; Garcia-Bellido, A.; García-González, J. A.; Gavrilov, V.; Geng, W.; Gerber, C. E.; Gershtein, Y.; Ginther, G.; Gogota, O.; Golovanov, G.; Grannis, P. D.; Greder, S.; Greenlee, H.; Grenier, G.; Gris, Ph.; Grivaz, J.-F.; Grohsjean, A.; Grünendahl, S.; Grünewald, M. W.; Guillemin, T.; Gutierrez, G.; Gutierrez, P.; Haley, J.; Han, L.; Harder, K.; Harel, A.; Hauptman, J. M.; Hays, J.; Head, T.; Hebbeker, T.; Hedin, D.; Hegab, H.; Heinson, A. P.; Heintz, U.; Hensel, C.; Heredia-De La Cruz, I.; Herner, K.; Hesketh, G.; Hildreth, M. D.; Hirosky, R.; Hoang, T.; Hobbs, J. D.; Hoeneisen, B.; Hogan, J.; Hohlfeld, M.; Holzbauer, J. L.; Howley, I.; Hubacek, Z.; Hynek, V.; Iashvili, I.; Ilchenko, Y.; Illingworth, R.; Ito, A. S.; Jabeen, S.; Jaffré, M.; Jayasinghe, A.; Jeong, M. S.; Jesik, R.; Jiang, P.; Johns, K.; Johnson, E.; Johnson, M.; Jonckheere, A.; Jonsson, P.; Joshi, J.; Jung, A. W.; Juste, A.; Kajfasz, E.; Karmanov, D.; Katsanos, I.; Kaur, M.; Kehoe, R.; Kermiche, S.; Khalatyan, N.; Khanov, A.; Kharchilava, A.; Kharzheev, Y. N.; Kiselevich, I.; Kohli, J. M.; Kozelov, A. V.; Kraus, J.; Kumar, A.; Kupco, A.; Kurča, T.; Kuzmin, V. A.; Lammers, S.; Lebrun, P.; Lee, H. S.; Lee, S. W.; Lee, W. M.; Lei, X.; Lellouch, J.; Li, D.; Li, H.; Li, L.; Li, Q. Z.; Lim, J. K.; Lincoln, D.; Linnemann, J.; Lipaev, V. V.; Lipton, R.; Liu, H.; Liu, Y.; Lobodenko, A.; Lokajicek, M.; Lopes de Sa, R.; Luna-Garcia, R.; Lyon, A. L.; Maciel, A. K. A.; Madar, R.; Magaña-Villalba, R.; Malik, S.; Malyshev, V. L.; Mansour, J.; Martínez-Ortega, J.; McCarthy, R.; McGivern, C. L.; Meijer, M. M.; Melnitchouk, A.; Menezes, D.; Mercadante, P. G.; Merkin, M.; Meyer, A.; Meyer, J.; Miconi, F.; Mondal, N. K.; Mulhearn, M.; Nagy, E.; Narain, M.; Nayyar, R.; Neal, H. A.; Negret, J. P.; Neustroev, P.; Nguyen, H. T.; Nunnemann, T.; Orduna, J.; Osman, N.; Pal, A.; Parashar, N.; Parihar, V.; Park, S. K.; Partridge, R.; Parua, N.; Patwa, A.; Penning, B.; Perfilov, M.; Peters, Y.; Petridis, K.; Petrillo, G.; Pétroff, P.; Pleier, M.-A.; Podstavkov, V. M.; Popov, A. V.; Prewitt, M.; Price, D.; Prokopenko, N.; Qian, J.; Quadt, A.; Quinn, B.; Ratoff, P. N.; Razumov, I.; Ripp-Baudot, I.; Rizatdinova, F.; Rominsky, M.; Ross, A.; Royon, C.; Rubinov, P.; Ruchti, R.; Sajot, G.; Sánchez-Hernández, A.; Sanders, M. P.; Santos, A. S.; Savage, G.; Savitskyi, M.; Sawyer, L.; Scanlon, T.; Schamberger, R. D.; Scheglov, Y.; Schellman, H.; Schott, M.; Schwanenberger, C.; Schwienhorst, R.; Sekaric, J.; Severini, H.; Shabalina, E.; Shary, V.; Shaw, S.; Shchukin, A. A.; Simak, V.; Skubic, P.; Slattery, P.; Snow, G. R.; Snow, J.; Snyder, S.; Söldner-Rembold, S.; Sonnenschein, L.; Soustruznik, K.; Stark, J.; Stefaniuk, N.; Stoyanova, D. A.; Strauss, M.; Suter, L.; Svoisky, P.; Titov, M.; Tokmenin, V. V.; Tsai, Y.-T.; Tsybychev, D.; Tuchming, B.; Tully, C.; Uvarov, L.; Uvarov, S.; Uzunyan, S.; Van Kooten, R.; van Leeuwen, W. M.; Varelas, N.; Varnes, E. W.; Vasilyev, I. A.; Verkheev, A. Y.; Vertogradov, L. S.; Verzocchi, M.; Vesterinen, M.; Vilanova, D.; Vokac, P.; Wahl, H. D.; Wang, M. H. L. S.; Warchol, J.; Watts, G.; Wayne, M.; Weichert, J.; Welty-Rieger, L.; Williams, M. R. J.; Wilson, G. W.; Wobisch, M.; Wood, D. R.; Wyatt, T. R.; Xie, Y.; Yamada, R.; Yang, S.; Yasuda, T.; Yatsunenko, Y. A.; Ye, W.; Ye, Z.; Yin, H.; Yip, K.; Youn, S. W.; Yu, J. M.; Zennamo, J.; Zhao, T. G.; Zhou, B.; Zhu, J.; Zielinski, M.; Zieminska, D.; Zivkovic, L.; D0 Collaboration
2016-08-01
We present a measurement of the top quark mass in p p ¯ collisions at a center-of-mass energy of 1.96 TeV at the Fermilab Tevatron collider. The data were collected by the D0 experiment corresponding to an integrated luminosity of 9.7 fb-1 . The matrix element technique is applied to t t ¯ events in the final state containing leptons (electrons or muons) with high transverse momenta and at least two jets. The calibration of the jet energy scale determined in the lepton +jets final state of t t ¯ decays is applied to jet energies. This correction provides a substantial reduction in systematic uncertainties. We obtain a top quark mass of mt=173.93 ±1.84 GeV .
NASA Astrophysics Data System (ADS)
Haddouche, Issam; Cherbi, Lynda
2017-01-01
In this paper, we investigate Surface Plasmon Polaritons (SPPs) in the visible regime at a metal/dielectric interface within two different waveguide structures, the first is a Photonic Crystal Fiber where the Full Vector Finite Element Method (FVFEM) is used and the second is a slab waveguide where the transfer matrix method (TMM) is used. Knowing the diversities between the two methods in terms of speed, simplicity, and scope of application, computation is implemented with respect to wavelength and metal layer thickness in order to analyze and compare the performances of the two methods. Simulation results show that the TMM can be a good approximation for the FVFEM and that SPPs behave more like modes propagating in a semi infinite metal/dielectric structure as metal thickness increases from about 150 nm.
Measurement of the top quark mass using the matrix element technique in dilepton final states
Abazov, V. M.; Abbott, B.; Acharya, B. S.; Adams, M.; Adams, T.; Agnew, J. P.; Alexeev, G. D.; Alkhazov, G.; Alton, A.; Askew, A.; Atkins, S.; Augsten, K.; Aushev, V.; Aushev, Y.; Avila, C.; Badaud, F.; Bagby, L.; Baldin, B.; Bandurin, D. V.; Banerjee, S.; Barberis, E.; Baringer, P.; Bartlett, J. F.; Bassler, U.; Bazterra, V.; Bean, A.; Begalli, M.; Bellantoni, L.; Beri, S. B.; Bernardi, G.; Bernhard, R.; Bertram, I.; Besançon, M.; Beuselinck, R.; Bhat, P. C.; Bhatia, S.; Bhatnagar, V.; Blazey, G.; Blessing, S.; Bloom, K.; Boehnlein, A.; Boline, D.; Boos, E. E.; Borissov, G.; Borysova, M.; Brandt, A.; Brandt, O.; Brochmann, M.; Brock, R.; Bross, A.; Brown, D.; Bu, X. B.; Buehler, M.; Buescher, V.; Bunichev, V.; Burdin, S.; Buszello, C. P.; Camacho-Pérez, E.; Casey, B. C. K.; Castilla-Valdez, H.; Caughron, S.; Chakrabarti, S.; Chan, K. M.; Chandra, A.; Chapon, E.; Chen, G.; Cho, S. W.; Choi, S.; Choudhary, B.; Cihangir, S.; Claes, D.; Clutter, J.; Cooke, M.; Cooper, W. E.; Corcoran, M.; Couderc, F.; Cousinou, M. -C.; Cuth, J.; Cutts, D.; Das, A.; Davies, G.; de Jong, S. J.; De La Cruz-Burelo, E.; Déliot, F.; Demina, R.; Denisov, D.; Denisov, S. P.; Desai, S.; Deterre, C.; DeVaughan, K.; Diehl, H. T.; Diesburg, M.; Ding, P. F.; Dominguez, A.; Dubey, A.; Dudko, L. V.; Duperrin, A.; Dutt, S.; Eads, M.; Edmunds, D.; Ellison, J.; Elvira, V. D.; Enari, Y.; Evans, H.; Evdokimov, A.; Evdokimov, V. N.; Fauré, A.; Feng, L.; Ferbel, T.; Fiedler, F.; Filthaut, F.; Fisher, W.; Fisk, H. E.; Fortner, M.; Fox, H.; Franc, J.; Fuess, S.; Garbincius, P. H.; Garcia-Bellido, A.; García-González, J. A.; Gavrilov, V.; Geng, W.; Gerber, C. E.; Gershtein, Y.; Ginther, G.; Gogota, O.; Golovanov, G.; Grannis, P. D.; Greder, S.; Greenlee, H.; Grenier, G.; Gris, Ph.; Grivaz, J. -F.; Grohsjean, A.; Grünendahl, S.; Grünewald, M. W.; Guillemin, T.; Gutierrez, G.; Gutierrez, P.; Haley, J.; Han, L.; Harder, K.; Harel, A.; Hauptman, J. M.; Hays, J.; Head, T.; Hebbeker, T.; Hedin, D.; Hegab, H.; Heinson, A. P.; Heintz, U.; Hensel, C.; Heredia-De La Cruz, I.; Herner, K.; Hesketh, G.; Hildreth, M. D.; Hirosky, R.; Hoang, T.; Hobbs, J. D.; Hoeneisen, B.; Hogan, J.; Hohlfeld, M.; Holzbauer, J. L.; Howley, I.; Hubacek, Z.; Hynek, V.; Iashvili, I.; Ilchenko, Y.; Illingworth, R.; Ito, A. S.; Jabeen, S.; Jaffré, M.; Jayasinghe, A.; Jeong, M. S.; Jesik, R.; Jiang, P.; Johns, K.; Johnson, E.; Johnson, M.; Jonckheere, A.; Jonsson, P.; Joshi, J.; Jung, A. W.; Juste, A.; Kajfasz, E.; Karmanov, D.; Katsanos, I.; Kaur, M.; Kehoe, R.; Kermiche, S.; Khalatyan, N.; Khanov, A.; Kharchilava, A.; Kharzheev, Y. N.; Kiselevich, I.; Kohli, J. M.; Kozelov, A. V.; Kraus, J.; Kumar, A.; Kupco, A.; Kurča, T.; Kuzmin, V. A.; Lammers, S.; Lebrun, P.; Lee, H. S.; Lee, S. W.; Lee, W. M.; Lei, X.; Lellouch, J.; Li, D.; Li, H.; Li, L.; Li, Q. Z.; Lim, J. K.; Lincoln, D.; Linnemann, J.; Lipaev, V. V.; Lipton, R.; Liu, H.; Liu, Y.; Lobodenko, A.; Lokajicek, M.; Lopes de Sa, R.; Luna-Garcia, R.; Lyon, A. L.; Maciel, A. K. A.; Madar, R.; Magaña-Villalba, R.; Malik, S.; Malyshev, V. L.; Mansour, J.; Martínez-Ortega, J.; McCarthy, R.; McGivern, C. L.; Meijer, M. M.; Melnitchouk, A.; Menezes, D.; Mercadante, P. G.; Merkin, M.; Meyer, A.; Meyer, J.; Miconi, F.; Mondal, N. K.; Mulhearn, M.; Nagy, E.; Narain, M.; Nayyar, R.; Neal, H. A.; Negret, J. P.; Neustroev, P.; Nguyen, H. T.; Nunnemann, T.; Orduna, J.; Osman, N.; Pal, A.; Parashar, N.; Parihar, V.; Park, S. K.; Partridge, R.; Parua, N.; Patwa, A.; Penning, B.; Perfilov, M.; Peters, Y.; Petridis, K.; Petrillo, G.; Pétroff, P.; Pleier, M. -A.; Podstavkov, V. M.; Popov, A. V.; Prewitt, M.; Price, D.; Prokopenko, N.; Qian, J.; Quadt, A.; Quinn, B.; Ratoff, P. N.; Razumov, I.; Ripp-Baudot, I.; Rizatdinova, F.; Rominsky, M.; Ross, A.; Royon, C.; Rubinov, P.; Ruchti, R.; Sajot, G.; Sánchez-Hernández, A.; Sanders, M. P.; Santos, A. S.; Savage, G.; Savitskyi, M.; Sawyer, L.; Scanlon, T.; Schamberger, R. D.; Scheglov, Y.; Schellman, H.; Schott, M.; Schwanenberger, C.; Schwienhorst, R.; Sekaric, J.; Severini, H.; Shabalina, E.; Shary, V.; Shaw, S.; Shchukin, A. A.; Simak, V.; Skubic, P.; Slattery, P.; Snow, G. R.; Snow, J.; Snyder, S.; Söldner-Rembold, S.; Sonnenschein, L.; Soustruznik, K.; Stark, J.; Stefaniuk, N.; Stoyanova, D. A.; Strauss, M.; Suter, L.; Svoisky, P.; Titov, M.; Tokmenin, V. V.; Tsai, Y. -T.; Tsybychev, D.; Tuchming, B.; Tully, C.; Uvarov, L.; Uvarov, S.; Uzunyan, S.; Van Kooten, R.; van Leeuwen, W. M.; Varelas, N.; Varnes, E. W.; Vasilyev, I. A.; Verkheev, A. Y.; Vertogradov, L. S.; Verzocchi, M.; Vesterinen, M.; Vilanova, D.; Vokac, P.; Wahl, H. D.; Wang, M. H. L. S.; Warchol, J.; Watts, G.; Wayne, M.; Weichert, J.; Welty-Rieger, L.; Williams, M. R. J.; Wilson, G. W.; Wobisch, M.; Wood, D. R.; Wyatt, T. R.; Xie, Y.; Yamada, R.; Yang, S.; Yasuda, T.; Yatsunenko, Y. A.; Ye, W.; Ye, Z.; Yin, H.; Yip, K.; Youn, S. W.; Yu, J. M.; Zennamo, J.; Zhao, T. G.; Zhou, B.; Zhu, J.; Zielinski, M.; Zieminska, D.; Zivkovic, L.
2016-08-18
Here, we present a measurement of the top quark mass in pp collisions at a center-of-mass energy of 1.96 TeV at the Fermilab Tevatron collider. The data were collected by the D0 experiment corresponding to an integrated luminosity of 9.7 fb^{-1}. The matrix element technique is applied to tt events in the final state containing leptons (electrons or muons) with high transverse momenta and at least two jets. The calibration of the jet energy scale determined in the lepton+jets final state of tt decays is applied to jet energies. This correction provides a substantial reduction in systematic uncertainties. We obtain a top quark mass of m_{t} = 173.93±1.84 GeV.
S -matrix element of two R-R and one NS states
NASA Astrophysics Data System (ADS)
Mohammadzadeh, Mojtaba; Garousi, Mohammad R.
2017-09-01
We explicitly calculate the disk-level S -matrix element of two closed string R-R and one open string NS vertex operators in RNS formalism. We show that the amplitude satisfies various duality Ward identities. In particular, when one of the R-R is zero form, the other one is two form, and the NS state is a gauge boson, the amplitude transforms under an S-duality Ward identity to the amplitude of one dilaton, one B-field, and one gauge boson, which has recently been calculated explicitly. We have also proposed a soft theorem for the disk-level scattering amplitude of an ar bitrary number of hard closed strings and one soft open string at the leading order of soft momentum, and we have shown that the above amplitude satisfies the soft theorem.
Nucleon distribution amplitudes and proton decay matrix elements on the lattice
Braun, Vladimir M.; Goeckeler, Meinulf; Kaltenbrunner, Thomas; Warkentin, Nikolaus; Horsley, Roger; Zanotti, James M.; Nakamura, Yoshifumi; Pleiter, Dirk; Rakow, Paul E. L.; Schaefer, Andreas; Schierholz, Gerrit; Stueben, Hinnerk
2009-02-01
Baryon distribution amplitudes (DAs) are crucial for the theory of hard exclusive reactions. We present a calculation of the first few moments of the leading-twist nucleon DA within lattice QCD. In addition we deal with the normalization of the next-to-leading (twist-four) DAs. The matrix elements determining the latter quantities are also responsible for proton decay in grand unified theories. Our lattice evaluation makes use of gauge field configurations generated with two flavors of clover fermions. The relevant operators are renormalized nonperturbatively with the final results given in the MS scheme. We find that the deviation of the leading-twist nucleon DA from its asymptotic form is less pronounced than sometimes claimed in the literature.
Single-particle parity-nonconserving matrix elements in {sup 207}Pb
Komives, A.; Knott, J.E.; Leuschner, M.; Szymanski, J.J.; Bowman, J.D.; Jamrisk, D.
1993-10-01
Measurements of the helicity dependence of neutron scattering off of heavy nuclei by the TRIPLE collaboration have yielded multiple parity-nonconserving asymmetries. The asymmetries are predominantly positive, in contradiction to the zero average asymmetry predicted by the statistical model of neutron- nucleus scattering. Theoretical calculations that explain the non-zero average asymmetry require single-particle parity- nonconserving matrix elements 10-100 times larger than those predicted by meson exchange models. We are determining the single-particle parity non-conserving mixing in {sup 207}Pb by measuring the circular polarization of the 1.064 MeV {gamma} ray. The experiment uses a transmission polarimeter and a fast data acquisition system. Initial results are presented.
NASA Astrophysics Data System (ADS)
Hill, Richard J.; Solon, Mikhail P.
2015-02-01
Models of weakly interacting massive particles (WIMPs) specified at the electroweak scale are systematically matched to effective theories at hadronic scales where WIMP-nucleus scattering observables are evaluated. Anomalous dimensions and heavy-quark threshold matching conditions are computed for the complete basis of lowest-dimension effective operators involving quarks and gluons. The resulting QCD renormalization group evolution equations are solved. The status of relevant hadronic matrix elements is reviewed and phenomenological illustrations are given, including details for the computation of the universal limit of nucleon scattering with heavy S U (2 )W×U (1 )Y charged WIMPs. Several cases of previously underestimated hadronic uncertainties are isolated. The results connect arbitrary models specified at the electroweak scale to a basis of nf=3 -flavor QCD operators. The complete basis of operators and Lorentz invariance constraints through order v2/c2 in the nonrelativistic nucleon effective theory are derived.
Spin dipole nuclear matrix elements for double beta decay nuclei by charge-exchange reactions
NASA Astrophysics Data System (ADS)
Ejiri, H.; Frekers, D.
2016-11-01
Spin dipole (SD) strengths for double beta-decay (DBD) nuclei were studied experimentally for the first time by using measured cross sections of (3He, t) charge-exchange reactions (CERs). Then SD nuclear matrix elements (NMEs) {M}α ({{SD}}) for low-lying 2- states were derived from the experimental SD strengths by referring to the experimental α = GT (Gamow-Teller) and α = F (Fermi) strengths. They are consistent with the empirical NMEs M({{SD}}) based on the quasi-particle model with the empirical effective SD coupling constant. The CERs are used to evaluate the SD NME, which is associated with one of the major components of the neutrino-less DBD NME.
Turek, Marko; Spehner, Dominique; Müller, Sebastian; Richter, Klaus
2005-01-01
We present a semiclassical calculation of the generalized form factor Kab(tau) which characterizes the fluctuations of matrix elements of the operators a and b in the eigenbasis of the Hamiltonian of a chaotic system. Our approach is based on some recently developed techniques for the spectral form factor of systems with hyperbolic and ergodic underlying classical dynamics and f = 2 degrees of freedom, that allow us to go beyond the diagonal approximation. First we extend these techniques to systems with f > 2. Then we use these results to calculate Kab(tau). We show that the dependence on the rescaled time tau (time in units of the Heisenberg time) is universal for both the spectral and the generalized form factor. Furthermore, we derive a relation between Kab(tau) and the classical time-correlation function of the Weyl symbols of a and b.
A simple representation of energy matrix elements in terms of symmetry-invariant bases.
Cui, Peng; Wu, Jian; Zhang, Guiqing; Boyd, Russell J
2010-02-01
When a system under consideration has some symmetry, usually its Hamiltonian space can be parallel partitioned into a set of subspaces, which is invariant under symmetry operations. The bases that span these invariant subspaces are also invariant under the symmetry operations, and they are the symmetry-invariant bases. A standard methodology is available to construct a series of generator functions (GFs) and corresponding symmetry-adapted basis (SAB) functions from these symmetry-invariant bases. Elements of the factorized Hamiltonian and overlap matrix can be expressed in terms of these SAB functions, and their simple representations can be deduced in terms of GFs. The application of this method to the Heisenberg spin Hamiltonian is demonstrated.
Quasi-particle energy spectra in local reduced density matrix functional theory
Lathiotakis, Nektarios N.; Helbig, Nicole; Rubio, Angel
2014-10-28
Recently, we introduced [N. N. Lathiotakis, N. Helbig, A. Rubio, and N. I. Gidopoulos, Phys. Rev. A 90, 032511 (2014)] local reduced density matrix functional theory (local RDMFT), a theoretical scheme capable of incorporating static correlation effects in Kohn-Sham equations. Here, we apply local RDMFT to molecular systems of relatively large size, as a demonstration of its computational efficiency and its accuracy in predicting single-electron properties from the eigenvalue spectrum of the single-particle Hamiltonian with a local effective potential. We present encouraging results on the photoelectron spectrum of molecular systems and the relative stability of C{sub 20} isotopes. In addition, we propose a modelling of the fractional occupancies as functions of the orbital energies that further improves the efficiency of the method useful in applications to large systems and solids.
NASA Astrophysics Data System (ADS)
Pan, Andrew; Burnett, Benjamin A.; Chui, Chi On; Williams, Benjamin S.
2017-08-01
We derive a density matrix (DM) theory for quantum cascade lasers (QCLs) that describes the influence of scattering on coherences through a generalized scattering superoperator. The theory enables quantitative modeling of QCLs, including localization and tunneling effects, using the well-defined energy eigenstates rather than the ad hoc localized basis states required by most previous DM models. Our microscopic approach to scattering also eliminates the need for phenomenological transition or dephasing rates. We discuss the physical interpretation and numerical implementation of the theory, presenting sets of both energy-resolved and thermally averaged equations, which can be used for detailed or compact device modeling. We illustrate the theory's applications by simulating a high performance resonant-phonon terahertz (THz) QCL design, which cannot be easily or accurately modeled using conventional DM methods. We show that the theory's inclusion of coherences is crucial for describing localization and tunneling effects consistent with experiment.
A Practical Guide to Density Matrix Embedding Theory in Quantum Chemistry.
Wouters, Sebastian; Jiménez-Hoyos, Carlos A; Sun, Qiming; Chan, Garnet K-L
2016-06-14
Density matrix embedding theory (DMET) (Knizia, G.; Chan, G. K.-L. Phys. Rev. Lett. 2012, 109, 186404) provides a theoretical framework to treat finite fragments in the presence of a surrounding molecular or bulk environment, even when there is significant correlation or entanglement between the two. In this work, we give a practically oriented and explicit description of the numerical and theoretical formulation of DMET. We also describe in detail how to perform self-consistent DMET optimizations. We explore different embedding strategies with and without a self-consistency condition in hydrogen rings, beryllium rings, and a sample SN2 reaction. The source code for the calculations in this work can be obtained from https://github.com/sebwouters/qc-dmet .
Baryogenesis from L -violating Higgs-doublet decay in the density-matrix formalism
NASA Astrophysics Data System (ADS)
Hambye, Thomas; Teresi, Daniele
2017-07-01
We compute in the density-matrix formalism the baryon asymmetry generated by the decay of the Higgs doublet into a right-handed (RH) neutrino and a Standard Model lepton. The emphasis is put on the baryon asymmetry produced by the total lepton-number violating decay. From the derivation of the corresponding evolution equations, and from their integration, we find that this contribution is fully relevant for large parts of the parameter space. This confirms the results found recently in the C P -violating decay formalism with thermal corrections and shows in particular that the lepton-number violating processes are important not only for high-scale leptogenesis but also when the RH-neutrino masses are in the GeV range. For large values of the Yukawa couplings, we also find that the strong washout is generically much milder for this total lepton-number violating part than for the usual RH-neutrino oscillation flavor part.
High-harmonic spectra from time-dependent two-particle reduced-density-matrix theory
NASA Astrophysics Data System (ADS)
Lackner, Fabian; Březinová, Iva; Sato, Takeshi; Ishikawa, Kenichi L.; Burgdörfer, Joachim
2017-03-01
The ab initio description of the nonlinear response of many-electron systems to strong-laser fields remains a major challenge. In order to address larger systems, alternative methods need to be developed that bypass the exponential scaling with particle number inherent to conventional wave-function-based approaches. In this paper we present a fully three-dimensional implementation of the time-dependent two-particle reduced-density-matrix (TD-2RDM) method for many-electron atoms. We benchmark this approach by a comparison with multiconfigurational time-dependent Hartree-Fock results for the harmonic spectra of beryllium and neon. We show that the TD-2RDM is very well suited to describe the nonlinear atomic response and to reveal the influence of electron-correlation effects.
N-leg spin-S Heisenberg ladders: A density-matrix renormalization group study
NASA Astrophysics Data System (ADS)
Ramos, F. B.; Xavier, J. C.
2014-03-01
We investigate the N-leg spin-S Heisenberg ladders by using the density matrix renormalization group method. We present estimates of the spin gap Δs and of the ground-state energy per site e∞N in the thermodynamic limit for ladders with widths up to six legs and spin S≤5/2. We also estimate the ground-state energy per site e∞2D for the infinite two-dimensional spin-S Heisenberg model. Our results support that for ladders with semi-integer spins the spin excitation is gapless for N odd and gapped for N even, whereas for integer spin ladders the spin gap is nonzero, independent of the number of legs. Those results agree with the well-known conjectures of Haldane and Sénéchal-Sierra for chains and ladders, respectively. We also observe edge states for ladders with N odd, similar to what happens in spin chains.
Density matrix renormalization group study of triangular Kitaev-Heisenberg model
NASA Astrophysics Data System (ADS)
Sota, Shigetoshi; Sjinjo, Kazuya; Shirakawa, Tomonori; Tohyama, Takami; Yunoki, Seiji
2015-03-01
Topological insulator has been one of the most active subjects in the current condensed matter physics. For most of topological insulators electron correlations are considered to be not essential. However, in the case where electron correlations are strong, novel phases such as a spin liquid phase can emerge in competition with a spin-orbit coupling. Here, using the density matrix renormalization group method, we investigate magnetic phase of a triangular Kitaev-Heisenberg (quantum compass) model that contains a spin-orbital interaction and spin frustration in the antiferromagnetic region. The triangular Kitaev-Heisenberg model is regarded as a dual model of the honeycomb Kitaev-Heisenberg model that is usually employed to discuss A2CuO3 (A=Na, K). Systematically calculating ground state energy, entanglement entropy, entanglement spectrum, and spin-spin correlation functions, we discuss the duality between the triangular and the honeycomb Kitaev-Heisenberg model as well as the ground state magnetic phases.
A note on the high temperature expansion of the density matrix for the isotropic Heisenberg chain
NASA Astrophysics Data System (ADS)
Tsuboi, Zengo
2007-04-01
Göhmann, Klümper and Seel derived the multiple integral formula of the density matrix of the XXZ Heisenberg chain at finite temperatures. We have applied the high temperature expansion (HTE) method to isotropic case of their formula in a finite magnetic field and obtained coefficients for several short-range correlation functions. For example, we have succeeded to obtain the coefficients of the HTE of the third neighbor correlation function <σjzσj+3z> for zero magnetic field up to the order of 25. These results expand our previous results on the emptiness formation probability [Z. Tsuboi, M. Shiroishi, J. Phys. A: Math. Gen. 38 (2005) L363-L370, condmat/0502569.] to more general correlation functions.
NASA Astrophysics Data System (ADS)
Ghosh, Debashree; Hachmann, Johannes; Yanai, Takeshi; Chan, Garnet Kin-Lic
2008-04-01
In previous work we have shown that the density matrix renormalization group (DMRG) enables near-exact calculations in active spaces much larger than are possible with traditional complete active space algorithms. Here, we implement orbital optimization with the DMRG to further allow the self-consistent improvement of the active orbitals, as is done in the complete active space self-consistent field (CASSCF) method. We use our resulting DMRG-CASSCF method to study the low-lying excited states of the all-trans polyenes up to C24H26 as well as β-carotene, correlating with near-exact accuracy the optimized complete π-valence space with up to 24 active electrons and orbitals, and analyze our results in the light of the recent discovery from resonance Raman experiments of new optically dark states in the spectrum.
NASA Astrophysics Data System (ADS)
Hachmann, Johannes; Cardoen, Wim; Chan, Garnet Kin-Lic
2006-10-01
We have devised a local ab initio density matrix renormalization group algorithm to describe multireference correlations in large systems. For long molecules that are extended in one of their spatial dimensions, we can obtain an exact characterization of correlation, in the given basis, with a cost that scales only quadratically with the size of the system. The reduced scaling is achieved solely through integral screening and without the construction of correlation domains. We demonstrate the scaling, convergence, and robustness of the algorithm in polyenes and hydrogen chains. We converge to exact correlation energies (in the sense of full configuration interaction, with 1-10μEh precision) in all cases and correlate up to 100 electrons in 100 active orbitals. We further use our algorithm to obtain exact energies for the metal-insulator transition in hydrogen chains and compare and contrast our results with those from conventional quantum chemical methods.
Hu, Weifeng; Chan, Garnet Kin-Lic
2015-07-14
We describe and extend the formalism of state-specific analytic density matrix renormalization group (DMRG) energy gradients, first used by Liu et al. [J. Chem. Theor. Comput. 2013, 9, 4462]. We introduce a DMRG wave function maximum overlap following technique to facilitate state-specific DMRG excited-state optimization. Using DMRG configuration interaction (DMRG-CI) gradients, we relax the low-lying singlet states of a series of trans-polyenes up to C20H22. Using the relaxed excited-state geometries, as well as correlation functions, we elucidate the exciton, soliton, and bimagnon ("single-fission") character of the excited states, and find evidence for a planar conical intersection.
NASA Astrophysics Data System (ADS)
Mukhopadhyay, S.; Ramasesha, S.
2009-08-01
We have used the density matrix renormalization group (DMRG) method to study the linear and nonlinear optical responses of first generation nitrogen based dendrimers with donor acceptor groups. We have employed Pariser-Parr-Pople Hamiltonian to model the interacting π electrons in these systems. Within the DMRG method we have used an innovative scheme to target excited states with large transition dipole to the ground state. This method reproduces exact optical gaps and polarization in systems where exact diagonalization of the Hamiltonian is possible. We have used a correction vector method which tacitly takes into account the contribution of all excited states, to obtain the ground state polarizibility, first hyperpolarizibility, and two photon absorption cross sections. We find that the lowest optical excitations as well as the lowest excited triplet states are localized. It is interesting to note that the first hyperpolarizibility saturates more rapidly with system size compared to linear polarizibility unlike that of linear polyenes.
NASA Astrophysics Data System (ADS)
Huo, Pengfei; Coker, David F.
2011-11-01
An approach for treating dissipative, non-adiabatic quantum dynamics in general model systems at finite temperature based on linearizing the density matrix evolution in the forward-backward path difference for the environment degrees of freedom is presented. We demonstrate that the approach can capture both short time coherent quantum dynamics and long time thermal equilibration in an application to excitation energy transfer in a model photosynthetic light harvesting complex. Results are also presented for some nonadiabatic scattering models which indicate that, even though the method is based on a "mean trajectory" like scheme, it can accurately capture electronic population branching through multiple avoided crossing regions and that the approach offers a robust and reliable way to treat quantum dynamical phenomena in a wide range of condensed phase applications.
NASA Astrophysics Data System (ADS)
Nocera, A.; Alvarez, G.
2016-11-01
Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. This paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper then studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases studied indicate that the Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.
Symmetry-conserving purification of quantum states within the density matrix renormalization group
Nocera, Alberto; Alvarez, Gonzalo
2016-01-28
The density matrix renormalization group (DMRG) algorithm was originally designed to efficiently compute the zero-temperature or ground-state properties of one-dimensional strongly correlated quantum systems. The development of the algorithm at finite temperature has been a topic of much interest, because of the usefulness of thermodynamics quantities in understanding the physics of condensed matter systems, and because of the increased complexity associated with efficiently computing temperature-dependent properties. The ancilla method is a DMRG technique that enables the computation of these thermodynamic quantities. In this paper, we review the ancilla method, and improve its performance by working on reduced Hilbert spaces andmore » using canonical approaches. Furthermore we explore its applicability beyond spins systems to t-J and Hubbard models.« less
Density matrix model for polarons in a terahertz quantum dot cascade laser
NASA Astrophysics Data System (ADS)
Burnett, Benjamin A.; Williams, Benjamin S.
2014-10-01
A density matrix based method is introduced for computation of steady-state dynamics in quantum cascade systems of arbitrary size, which incorporates an optical field coherently. The method is applied to a model terahertz quantum dot cascade laser system, where a means of treating coherent electron-optical-phonon coupling is also introduced. Results predict a strong increase in the upper state lifetime and operating temperature as compared to traditional well-based terahertz quantum cascade lasers. However, new complications also arise, including multiple peaks in the gain spectrum due to strong electron-phonon coupling, and strong parasitic subthreshold current channels that arise due to reduced dephasing. It is anticipated that novel design schemes will be necessary for such lasers to become a reality.
None, None
2016-11-21
Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. Our paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper also studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases we studied indicate that themore » Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.« less
Electrically tunable spin polarization in silicene: A multi-terminal spin density matrix approach
NASA Astrophysics Data System (ADS)
Chen, Son-Hsien
2016-05-01
Recent realized silicene field-effect transistor yields promising electronic applications. Using a multi-terminal spin density matrix approach, this paper presents an analysis of the spin polarizations in a silicene structure of the spin field-effect transistor by considering the intertwined intrinsic and Rashba spin-orbit couplings, gate voltage, Zeeman splitting, as well as disorder. Coexistence of the stagger potential and intrinsic spin-orbit coupling results in spin precession, making any in-plane polarization directions reachable by the gate voltage; specifically, the intrinsic coupling allows one to electrically adjust the in-plane components of the polarizations, while the Rashba coupling to adjust the out-of-plan polarizations. Larger electrically tunable ranges of in-plan polarizations are found in oppositely gated silicene than in the uniformly gated silicene. Polarizations in different phases behave distinguishably in weak disorder regime, while independent of the phases, stronger disorder leads to a saturation value.
2017-01-01
We present a second-order N-electron valence state perturbation theory (NEVPT2) based on a density matrix renormalization group (DMRG) reference wave function that exploits a Cholesky decomposition of the two-electron repulsion integrals (CD-DMRG-NEVPT2). With a parameter-free multireference perturbation theory approach at hand, the latter allows us to efficiently describe static and dynamic correlation in large molecular systems. We demonstrate the applicability of CD-DMRG-NEVPT2 for spin-state energetics of spin-crossover complexes involving calculations with more than 1000 atomic basis functions. We first assess, in a study of a heme model, the accuracy of the strongly and partially contracted variant of CD-DMRG-NEVPT2 before embarking on resolving a controversy about the spin ground state of a cobalt tropocoronand complex. PMID:28094988
None, None
2016-11-21
Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. Our paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper also studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases we studied indicate that the Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.
Symmetry-conserving purification of quantum states within the density matrix renormalization group
Nocera, Alberto; Alvarez, Gonzalo
2016-01-28
The density matrix renormalization group (DMRG) algorithm was originally designed to efficiently compute the zero-temperature or ground-state properties of one-dimensional strongly correlated quantum systems. The development of the algorithm at finite temperature has been a topic of much interest, because of the usefulness of thermodynamics quantities in understanding the physics of condensed matter systems, and because of the increased complexity associated with efficiently computing temperature-dependent properties. The ancilla method is a DMRG technique that enables the computation of these thermodynamic quantities. In this paper, we review the ancilla method, and improve its performance by working on reduced Hilbert spaces and using canonical approaches. Furthermore we explore its applicability beyond spins systems to t-J and Hubbard models.
Freitag, Leon; Knecht, Stefan; Angeli, Celestino; Reiher, Markus
2017-02-14
We present a second-order N-electron valence state perturbation theory (NEVPT2) based on a density matrix renormalization group (DMRG) reference wave function that exploits a Cholesky decomposition of the two-electron repulsion integrals (CD-DMRG-NEVPT2). With a parameter-free multireference perturbation theory approach at hand, the latter allows us to efficiently describe static and dynamic correlation in large molecular systems. We demonstrate the applicability of CD-DMRG-NEVPT2 for spin-state energetics of spin-crossover complexes involving calculations with more than 1000 atomic basis functions. We first assess, in a study of a heme model, the accuracy of the strongly and partially contracted variant of CD-DMRG-NEVPT2 before embarking on resolving a controversy about the spin ground state of a cobalt tropocoronand complex.
Nocera, A; Alvarez, G
2016-11-01
Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. This paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper then studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases studied indicate that the Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.
Pižorn, Iztok; Verstraete, Frank
2012-02-10
The numerical renormalization group (NRG) is rephrased as a variational method with the cost function given by the sum of all the energies of the effective low-energy Hamiltonian. This allows us to systematically improve the spectrum obtained by NRG through sweeping. The ensuing algorithm has a lot of similarities to the density matrix renormalization group (DMRG) when targeting many states, and this synergy of NRG and DMRG combines the best of both worlds and extends their applicability. We illustrate this approach with simulations of a quantum spin chain and a single impurity Anderson model where the accuracy of the effective eigenstates is greatly enhanced as compared to the NRG, especially in the transition to the continuum limit.
Density matrix renormalization group approach to two-fluid open many-fermion systems
NASA Astrophysics Data System (ADS)
Rotureau, J.; Michel, N.; Nazarewicz, W.; Płoszajczak, M.; Dukelsky, J.
2009-01-01
We have extended the density matrix renormalization group (DMRG) approach to two-fluid open many-fermion systems governed by complex-symmetric Hamiltonians. The applications are carried out for three- and four-nucleon (proton-neutron) systems within the Gamow shell model (GSM) in the complex-energy plane. We study necessary and sufficient conditions for the GSM+DMRG method to yield the correct ground-state eigenvalue and discuss different truncation schemes within the DMRG. The proposed approach will enable configuration interaction studies of weakly bound and unbound strongly interacting complex systems, which, because of a prohibitively large size of Fock space, cannot be treated by means of the direct diagonalization.
Mukhopadhyay, S; Ramasesha, S
2009-08-21
We have used the density matrix renormalization group (DMRG) method to study the linear and nonlinear optical responses of first generation nitrogen based dendrimers with donor acceptor groups. We have employed Pariser-Parr-Pople Hamiltonian to model the interacting pi electrons in these systems. Within the DMRG method we have used an innovative scheme to target excited states with large transition dipole to the ground state. This method reproduces exact optical gaps and polarization in systems where exact diagonalization of the Hamiltonian is possible. We have used a correction vector method which tacitly takes into account the contribution of all excited states, to obtain the ground state polarizibility, first hyperpolarizibility, and two photon absorption cross sections. We find that the lowest optical excitations as well as the lowest excited triplet states are localized. It is interesting to note that the first hyperpolarizibility saturates more rapidly with system size compared to linear polarizibility unlike that of linear polyenes.
Low-density, high-strength intermetallic matrix composites by XD (trademark) synthesis
NASA Technical Reports Server (NTRS)
Kumar, K. S.; Dipietro, M. S.; Brown, S. A.; Whittenberger, J. D.
1991-01-01
A feasibility study was conducted to evaluate the potential of particulate composites based on low-density, L1(sub 2) trialuminide matrices for high-temperature applications. The compounds evaluated included Al22Fe3Ti8 (as a multiphase matrix), Al67Ti25Cr8, and Al66Ti25Mn9. The reinforcement consisted of TiB2 particulates. The TiB2 composites were processed by ingot and powder metallurgy techniques. Microstructural characterization and mechanical testing were performed in the hot-pressed and hot-isostatic-pressed condition. The casting were sectioned and isothermally forged into pancakes. All the materials were tested in compression as a function of temperature, and at high temperatures as a function of strain rate. The test results are discussed.
Determination of an Initial Mesh Density for Finite Element Computations via Data Mining
Kanapady, R; Bathina, S K; Tamma, K K; Kamath, C; Kumar, V
2001-07-23
Numerical analysis software packages which employ a coarse first mesh or an inadequate initial mesh need to undergo a cumbersome and time consuming mesh refinement studies to obtain solutions with acceptable accuracy. Hence, it is critical for numerical methods such as finite element analysis to be able to determine a good initial mesh density for the subsequent finite element computations or as an input to a subsequent adaptive mesh generator. This paper explores the use of data mining techniques for obtaining an initial approximate finite element density that avoids significant trial and error to start finite element computations. As an illustration of proof of concept, a square plate which is simply supported at its edges and is subjected to a concentrated load is employed for the test case. Although simplistic, the present study provides insight into addressing the above considerations.
Nuclear-Structure Data Relevant to Neutinoless-Double-Beta-Decay Matrix Elements
NASA Astrophysics Data System (ADS)
Kay, Benjamin
2015-10-01
An observation of neutrinoless double beta decay is one of the most exciting prospects in contemporary physics. It follows that calculations of the nuclear matrix elements for this process are of high priority. The change in the wave functions between the initial and final states of the neutrinoless-double-beta-decay candidates 76Ge-->76Se, 100Mo-->100Ru, 130Te-->130Xe, and 136Xe-->136Ba have been studied with transfer reactions. The data are focused on the change in the occupancies of the valence orbitals in the ground states as two neutrons decay into two protons. The results set a strict constraint on any theoretical calculations describing this rearrangement and thus on the magnitude of the nuclear matrix elements for this process, which currently exhibit uncertainties at the factor of 2-4 level. Prior to these measurements there were limited experimental data were available A = 76 and 100 systems, and very limited data for the A = 130 and 136 systems, in a large part due to the gaseous Xe isotopes involved. The uncertainties on most of these data are estimated to range from 0.1-0.3 nucleons. The program started with the A = 76 system, with subsequent calculations, modified to reproduce the experimental occupancies, exhibiting a significant reduction in the discrepancy between various models. New data are available for the A = 100 , 130, and 136 systems. I review the program, making detailed comparisons between the latest theoretical calculations and the experimental data where available. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under Contract Number DE-AC02-06CH11357.
On-shell Delta I= 3/2 kaon weak matrix elements with nonzero total momentum
Yamazaki, T.
2009-05-20
We present our results for the on-shell {Delta}I = 3/2 kaon decay matrix elements using domain wall fermions and the DBW2 gauge action at one coarse lattice spacing corresponding to a{sup -1} = 1.31 GeV in the quenched approximation. The on-shell matrix elements are evaluated in two different frames: the center-of-mass frame and nonzero total-momentum frame. We employ the formula proposed by Lellouch and Luescher in the center-of-mass frame, and its extension for a nonzero total-momentum frame to extract the infinite volume, on-shell, center-of-mass frame decay amplitudes. We determine the decay amplitude at the physical pion mass and momentum from the chiral extrapolation and an interpolation of the relative momentum using the results calculated in the two frames. We have obtained ReA{sub 2} = 1.66(23)(+48/-03)(+53/-0) x 10{sup -8} GeV and ImA{sub 2} = -1.181(26)(+141/-014)(+44/-0) x 10{sup -12} GeV at the physical point, using the data at the relatively large pion mass, m{sub {pi}} > 0.35 GeV. The first error is statistic, and the second and third are systematic. The second error is estimated with several fits of the chiral extrapolation including the (quenched) chiral perturbation formula at next to leading order using only lighter pion masses. The third one is estimated with an analysis using the lattice dispersion relation. The result of ReA{sub 2} is reasonably consistent with experiment.
Minimizing matrix effect by femtosecond laser ablation and ionization in elemental determination.
Zhang, Bochao; He, Miaohong; Hang, Wei; Huang, Benli
2013-05-07
Matrix effect is unavoidable in direct solid analysis, which usually is a leading cause of the nonstoichiometric effect in quantitative analysis. In this research, experiments were carried out to study the overall characteristics of atomization and ionization in laser-solid interaction. Both nanosecond (ns) and femtosecond (fs) lasers were applied in a buffer-gas-assisted ionization source coupled with an orthogonal time-of-flight mass spectrometer. Twenty-nine solid standards of ten different matrices, including six metals and four dielectrics, were analyzed. The results indicate that the fs-laser mode offers more stable relative sensitivity coefficients (RSCs) with irradiance higher than 7 × 10(13) W·cm(-2), which could be more reliable in the determination of element composition of solids. The matrix effect is reduced by half when the fs-laser is employed, owing to the fact that the fs-laser ablation and ionization (fs-LAI) incurs an almost heat-free ablation process and creates a dense plasma for the stable ionization.
Leptonic CP phase determined by an equation involving PMNS matrix elements
NASA Astrophysics Data System (ADS)
Ke, Hong-Wei; Zhou, Jia-Hui; Li, Xue-Qian
2017-04-01
Several approximate equalities among the matrix elements of the Cabibbo–Kobayashi–Maskawa (CKM) and Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrices imply that hidden symmetries may exist and be common for both quark and neutrino sectors. The charge parity (CP) phase of the CKM matrix ({δ }{CKM}) is involved in these equalities and can be investigated when these equalities turn into several equations. As we substitute those experimentally measured values of the three mixing angles into the equations for quarks, it is noted that one of the equations which holds exactly has a solution {δ }{CKM}=({68.95}-1.15+1.15)^\\circ . That value accords with ({69.1}-3.85+2.02)^\\circ determined from available data. Generalizing the scenario to the lepton sector, the same equality determines the leptonic CP phase {δ }{PMNS} to be ({275.20}-1.15+1.15)^\\circ . Thus we predict the value of {δ }{PMNS} from the equation. So far there is no direct measurement on {δ }{PMNS}, but a recent analysis based on the neutrino oscillation data prefers a phase close to 270°.
Andrews, Lester
2004-02-20
Metal hydrides are of considerable importance in chemical synthesis as intermediates in catalytic hydrogenation reactions. Transition metal atoms react with dihydrogen to produce metal dihydrides or dihydrogen complexes and these may be trapped in solid matrix samples for infrared spectroscopic study. The MH(2) or M(H(2)) molecules so formed react further to form higher MH(4), (H(2))MH(2), or M(H(2))(2), and MH(6), (H(2))(2)MH(2), or M(H(2))(3) hydrides or complexes depending on the metal. In this critical review these transition metal and dihydrogen reaction products are surveyed for Groups 3 though 12 and the contrasting behaviour in Groups 6 and 10 is discussed. Minimum energy structures and vibrational frequencies predicted by Density Functional Theory agree with the experimental results, strongly supporting the identification of novel binary transition metal hydride species, which the matrix-isolation method is well-suited to investigate. 104 references are cited.
NASA Astrophysics Data System (ADS)
Nakatani, Naoki; Wouters, Sebastian; Van Neck, Dimitri; Chan, Garnet Kin-Lic
2014-01-01
Linear response theory for the density matrix renormalization group (DMRG-LRT) was first presented in terms of the DMRG renormalization projectors [J. J. Dorando, J. Hachmann, and G. K.-L. Chan, J. Chem. Phys. 130, 184111 (2009)]. Later, with an understanding of the manifold structure of the matrix product state (MPS) ansatz, which lies at the basis of the DMRG algorithm, a way was found to construct the linear response space for general choices of the MPS gauge in terms of the tangent space vectors [J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde, and F. Verstraete, Phys. Rev. Lett. 107, 070601 (2011)]. These two developments led to the formulation of the Tamm-Dancoff and random phase approximations (TDA and RPA) for MPS. This work describes how these LRTs may be efficiently implemented through minor modifications of the DMRG sweep algorithm, at a computational cost which scales the same as the ground-state DMRG algorithm. In fact, the mixed canonical MPS form implicit to the DMRG sweep is essential for efficient implementation of the RPA, due to the structure of the second-order tangent space. We present ab initio DMRG-TDA results for excited states of polyenes, the water molecule, and a [2Fe-2S] iron-sulfur cluster.
TIEG1-NULL OSTEOCYTES DISPLAY DEFECTS IN THEIR MORPHOLOGY, DENSITY AND SURROUNDING BONE MATRIX
Haddad, Oualid; Hawse, John R.; Subramaniam, Malayannan; Spelsberg, Thomas C.; Bensamoun, Sabine F.
2011-01-01
Through the development of TGFβ-inducible early gene-1 (TIEG1) knockout (KO) mice, we have demonstrated that TIEG1 plays an important role in osteoblast-mediated bone mineralization, and in bone resistance to mechanical strain. To further investigate the influence of TIEG1 in skeletal maintenance, osteocytes were analyzed by transmission electron microscopy using TIEG1 KO and wild-type mouse femurs at one, three and eight months of age. The results revealed an age-dependent change in osteocyte surface and density, suggesting a role for TIEG1 in osteocyte development. Moreover, there was a decrease in the amount of hypomineralized bone matrix surrounding the osteocytes in TIEG1 KO mice relative to wild-type controls. While little is known about the function or importance of this hypomineralized bone matrix immediately adjacent to osteocytes, this study reveals significant differences in this bone microenvironment and suggests that osteocyte function may be compromised in the absence of TIEG1 expression. PMID:22121306
Nakatani, Naoki; Wouters, Sebastian; Van Neck, Dimitri; Chan, Garnet Kin-Lic
2014-01-14
Linear response theory for the density matrix renormalization group (DMRG-LRT) was first presented in terms of the DMRG renormalization projectors [J. J. Dorando, J. Hachmann, and G. K.-L. Chan, J. Chem. Phys. 130, 184111 (2009)]. Later, with an understanding of the manifold structure of the matrix product state (MPS) ansatz, which lies at the basis of the DMRG algorithm, a way was found to construct the linear response space for general choices of the MPS gauge in terms of the tangent space vectors [J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde, and F. Verstraete, Phys. Rev. Lett. 107, 070601 (2011)]. These two developments led to the formulation of the Tamm-Dancoff and random phase approximations (TDA and RPA) for MPS. This work describes how these LRTs may be efficiently implemented through minor modifications of the DMRG sweep algorithm, at a computational cost which scales the same as the ground-state DMRG algorithm. In fact, the mixed canonical MPS form implicit to the DMRG sweep is essential for efficient implementation of the RPA, due to the structure of the second-order tangent space. We present ab initio DMRG-TDA results for excited states of polyenes, the water molecule, and a [2Fe-2S] iron-sulfur cluster.
The variational two-electron reduced-density-matrix method for extended systems
NASA Astrophysics Data System (ADS)
Rubin, Nicholas C.
In this thesis we develop the variational two-electron reduced-density-matrix method for extended systems. Extended systems are represented in two ways: i) lattice models describing the dominant valence electronic structure with periodic boundaries to account for their extended nature and ii) a crystalline-orbital basis built from atomic orbitals using the generalization of molecular orbital theory to polymers. The first part of this thesis (Ch. 3--4) examines the performance of the variational 2-RDM method on lattice systems with tunable electron correlation. The first of these systems is the classic Hubbard model with linear and ladder lattice topologies. Because electron correlation functions, such as charge- and spin-ordering, are linear functions of the 2-RDM, the difference in electronic structure between one- and quasi-one-dimensional systems is accurately characterized. The second model contains only two-body interactions and is unique among typical spin models in that it does not have a mean-field reference wave function. The ground state wave functions from all Hamiltonians in the model have the same 1-electron reduced density matrix; consequently, one-electron theories are largely inapplicable. The superconducting eta-pairing ground states make the model a unique tool for demonstrating the necessary N-representability in highly correlated environments. The second part of this thesis (Ch. 5--6) develops a formalism for modeling materials by solving the full Schrodinger equation. Crystalline-orbital Hartree-Fock provides a set of orbitals and integral tensors for the variational 2-RDM method. We demonstrate that time-reversal symmetry, which is implicitly included in position space electronic structure calculations, must be explicitly included as an N-representability constraint on the 2-RDM when using a momentum space basis. The necessity of these equality constraints is demonstrated by the accurate recovery of the binding energy of two polymers and the
One plus two-body random matrix ensembles with parity: Density of states and parity ratios
Vyas, Manan; Srivastava, P. C.; Kota, V. K. B.
2011-06-15
One plus two-body embedded Gaussian orthogonal ensemble of random matrices with parity [EGOE(1+2)-{pi}] generated by a random two-body interaction (modeled by GOE in two-particle spaces) in the presence of a mean field for spinless identical fermion systems is defined, generalizing the two-body ensemble with parity analyzed by Papenbrock and Weidenmueller [Phys. Rev. C 78, 054305 (2008)], in terms of two mixing parameters and a gap between the positive ({pi}=+) and negative ({pi}=-) parity single-particle (sp) states. Numerical calculations are used to demonstrate, using realistic values of the mixing parameters appropriate for some nuclei, that the EGOE(1+2)-{pi} ensemble generates Gaussian form (with corrections) for fixed parity eigenvalue densities (i.e., state densities). The random matrix model also generates many features in parity ratios of state densities that are similar to those predicted by a method based on the Fermi-gas model for nuclei. We have also obtained, by applying the formulation due to Chang et al. [Ann. Phys. (NY) 66, 137 (1971)], a simple formula for the spectral variances defined over fixed-(m{sub 1},m{sub 2}) spaces, where m{sub 1} is the number of fermions in the positive parity sp states and m{sub 2} is the number of fermions in the negative parity sp states. Similarly, using the binary correlation approximation, in the dilute limit, we have derived expressions for the lowest two-shape parameters. The smoothed densities generated by the sum of fixed-(m{sub 1},m{sub 2}) Gaussians with lowest two-shape corrections describe the numerical results in many situations. The model also generates preponderance of positive parity ground states for small values of the mixing parameters, and this is a feature seen in nuclear shell-model results.
Non-Periodic Finite-Element Formulation of Orbital-Free Density Functional Theory
Gavini, V; Knap, J; Bhattacharya, K; Ortiz, M
2006-10-06
We propose an approach to perform orbital-free density functional theory calculations in a non-periodic setting using the finite-element method. We consider this a step towards constructing a seamless multi-scale approach for studying defects like vacancies, dislocations and cracks that require quantum mechanical resolution at the core and are sensitive to long range continuum stresses. In this paper, we describe a local real space variational formulation for orbital-free density functional theory, including the electrostatic terms and prove existence results. We prove the convergence of the finite-element approximation including numerical quadratures for our variational formulation. Finally, we demonstrate our method using examples.
Improved EPMA Trace Element Accuracy Using a Matrix Iterated Quantitative Blank Correction
NASA Astrophysics Data System (ADS)
Donovan, J. J.; Wark, D. A.; Jercinovic, M. J.
2007-12-01
At trace element levels below several hundred PPM, accuracy is more often the limiting factor for EPMA quantification rather than precision. Modern EPMA instruments equipped with low noise detectors, counting electronics and large area analyzing crystals can now routinely achieve sensitivities for most elements in the 10 to 100 PPM levels (or even lower). But due to various sample and instrumental artifacts in the x-ray continuum, absolute accuracy is often the limiting factor for ultra trace element quantification. These artifacts have various mechanisms, but are usually attributed to sample artifacts (e.g., sample matrix absorption edges)1, detector artifacts (e.g., Ar or Xe absorption edges) 2 and analyzing crystal artifacts (extended peak tails preventing accurate determination of the true background and ¡§negative peaks¡¨ or ¡§holes¡¨ in the x-ray continuum). The latter being first described3 by Self, et al. and recently documented for the Ti kÑ in quartz geo-thermometer. 4 Ti (ka) Ti (ka) Ti (ka) Ti (ka) Ti (ka) Si () O () Total Average: -.00146 -.00031 -.00180 .00013 .00240 46.7430 53.2563 99.9983 Std Dev: .00069 .00075 .00036 .00190 .00117 .00000 .00168 .00419 The general magnitude of these artifacts can be seen in the above analyses of Ti ka in a synthetic quartz standard. The values for each spectrometer/crystal vary systematically from ¡V18 PPM to + 24 PPM. The exact mechanism for these continuum ¡§holes¡¨ is not known but may be related to secondary lattice diffraction occurring at certain Bragg angles depending on crystal mounting orientation for non-isometric analyzing crystals5. These x-ray continuum artifacts can produce systematic errors at levels up to 100 PPM or more depending on the particular analytical situation. In order to correct for these inaccuracies, a ¡§blank¡¨ correction has been developed that applies a quantitative correction to the measured x-ray intensities during the matrix iteration, by calculating the intensity
NASA Technical Reports Server (NTRS)
Abdul-Aziz, Ali; Baaklini, George Y.; Bhatt, Ramakrishna T.
2003-01-01
Most reverse engineering approaches involve imaging or digitizing an object and then creating a computerized reconstruction that can be integrated, in three dimensions, into a particular design environment. The rapid prototyping technique builds high-quality physical prototypes directly from computer-aided design files. This fundamental technique for interpreting and interacting with large data sets is being used here via Velocity2 (an integrated image-processing software, ref. 1) using computed tomography (CT) data to produce a prototype three-dimensional test specimen model for analyses. A study at the NASA Glenn Research Center proposes to use these capabilities to conduct a combined nondestructive evaluation (NDE) and finite element analysis (FEA) to screen pretest and posttest structural anomalies in structural components. A tensile specimen made of silicon nitrite (Si3N4) ceramic matrix composite was considered to evaluate structural durability and deformity. Ceramic matrix composites are being sought as candidate materials to replace nickel-base superalloys for turbine engine applications. They have the unique characteristics of being able to withstand higher operating temperatures and harsh combustion environments. In addition, their low densities relative to metals help reduce component mass (ref. 2). Detailed three-dimensional volume rendering of the tensile test specimen was successfully carried out with Velocity2 (ref. 1) using two-dimensional images that were generated via computed tomography. Subsequent, three-dimensional finite element analyses were performed, and the results obtained were compared with those predicted by NDE-based calculations and experimental tests. It was shown that Velocity2 software can be used to render a three-dimensional object from a series of CT scan images with a minimum level of complexity. The analytical results (ref. 3) show that the high-stress regions correlated well with the damage sites identified by the CT scans
Heavy-ion double charge exchange reactions: A tool toward 0 νββ nuclear matrix elements
NASA Astrophysics Data System (ADS)
Cappuzzello, F.; Cavallaro, M.; Agodi, C.; Bondì, M.; Carbone, D.; Cunsolo, A.; Foti, A.
2015-11-01
The knowledge of the nuclear matrix elements for the neutrinoless double beta decay is fundamental for neutrino physics. In this paper, an innovative technique to extract information on the nuclear matrix elements by measuring the cross section of a double charge exchange nuclear reaction is proposed. The basic point is that the initial- and final-state wave functions in the two processes are the same and the transition operators are similar. The double charge exchange cross sections can be factorized in a nuclear structure term containing the matrix elements and a nuclear reaction factor. First pioneering experimental results for the 40Ca(18O,18Ne)40Ar reaction at 270 MeV incident energy show that such cross section factorization reasonably holds for the crucial 0+ → 0+ transition to 40Args, at least at very forward angles.
Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions
Changlani, Hitesh J.; Zheng, Huihuo; Wagner, Lucas K.
2015-09-14
We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding. For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard U{sup ∗}/t to be 1.3 ± 0.2, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large-scale calculations using techniques designed for lattice models.
Density matrix renormalization group study of the Anyon-Hubbard model
NASA Astrophysics Data System (ADS)
Arcila-Forero, J.; Franco, R.; Silva-Valencia, J.
2016-02-01
Recently optical lattices allow us to observe phase transition without the uncertainty posed by complex materials, and the simulations of these systems are an excellent bridge between materials-based condensed matter physics and cold atoms. In this way, the computational physics related to many-body problems have increased in importance. Using the density matrix renormalization group method, we studied a Hubbard model for anyons, which is an equivalent to a variant of the Bose-Hubbard model in which the bosonic hopping depends on the local density. This is an exact mapping between anyons and bosons in one dimension. The anyons interlope between bosons and fermions. For two anyons under particle exchange, the wave function acquires a fractional phase eiθ . We conclude that this system exhibits two phases: Mott-insulator and superfluid. We present the phase diagram for some angles. The Mott lobe increases with an increase of the statistical. We observed a reentrance phase transition for all lobes. We showed that the model studied is in the same universality class as the Bose-Hubbard model with two-body interactions.
NASA Astrophysics Data System (ADS)
Gavryusev, V.; Signoles, A.; Ferreira-Cao, M.; Zürn, G.; Hofmann, C. S.; Günter, G.; Schempp, H.; Robert-de-Saint-Vincent, M.; Whitlock, S.; Weidemüller, M.
2016-08-01
We present combined measurements of the spatially resolved optical spectrum and the total excited-atom number in an ultracold gas of three-level atoms under electromagnetically induced transparency conditions involving high-lying Rydberg states. The observed optical transmission of a weak probe laser at the center of the coupling region exhibits a double peaked spectrum as a function of detuning, while the Rydberg atom number shows a comparatively narrow single resonance. By imaging the transmitted light onto a charge-coupled-device camera, we record hundreds of spectra in parallel, which are used to map out the spatial profile of Rabi frequencies of the coupling laser. Using all the information available we can reconstruct the full one-body density matrix of the three-level system, which provides the optical susceptibility and the Rydberg density as a function of spatial position. These results help elucidate the connection between three-level interference phenomena, including the interplay of matter and light degrees of freedom and will facilitate new studies of many-body effects in optically driven Rydberg gases.
The single-particle density matrix of a quantum bright soliton from the coordinate Bethe ansatz
NASA Astrophysics Data System (ADS)
Ayet, Alex; Brand, Joachim
2017-02-01
We present a novel approach for computing reduced density matrices for superpositions of eigenstates of a Bethe-ansatz solvable model by direct integration of the wave function in coordinate representation. A diagrammatic approach is developed to keep track of relevant terms and identify symmetries, which helps to reduce the number of terms that have to be evaluated numerically. As a first application we compute with modest numerical resources the single-particle density matrix and its eigenvalues including the condensate fraction for a quantum bright soliton with up to N = 10 bosons. The latter are constructed as superpositions of string-type Bethe-ansatz eigenstates of nonrelativistic bosons in one spatial dimension with attractive contact interaction. Upon delocalising the superposition in momentum space we find that the condensate fraction reaches maximum values larger than 97% with weak particle-number dependence in the range of particles studied. The presented approach is suitable for studying time-dependent problems and generalises to higher-order correlation functions.
SCDM-k: Localized orbitals for solids via selected columns of the density matrix
NASA Astrophysics Data System (ADS)
Damle, Anil; Lin, Lin; Ying, Lexing
2017-04-01
The recently developed selected columns of the density matrix (SCDM) method (Damle et al. 2015, [16]) is a simple, robust, efficient and highly parallelizable method for constructing localized orbitals from a set of delocalized Kohn-Sham orbitals for insulators and semiconductors with Γ point sampling of the Brillouin zone. In this work we generalize the SCDM method to Kohn-Sham density functional theory calculations with k-point sampling of the Brillouin zone, which is needed for more general electronic structure calculations for solids. We demonstrate that our new method, called SCDM-k, is by construction gauge independent and a natural way to describe localized orbitals. SCDM-k computes localized orbitals without the use of an optimization procedure, and thus does not suffer from the possibility of being trapped in a local minimum. Furthermore, the computational complexity of using SCDM-k to construct orthogonal and localized orbitals scales as O (Nlog N) where N is the total number of k-points in the Brillouin zone. SCDM-k is therefore efficient even when a large number of k-points are used for Brillouin zone sampling. We demonstrate the numerical performance of SCDM-k using systems with model potentials in two and three dimensions.
Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model
NASA Astrophysics Data System (ADS)
Ehlers, G.; White, S. R.; Noack, R. M.
2017-03-01
The performance of the density matrix renormalization group (DMRG) is strongly influenced by the choice of the local basis of the underlying physical lattice. We demonstrate that, for the two-dimensional Hubbard model, the hybrid-real-momentum-space formulation of the DMRG is computationally more efficient than the standard real-space formulation. In particular, we show that the computational cost for fixed bond dimension of the hybrid-space DMRG is approximately independent of the width of the lattice, in contrast to the real-space DMRG, for which it is proportional to the width squared. We apply the hybrid-space algorithm to calculate the ground state of the doped two-dimensional Hubbard model on cylinders of width four and six sites; at n =0.875 filling, the ground state exhibits a striped charge-density distribution with a wavelength of eight sites for both U /t =4.0 and 8.0 . We find that the strength of the charge ordering depends on U /t and on the boundary conditions. Furthermore, we investigate the magnetic ordering as well as the decay of the static spin, charge, and pair-field correlation functions.
Requist, Ryan; Pankratov, Oleg
2011-05-15
We prove that if the two-body terms in the equation of motion for the one-body reduced density matrix are approximated by ground-state functionals, the eigenvalues of the one-body reduced density matrix (occupation numbers) remain constant in time. This deficiency is related to the inability of such an approximation to account for relative phases in the two-body reduced density matrix. We derive an exact differential equation giving the functional dependence of these phases in an interacting Landau-Zener model and study their behavior in short- and long-time regimes. The phases undergo resonances whenever the occupation numbers approach the boundaries of the interval [0,1]. In the long-time regime, the occupation numbers display correlation-induced oscillations and the memory dependence of the functionals assumes a simple form.
Matrix elements in the coupled-cluster approach - With application to low-lying states in Li
NASA Technical Reports Server (NTRS)
Martensson-Pendrill, Ann-Marie; Ynnerman, Anders
1990-01-01
A procedure is suggested for evaluating matrix elements of an operator between wavefunctions in the coupled-cluster form. The use of the exponential ansatz leads to compact exponential expressions also for matrix elements. Algorithms are developed for summing all effects of one-particle clusters and certain chains of two-particle clusters (containing the well-known random-phase approximation as a subset). The treatment of one-particle perturbations in single valence states is investigated in detail. As examples the oscillator strength for the 2s-2p transition in Li as well as the hyperfine structure for the two states are studied and compared to earlier work.
Identification of secondary structure elements in intermediate-resolution density maps.
Baker, Matthew L; Ju, Tao; Chiu, Wah
2007-01-01
An increasing number of structural studies of large macromolecular complexes, both in X-ray crystallography and cryo-electron microscopy, have resulted in intermediate-resolution (5-10 A) density maps. Despite being limited in resolution, significant structural and functional information may be extractable from these maps. To aid in the analysis and annotation of these complexes, we have developed SSEhunter, a tool for the quantitative detection of alpha helices and beta sheets. Based on density skeletonization, local geometry calculations, and a template-based search, SSEhunter has been tested and validated on a variety of simulated and authentic subnanometer-resolution density maps. The result is a robust, user-friendly approach that allows users to quickly visualize, assess, and annotate intermediate-resolution density maps. Beyond secondary structure element identification, the skeletonization algorithm in SSEhunter provides secondary structure topology, which is potentially useful in leading to structural models of individual molecular components directly from the density.
NASA Technical Reports Server (NTRS)
Sanfeliz, Jose G.
1993-01-01
Micromechanical modeling via elastic-plastic finite element analyses were performed to investigate the effects that the residual stresses and the degree of matrix work hardening (i.e., cold-worked, annealed) have upon the behavior of a 9 vol percent, unidirectional W/Cu composite, undergoing tensile loading. The inclusion of the residual stress-containing state as well as the simulated matrix material conditions proved to be significant since the Cu matrix material exhibited plastic deformation, which affected the subsequent tensile response of the composite system. The stresses generated during cooldown to room temperature from the manufacturing temperature were more of a factor on the annealed-matrix composite, since they induced the softened matrix to plastically flow. This event limited the total load-carrying capacity of this matrix-dominated, ductile-ductile type material system. Plastic deformation of the hardened-matrix composite during the thermal cooldown stage was not considerable, therefore, the composite was able to sustain a higher stress before showing any appreciable matrix plasticity. The predicted room temperature, stress-strain response, and deformation stages under both material conditions represented upper and lower bounds characteristic of the composite's tensile behavior. The initial deformation stage for the hardened material condition showed negligible matrix plastic deformation while for the annealed state, its initial deformation stage showed extensive matrix plasticity. Both material conditions exhibited a final deformation stage where the fiber and matrix were straining plastically. The predicted stress-strain results were compared to the experimental, room temperature, tensile stress-strain curve generated from this particular composite system. The analyses indicated that the actual thermal-mechanical state of the composite's Cu matrix, represented by the experimental data, followed the annealed material condition.
Kussmann, Jörg; Luenser, Arne; Beer, Matthias; Ochsenfeld, Christian
2015-03-07
An analytical method to calculate the molecular vibrational Hessian matrix at the self-consistent field level is presented. By analysis of the multipole expansions of the relevant derivatives of Coulomb-type two-electron integral contractions, we show that the effect of the perturbation on the electronic structure due to the displacement of nuclei decays at least as r{sup −2} instead of r{sup −1}. The perturbation is asymptotically local, and the computation of the Hessian matrix can, in principle, be performed with O(N) complexity. Our implementation exhibits linear scaling in all time-determining steps, with some rapid but quadratic-complexity steps remaining. Sample calculations illustrate linear or near-linear scaling in the construction of the complete nuclear Hessian matrix for sparse systems. For more demanding systems, scaling is still considerably sub-quadratic to quadratic, depending on the density of the underlying electronic structure.
Fermionic Symmetries: Degeneracies when T=0 Two body matrix elements are set equal to zero
NASA Astrophysics Data System (ADS)
Zamick, Larry; Robinson, Shadow Jq
2001-10-01
In shell model calculations for ^43Ti and ^44Ti not perfect but surprisingly good results are obtained when all the T=0 two body matrix elements are set equal to zero. In this model and in the single j shell approximation (j=f_7/2) many degeneracies arise. For example for the T=1/2 states in ^43Ti(^43Sc) the I=1/2_1^- and 1/32_1^- states are degenerate as are the 1/32_2^-, 1/72_1^- and 1/92_1^- T=1/2 states. In ^44Ti the T=0 states 3^+_2, 7^+_2,9^+_1, and 10^+1 are degenerate and so are the 10^+2 and 12^+1 states. Concerning the 1/2_1^- and 1/32_1^- we find that both have (J_p,J_n) configuration (4,7/2). For the 3^+_2, 7^+_2,9^+_1, and 10^+1 all four states have the configurations (4,6) and (6,4). This means that couplings to other states will vanish. This means that certain 6j and 9j symbols will vanish e.g. j & j& 4 j&1/32& 6 \\=0 and j & j& 6 j&j& 6 4 & 6 &10 \\=0. One can explain these vanishings in terms of Talmi's method of calculating coeffiecients of fractional parentage to states not allowed by the Pauli principle. For example for the T=3/2 states of ^43Ca there are no f_7/2^3 I=1/32^- states. Hence the c.f.p. to these states must vanish. One c.f.p. contains the above 6j symbol and so this 6j symbol will vanish. For the T=2 states in ^44Ca there is no f_7/2^4 state with I=10^+. One of the two particle c.f.p to this state is proportional to the above 9j symbol and so the 9j must vanish. Note that we are using arguments about T=3/2 states to explain degeneracies of T=1/2 states; and we are using arguments about T=2 states to explain degeneracies of T=0 states. When T=0 two body matrix elements are reintroduced the 9^+1 and 10^+1 are no longer degenerate and the splitting even in a full fp space calculation is due almost entirely to the T=0 matrix elements. The common thread for the T=1/2 and T=0 states that are degenerate is that they have angular momentum which in the single j shell calculation cannot occur for identical particles. For these angular momenta
LATTICE MATRIX ELEMENTS AND CP VIOLATION IN B AND KA PHYSICS: STATUS AND OUTLOOK.
SONI,A.
2003-01-03
Status of lattice calculations of hadron matrix elements along with CP violation in B and in K systems is reviewed. Lattice has provided useful input which, in conjunction with experimental data, leads to the conclusion that CP-odd phase in the CKM matrix plays the dominant role in the observed asymmetry in B {yields} {psi}K{sub s}. It is now quite likely that any beyond the SM, CP-odd, phase will cause only small deviations in B-physics. Search for the effects of the new phase(s) will consequently require very large data samples as well as very precise theoretical predictions. Clean determination of all the angles of the unitarity triangle therefore becomes essential. In this regard B {yields} KD{sup 0} processes play a unique role. Regarding K-decays, remarkable progress made by theory with regard to maintenance of chiral symmetry on the lattice is briefly discussed. First application already provide quantitative information on B{sub K} and the {Delta}I = 1/2 rule. The enhancement in ReA{sub 0} appears to arise solely from tree operators, esp. Q{sub 2}; penguin contribution to ReA{sub 0} appears to be very small. However, improved calculations are necessary for {epsilon}{prime}/{epsilon} as there the contributions of QCD penguins and electroweak penguins largely seem to cancel. There are good reasons, though, to believe that these cancellations will not survive improvements that are now underway. Importance of determining the unitarity triangle purely from K-decays is also emphasized.
Senior, C.L.; Zeng, T.; Che, J.; Ames, M.R.; Sarofim, A.F.; Olmez, I.; Huggins, Frank E.; Shah, N.; Huffman, G.P.; Kolker, A.; Mroczkowski, S.; Palmer, C.; Finkelman, R.
2000-01-01
Trace elements in coal have diverse modes of occurrence that will greatly influence their behavior in many coal utilization processes. Mode of occurrence is important in determining the partitioning during coal cleaning by conventional processes, the susceptibility to oxidation upon exposure to air, as well as the changes in physical properties upon heating. In this study, three complementary methods were used to determine the concentrations and chemical states of trace elements in pulverized samples of four US coals: Pittsburgh, Illinois No. 6, Elkhorn and Hazard, and Wyodak coals. Neutron Activation Analysis (NAA) was used to measure the absolute concentration of elements in the parent coals and in the size- and density-fractionated samples. Chemical leaching and X-ray absorption fine structure (XAFS) spectroscopy were used to provide information on the form of occurrence of an element in the parent coals. The composition differences between size-segregated coal samples of different density mainly reflect the large density difference between minerals, especially pyrite, and the organic portion of the coal. The heavy density fractions are therefore enriched in pyrite and the elements associated with pyrite, as also shown by the leaching and XAFS methods. Nearly all the As is associated with pyrite in the three bituminous coals studied. The sub-bituminous coal has a very low content of pyrite and arsenic; in this coal arsenic appears to be primarily organically associated. Selenium is mainly associated with pyrite in the bituminous coal samples. In two bituminous coal samples, zinc is mostly in the form of ZnS or associated with pyrite, whereas it appears to be associated with other minerals in the other two coals. Zinc is also the only trace element studied that is significantly more concentrated in the smaller (45 to 63 ??m) coal particles.
NASA Technical Reports Server (NTRS)
Duffy, Stephen F.
1998-01-01
The development of modeling approaches for the failure analysis of ceramic-based material systems used in high temperature environments was the primary objective of this research effort. These materials have the potential to support many key engineering technologies related to the design of aeropropulsion systems. Monolithic ceramics exhibit a number of useful properties such as retention of strength at high temperatures, chemical inertness, and low density. However, the use of monolithic ceramics has been limited by their inherent brittleness and a large variation in strength. This behavior has motivated material scientists to reinforce the monolithic material with a ceramic fiber. The addition of a second ceramic phase with an optimized interface increases toughness and marginally increases strength. The primary purpose of the fiber is to arrest crack growth, not to increase strength. The material systems of interest in this research effort were laminated ceramic matrix composites, as well as two- and three- dimensional fabric reinforced ceramic composites. These emerging composite systems can compete with metals in many demanding applications. However, the ongoing metamorphosis of ceramic composite material systems, and the lack of standardized design data has in the past tended to minimize research efforts related to structural analysis. Many structural components fabricated from ceramic matrix composites (CMC) have been designed by "trial and error." The justification for this approach lies in the fact that during the initial developmental phases for a material system fabrication issues are paramount. Emphasis is placed on demonstrating feasibility rather than fully understanding the processes controlling mechanical behavior. This is understandable during periods of rapid improvements in material properties for any composite system. But to avoid the ad hoc approach, the analytical methods developed under this effort can be used to develop rational structural
Bubin, Sergiy; Adamowicz, Ludwik
2008-03-21
In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N-particle system with the L=1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.
NASA Astrophysics Data System (ADS)
Bubin, Sergiy; Adamowicz, Ludwik
2008-03-01
In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N-particle system with the L =1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.
NASA Astrophysics Data System (ADS)
Lim, S. P.; Sheng, D. N.
2016-07-01
A many-body localized (MBL) state is a new state of matter emerging in a disordered interacting system at high-energy densities through a disorder-driven dynamic phase transition. The nature of the phase transition and the evolution of the MBL phase near the transition are the focus of intense theoretical studies with open issues in the field. We develop an entanglement density matrix renormalization group (En-DMRG) algorithm to accurately target highly excited states for MBL systems. By studying the one-dimensional Heisenberg spin chain in a random field, we demonstrate the accuracy of the method in obtaining energy eigenstates and the corresponding statistical results of quantum states in the MBL phase. Based on large system simulations by En-DMRG for excited states, we demonstrate some interesting features in the entanglement entropy distribution function, which is characterized by two peaks: one at zero and another one at the quantized entropy S =ln2 with an exponential decay tail on the S >ln2 side. Combining En-DMRG with exact diagonalization simulations, we demonstrate that the transition from the MBL phase to the delocalized ergodic phase is driven by rare events where the locally entangled spin pairs develop power-law correlations. The corresponding phase diagram contains an intermediate or crossover regime, which has power-law spin-z correlations resulting from contributions of the rare events. We discuss the physical picture for the numerical observations in this regime, where various distribution functions are distinctly different from results deep in the ergodic and MBL phases for finite-size systems. Our results may provide new insights for understanding the phase transition in such systems.
NASA Astrophysics Data System (ADS)
Giesbertz, K. J. H.; Gritsenko, O. V.; Baerends, E. J.
2012-03-01
Adiabatic response time-dependent density functional theory (TDDFT) suffers from the restriction to basically an occupied → virtual single excitation formulation. Adiabatic time-dependent density matrix functional theory allows to break away from this restriction. Problematic excitations for TDDFT, viz. bonding-antibonding, double, charge transfer, and higher excitations, are calculated along the bond-dissociation coordinate of the prototype molecules H2 and HeH+ using the recently developed adiabatic linear response phase-including (PI) natural orbital theory (PINO). The possibility to systematically increase the scope of the calculation from excitations out of (strongly) occupied into weakly occupied ("virtual") natural orbitals to larger ranges of excitations is explored. The quality of the PINO response calculations is already much improved over TDDFT even when the severest restriction is made, to virtually the size of the TDDFT diagonalization problem (only single excitation out of occupied orbitals plus all diagonal doubles). Further marked improvement is obtained with moderate extension to allow for excitation out of the lumo and lumo+1, which become fractionally occupied in particular at longer distances due to left-right correlation effects. In the second place the interpretation of density matrix response calculations is elucidated. The one-particle reduced density matrix response for an excitation is related to the transition density matrix to the corresponding excited state. The interpretation of the transition density matrix in terms of the familiar excitation character (single excitations, double excitations of various types, etc.) is detailed. The adiabatic PINO theory is shown to successfully resolve the problematic cases of adiabatic TDDFT when it uses a proper PI orbital functional such as the PILS functional.
Giesbertz, K J H; Gritsenko, O V; Baerends, E J
2012-03-07
Adiabatic response time-dependent density functional theory (TDDFT) suffers from the restriction to basically an occupied → virtual single excitation formulation. Adiabatic time-dependent density matrix functional theory allows to break away from this restriction. Problematic excitations for TDDFT, viz. bonding-antibonding, double, charge transfer, and higher excitations, are calculated along the bond-dissociation coordinate of the prototype molecules H(2) and HeH(+) using the recently developed adiabatic linear response phase-including (PI) natural orbital theory (PINO). The possibility to systematically increase the scope of the calculation from excitations out of (strongly) occupied into weakly occupied ("virtual") natural orbitals to larger ranges of excitations is explored. The quality of the PINO response calculations is already much improved over TDDFT even when the severest restriction is made, to virtually the size of the TDDFT diagonalization problem (only single excitation out of occupied orbitals plus all diagonal doubles). Further marked improvement is obtained with moderate extension to allow for excitation out of the lumo and lumo+1, which become fractionally occupied in particular at longer distances due to left-right correlation effects. In the second place the interpretation of density matrix response calculations is elucidated. The one-particle reduced density matrix response for an excitation is related to the transition density matrix to the corresponding excited state. The interpretation of the transition density matrix in terms of the familiar excitation character (single excitations, double excitations of various types, etc.) is detailed. The adiabatic PINO theory is shown to successfully resolve the problematic cases of adiabatic TDDFT when it uses a proper PI orbital functional such as the PILS functional.
A measurement of the top quark mass with a matrix element method
Gibson, Adam Paul
2006-01-01
The authors present a measurement of the mass of the top quark. The event sample is selected from proton-antiproton collisions, at 1.96 TeV center-of-mass energy, observed with the CDF detector at Fermilab's Tevatron. They consider a 318 pb^{-1} dataset collected between March 2002 and August 2004. They select events that contain one energetic lepton, large missing transverse energy, exactly four energetic jets, and at least one displaced vertex b tag. The analysis uses leading-order t$\\bar{t}$ and background matrix elements along with parameterized parton showering to construct event-by-event likelihoods as a function of top quark mass. From the 63 events observed with the 318 pb^{-1} dataset they extract a top quark mass of 172.0 ± 2.6(stat) ± 3.3(syst) GeV/c^{2} from the joint likelihood. The mean expected statistical uncertainty is 3.2 GeV/c^{2} for m $\\bar{t}$ = 178 GTeV/c^{2} and 3.1 GeV/c^{2} for m $\\bar{t}$ = 172.5 GeV/c^{2}. The systematic error is dominated by the uncertainty of the jet energy scale.
NASA Astrophysics Data System (ADS)
Fatchurrohman, N.; Marini, C. D.; Suraya, S.; Iqbal, AKM Asif
2016-02-01
The increasing demand of fuel efficiency and light weight components in automobile sectors have led to the development of advanced material parts with improved performance. A specific class of MMCs which has gained a lot of attention due to its potential is aluminium metal matrix composites (Al-MMCs). Product performance investigation of Al- MMCs is presented in this article, where an Al-MMCs brake disc is analyzed using finite element analysis. The objective is to identify the potentiality of replacing the conventional iron brake disc with Al-MMCs brake disc. The simulation results suggested that the MMCs brake disc provided better thermal and mechanical performance as compared to the conventional cast iron brake disc. Although, the Al-MMCs brake disc dissipated higher maximum temperature compared to cast iron brake disc's maximum temperature. The Al-MMCs brake disc showed a well distributed temperature than the cast iron brake disc. The high temperature developed at the ring of the disc and heat was dissipated in circumferential direction. Moreover, better thermal dissipation and conduction at brake disc rotor surface played a major influence on the stress. As a comparison, the maximum stress and strain of Al-MMCs brake disc was lower than that induced on the cast iron brake disc.
NASA Astrophysics Data System (ADS)
Ablinger, J.; Behring, A.; Blümlein, J.; De Freitas, A.; von Manteuffel, A.; Schneider, C.
2016-05-01
Three loop ladder and V-topology diagrams contributing to the massive operator matrix element AQg are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable N and the dimensional parameter ε. Given these representations, the desired Laurent series expansions in ε can be obtained with the help of our computer algebra toolbox. Here we rely on generalized hypergeometric functions and Mellin-Barnes representations, on difference ring algorithms for symbolic summation, on an optimized version of the multivariate Almkvist-Zeilberger algorithm for symbolic integration, and on new methods to calculate Laurent series solutions of coupled systems of differential equations. The solutions can be computed for general coefficient matrices directly for any basis also performing the expansion in the dimensional parameter in case it is expressible in terms of indefinite nested product-sum expressions. This structural result is based on new results of our difference ring theory. In the cases discussed we deal with iterative sum- and integral-solutions over general alphabets. The final results are expressed in terms of special sums, forming quasi-shuffle algebras, such as nested harmonic sums, generalized harmonic sums, and nested binomially weighted (cyclotomic) sums. Analytic continuations to complex values of N are possible through the recursion relations obeyed by these quantities and their analytic asymptotic expansions. The latter lead to a host of new constants beyond the multiple zeta values, the infinite generalized harmonic and cyclotomic sums in the case of V-topologies.
Characterization of metal matrix composites by linear ultrasonics and finite element modeling.
Chen, Xuesheng; Sharples, Steve D; Clark, Matt; Wright, David
2013-02-01
Titanium metal matrix composites (TiMMCs) offer advantages over traditional materials for aerospace applications due to the increased mechanical strength of the materials. But the non-destructive inspection of these materials, especially with ultrasound, is in an infancy stage. If the manufacturing process of TiMMC is not correctly controlled, then disbonds and voids between the fibers can result. The effective microstructure of the composite makes difficulty to interpret results from traditional ultrasound techniques because of the scattering caused by fibers; the scattering prevents the ultrasound from penetrating far into the composite region and produces a background signal masking any reflections from voids. In this paper, relatively low frequency ultrasound is used to probe the composite region, and the state of the composite (porosity) is inferred from the velocity of the ultrasound traversing the composite. The relationship between the velocity and porosity is complex in this regime, so finite element (FE) analysis is used to model the composite regions and relate the velocity to the porosity. The FE simulated results are validated by ultrasound velocity measurements.
Quarkonium polarization and the long distance matrix elements hierarchies using jet substructure
NASA Astrophysics Data System (ADS)
Dai, Lin; Shrivastava, Prashant
2017-08-01
We investigate the quarkonium production mechanisms in jets at the LHC, using the fragmenting jet functions (FJF) approach. Specifically, we discuss the jet energy dependence of the J /ψ production cross section at the LHC. By comparing the cross sections for the different NRQCD production channels (1S0[8], 3S1[8], 3PJ[8], and 3cripts>S1[1]), we find that at fixed values of energy fraction z carried by the J /ψ , if the normalized cross section is a decreasing function of the jet energy, in particular for z >0.5 , then the depolarizing 1S0[8] must be the dominant channel. This makes the prediction made in [Baumgart et al., J. High Energy Phys. 11 (2014) 003, 10.1007/JHEP11(2014)003] for the FJF's also true for the cross section. We also make comparisons between the long distance matrix elements extracted by various groups. This analysis could potentially shed light on the polarization properties of the J /ψ production in high pT region.
Menéndez, Javier
2013-12-30
We explore the theoretical uncertainties related to the transition operator of neutrinoless double-beta (0νββ) decay. The transition operator used in standard calculations is a product of one-body currents, that can be obtained phenomenologically as in Tomoda [1] or Šimkovic et al. [2]. However, corrections to the operator are hard to obtain in the phenomenological approach. Instead, we calculate the 0νββ decay operator in the framework of chiral effective theory (EFT), which gives a systematic order-by-order expansion of the transition currents. At leading orders in chiral EFT we reproduce the standard one-body currents of Refs. [1] and [2]. Corrections appear as two-body (2b) currents predicted by chiral EFT. We compute the effects of the leading 2b currents to the nuclear matrix elements of 0νββ decay for several transition candidates. The 2b current contributions are related to the quenching of Gamow-Teller transitions found in nuclear structure calculations.
NASA Technical Reports Server (NTRS)
Jenkins, J. M.; Taylor, A. H.; Sakata, I. F.
1985-01-01
A hybrid spar of titanium with an integrally brazed composite, consisting of an aluminum matrix reinforced with boron-carbide-coated fibers, was heated in an oven and the resulting thermal stresses were measured. Uniform heating of the spar in an oven resulted in thermal stresses arising from the effects of dissimilar materials and anisotropy of the metal matrix composite. Thermal stresses were calculated from a finite element structural model using anisotropic material properties deduced from constituent properties and rules of mixtures. Comparisons of calculated thermal stresses with measured thermal stresses on the spar are presented. It was shown that failure to account for anisotropy in the metal matrix composite elements would result in large errors in correlating measured and calculated thermal stresses. It was concluded that very strong material characterization efforts are required to predict accurate thermal stresses in anisotropic composite structures.
Hollaus, K; Magele, C; Merwa, R; Scharfetter, H
2004-02-01
Magnetic induction tomography of biological tissue is used to reconstruct the changes in the complex conductivity distribution by measuring the perturbation of an alternating primary magnetic field. To facilitate the sensitivity analysis and the solution of the inverse problem a fast calculation of the sensitivity matrix, i.e. the Jacobian matrix, which maps the changes of the conductivity distribution onto the changes of the voltage induced in a receiver coil, is needed. The use of finite differences to determine the entries of the sensitivity matrix does not represent a feasible solution because of the high computational costs of the basic eddy current problem. Therefore, the reciprocity theorem was exploited. The basic eddy current problem was simulated by the finite element method using symmetric tetrahedral edge elements of second order. To test the method various simulations were carried out and discussed.
Nuclear motion effects on the density matrix of crystals: An ab initio Monte Carlo harmonic approach
NASA Astrophysics Data System (ADS)
Pisani, Cesare; Erba, Alessandro; Ferrabone, Matteo; Dovesi, Roberto
2012-07-01
In the frame of the Born-Oppenheimer approximation, nuclear motions in crystals can be simulated rather accurately using a harmonic model. In turn, the electronic first-order density matrix (DM) can be expressed as the statistically weighted average over all its determinations each resulting from an instantaneous nuclear configuration. This model has been implemented in a computational scheme which adopts an ab initio one-electron (Hartree-Fock or Kohn-Sham) Hamiltonian in the CRYSTAL program. After selecting a supercell of reasonable size and solving the corresponding vibrational problem in the harmonic approximation, a Metropolis algorithm is adopted for generating a sample of nuclear configurations which reflects their probability distribution at a given temperature. For each configuration in the sample the "instantaneous" DM is calculated, and its contribution to the observables of interest is extracted. Translational and point symmetry of the crystal as reflected in its average DM are fully exploited. The influence of zero-point and thermal motion of nuclei on such important first-order observables as x-ray structure factors and Compton profiles can thus be estimated.
Entanglement or separability: the choice of how to factorize the algebra of a density matrix
NASA Astrophysics Data System (ADS)
Thirring, W.; Bertlmann, R. A.; Köhler, P.; Narnhofer, H.
2011-10-01
Quantum entanglement has become a resource for the fascinating developments in quantum information and quantum communication during the last decades. It quantifies a certain nonclassical correlation property of a density matrix representing the quantum state of a composite system. We discuss the concept of how entanglement changes with respect to different factorizations of the algebra which describes the total quantum system. Depending on the considered factorization a quantum state appears either entangled or separable. For pure states we always can switch unitarily between separability and entanglement, however, for mixed states a minimal amount of mixedness is needed. We discuss our general statements in detail for the familiar case of qubits, the GHZ states, Werner states and Gisin states, emphasizing their geometric features. As theorists we use and play with this free choice of factorization, which for an experimentalist is often naturally fixed. For theorists it offers an extension of the interpretations and is adequate to generalizations, as we point out in the examples of quantum teleportation and entanglement swapping.
Pisani, Cesare; Erba, Alessandro; Ferrabone, Matteo; Dovesi, Roberto
2012-07-28
In the frame of the Born-Oppenheimer approximation, nuclear motions in crystals can be simulated rather accurately using a harmonic model. In turn, the electronic first-order density matrix (DM) can be expressed as the statistically weighted average over all its determinations each resulting from an instantaneous nuclear configuration. This model has been implemented in a computational scheme which adopts an ab initio one-electron (Hartree-Fock or Kohn-Sham) Hamiltonian in the CRYSTAL program. After selecting a supercell of reasonable size and solving the corresponding vibrational problem in the harmonic approximation, a Metropolis algorithm is adopted for generating a sample of nuclear configurations which reflects their probability distribution at a given temperature. For each configuration in the sample the "instantaneous" DM is calculated, and its contribution to the observables of interest is extracted. Translational and point symmetry of the crystal as reflected in its average DM are fully exploited. The influence of zero-point and thermal motion of nuclei on such important first-order observables as x-ray structure factors and Compton profiles can thus be estimated.
Application of variational reduced-density-matrix theory to organic molecules
NASA Astrophysics Data System (ADS)
Gidofalvi, Gergely; Mazziotti, David A.
2005-03-01
Variational calculation of the two-electron reduced-density matrix (2-RDM), using a new first-order algorithm [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)], is applied to medium-sized organic molecules. The calculations reveal systematic trends in the accuracy of the energy with well-known chemical concepts such as hybridization, electronegativity, and atomic size. Furthermore, correlation energies from hydrocarbon chains indicate that the calculation of the 2-RDM subject to two-positivity conditions is size extensive, that is, the energy grows linearly with the number of electrons. Because organic molecules have a well-defined set of functional groups, we employ the trends in energy accuracy of the functional groups to design a correction to the 2-RDM energy for an arbitrary organic molecule. We apply the 2-RDM calculations with the functional-group correction to a large set of organic molecules with different functional groups. Energies with millihartree accuracy are obtained both at equilibrium and nonequilibrium geometries.
Analytical nuclear derivatives for the parametric two-electron reduced density matrix method
NASA Astrophysics Data System (ADS)
Valentine, Andrew J. S.; Mazziotti, David A.
2017-10-01
Efficient and accurate nuclear gradients are essential to performing molecular optimizations. Here for the first time we present analytical nuclear gradients for the parametric two-electron reduced-density-matrix method (p2-RDM), which uses the 2-RDM as the primary variable in calculations in lieu of the many-electron wavefunction. While numerical gradients require six energy evaluations for each atom, analytical gradients require only a single calculation for each geometry sampled. We present benchmark p2-RDM geometry optimizations that show analytical gradients reduce CPU times by as much as 80%, even for small molecules. We also use p2-RDM to evaluate the bond length alternation (BLA), or the difference in length between adjacent single and double bonds, of trans-polyacetylene (PA). We find that the BLA in the extrapolated limit to be 0.080 Å, in agreement with experiment and closely mirroring the prediction of the more expensive coupled-cluster with single and double excitations with perturbative triples (CCSD(T)).
Extended density-matrix model applied to silicon-based terahertz quantum cascade lasers
NASA Astrophysics Data System (ADS)
Dinh, T. V.; Valavanis, A.; Lever, L. J. M.; Ikonić, Z.; Kelsall, R. W.
2012-06-01
Silicon-based terahertz quantum cascade lasers (QCLs) offer potential advantages over existing III-V devices. Although coherent electron transport effects are known to be important in QCLs, they have never been considered in Si-based device designs. We describe a density-matrix transport model that is designed to be more general than those in previous studies and to require less a priori knowledge of electronic band structure, allowing its use in semiautomated design procedures. The basis of the model includes all states involved in interperiod transport, and our steady-state solution extends beyond the rotating-wave approximation by including dc and counterpropagating terms. We simulate the potential performance of bound-to-continuum Ge/SiGe QCLs and find that devices with 4-5-nm-thick barriers give the highest simulated optical gain. We also examine the effects of interdiffusion between Ge and SiGe layers; we show that if it is taken into account in the design, interdiffusion lengths of up to 1.5 nm do not significantly affect the simulated device performance.
Permutationally Invariant Part of a Density Matrix and Nonseparability of N-Qubit States
NASA Astrophysics Data System (ADS)
Gao, Ting; Yan, Fengli; van Enk, S. J.
2014-05-01
We consider the concept of "the permutationally invariant (PI) part of a density matrix," which has proven very useful for both efficient quantum state estimation and entanglement characterization of N-qubit systems. We show here that the concept is, in fact, basis dependent but that this basis dependence makes it an even more powerful concept than has been appreciated so far. By considering the PI part ρPI of a general (mixed) N-qubit state ρ, we obtain (i) strong bounds on quantitative nonseparability measures, (ii) a whole hierarchy of multipartite separability criteria (one of which entails a sufficient criterion for genuine N-partite entanglement) that can be experimentally determined by just 2N +1 measurement settings, (iii) a definition of an efficiently measurable degree of separability, which can be used for quantifying a novel aspect of decoherence of N qubits, and (iv) an explicit example that shows there are, for increasing N, genuinely N-partite entangled states lying closer and closer to the maximally mixed state. Moreover, we show that if the PI part of a state is k nonseparable, then so is the actual state. We further argue to add as requirement on any multipartite entanglement measure E that it satisfy E(ρ)≥E(ρPI), even though the operation that maps ρ→ρPI is not local.
Coe, Jeremy P; Almeida, Nuno M S; Paterson, Martin J
2017-09-02
We investigate if a range of challenging spin systems can be described sufficiently well using Monte Carlo configuration interaction (MCCI) and the density matrix renormalization group (DMRG) in a way that heads toward a more "black box" approach. Experimental results and other computational methods are used for comparison. The gap between the lowest doublet and quartet state of methylidyne (CH) is first considered. We then look at a range of first-row transition metal monocarbonyls: MCO when M is titanium, vanadium, chromium, or manganese. For these MCO systems we also employ partially spin restricted open-shell coupled-cluster (RCCSD). We finally investigate the high-spin low-lying states of the iron dimer, its cation and its anion. The multireference character of these molecules is also considered. We find that these systems can be computationally challenging with close low-lying states and often multireference character. For this more straightforward application and for the basis sets considered, we generally find qualitative agreement between DMRG and MCCI. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
Reduced-density-matrix spectrum and block entropy of permutationally invariant many-body systems.
Salerno, Mario; Popkov, Vladislav
2010-07-01
Spectral properties of the reduced density matrix (RDM) of permutational invariant quantum many-body systems are investigated. The RDM block diagonalization which accounts for all symmetries of the Hamiltonian is achieved. The analytical expression of the RDM spectrum is provided for arbitrary parameters and rigorously proved in the thermodynamical limit. The existence of several sum rules and recurrence relations among RDM eigenvalues is also demonstrated and the distribution function of RDM eigenvalues (including degeneracies) characterized. In particular, we prove that the distribution function approaches a two-dimensional Gaussian in the limit of large subsystem sizes n>1. As a physical application we discuss the von Neumann entropy (VNE) of a block of size n for a system of hard-core bosons on a complete graph, as a function of n and of the temperature T. The occurrence of a crossover of VNE from purely logarithmic behavior at T=0 to a purely linear behavior in n for T≥Tc, is demonstrated.
Higher-order adaptive finite-element methods for Kohn-Sham density functional theory
NASA Astrophysics Data System (ADS)
Motamarri, P.; Nowak, M. R.; Leiter, K.; Knap, J.; Gavini, V.
2013-11-01
We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn-Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss-Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100-200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposed solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretizations of the Kohn-Sham DFT problem. Our studies suggest that staggering computational savings-of the order of 1000-fold-relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations, by using higher-order finite-element discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-element may be an optimal choice for the finite-element discretization of the Kohn-Sham DFT problem. A comparative study of the computational efficiency of the proposed higher-order finite-element discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688 atoms using
Higher-order adaptive finite-element methods for Kohn–Sham density functional theory
Motamarri, P.; Nowak, M.R.; Leiter, K.; Knap, J.; Gavini, V.
2013-11-15
We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn–Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss–Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100–200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposed solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretizations of the Kohn–Sham DFT problem. Our studies suggest that staggering computational savings—of the order of 1000-fold—relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations, by using higher-order finite-element discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-element may be an optimal choice for the finite-element discretization of the Kohn–Sham DFT problem. A comparative study of the computational efficiency of the proposed higher-order finite-element discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688
Alghadir, Ahmad H; Gabr, Sami A; Al-Eisa, Einas S; Alghadir, Muaz H
2016-01-01
. Conclusion The observed changes in the levels of Ca, Mn, Cu, and Zn were shown to be positively correlated with improved bone mass density among control and osteoporosis subjects of both sexes. These results demonstrate that aerobic exercise of moderate intensity might protect bone and cartilage by regulation of body trace elements which are involved in the biosynthesis of bone matrix structures and inhibition of bone resorption process via a proposed anti-free radical mechanism. PMID:27013870
Alghadir, Ahmad H; Gabr, Sami A; Al-Eisa, Einas S; Alghadir, Muaz H
2016-01-01
, Cu, and Zn were shown to be positively correlated with improved bone mass density among control and osteoporosis subjects of both sexes. These results demonstrate that aerobic exercise of moderate intensity might protect bone and cartilage by regulation of body trace elements which are involved in the biosynthesis of bone matrix structures and inhibition of bone resorption process via a proposed anti-free radical mechanism.
Cao, Haihui; Ackerman, Jerome L; Hrovat, Mirko I; Graham, Lila; Glimcher, Melvin J; Wu, Yaotang
2008-12-01
The density of the organic matrix of bone substance is a critical parameter necessary to clinically evaluate and distinguish structural and metabolic pathological conditions such as osteomalacia in adults and rickets in growing children. Water- and fat-suppressed proton projection MRI (WASPI) was developed as a noninvasive means to obtain this information. In this study, a density calibration phantom was developed to convert WASPI intensity to true bone matrix density. The phantom contained a specifically designed poly(ethylene oxide)/poly(methyl methacrylate) (PEO/PMMA) blend, whose MRI properties (T(1), T(2), and resonance linewidth) were similar to those of solid bone matrix (collagen, tightly bound water, and other immobile molecules), minimizing the need to correct for differences in T(1) and/or T(2) relaxation between the phantom and the subject. Cortical and trabecular porcine bone specimens were imaged using WASPI with the calibration phantom in the field of view (FOV) as a stable intensity reference. Gravimetric and amino acid analyses were carried out on the same specimens after WASPI, and the chemical results were found to be highly correlated (r(2) = 0.98 and 0.95, respectively) to the WASPI intensity. By this procedure the WASPI intensity can be used to obtain the true bone matrix mass density in g cm(-3).
NASA Technical Reports Server (NTRS)
Akhundova, E. A.; Dodonov, V. V.; Manko, V. I.
1993-01-01
The exact expressions for density matrix and Wigner functions of quantum systems are known only in special cases. Corresponding Hamiltonians are quadratic forms of Euclidean coordinates and momenta. In this paper we consider the problem of one-dimensional free particle movement in the bounded region 0 is less than x is less than a (including the case a = infinity).
Fabricating high-density magnetic storage elements by low-dose ion beam irradiation
Neb, R.; Sebastian, T.; Pirro, P.; Hillebrands, B.; Pofahl, S.; Schaefer, R.; Reuscher, B.
2012-09-10
We fabricate magnetic storage elements by irradiating an antiferromagnetically coupled ferromagnetic/nonmagnetic/ferromagnetic trilayer by a low-dose ion beam. The irradiated areas become ferromagnetically coupled and are capable of storing information if their size is small enough. We employ Fe/Cr/Fe trilayers and a 30 keV focused Ga{sup +}-ion beam to demonstrate the working principle for a storage array with a bit density of 7 Gbit/in.{sup 2}. Micromagnetic simulations suggest that bit densities of at least two magnitudes of order larger should be possible.
Ground-state properties of third-row elements with nonlocal density functionals
Bagno, P.; Jepsen, O.; Gunnarsson, O.
1989-07-15
The cohesive energy, the lattice parameter, and the bulk modulus of third-row elements are calculated using the Langreth-Mehl-Hu (LMH), the Perdew-Wang (PW), and the gradient expansion functionals. The PW functional is found to give somewhat better results than the LMH functional and both are found to typically remove half the errors in the local-spin-density (LSD) approximation, while the gradient expansion gives worse results than the local-density approximation. For Fe both the LMH and PW functionals correctly predict a ferromagnetic bcc ground state, while the LSD approximation and the gradient expansion predict a nonmagnetic fcc ground state.
Deriving Plasma Densities and Elemental Abundances from SERTS Differential Emission Measure Analysis
NASA Technical Reports Server (NTRS)
Schmelz, J. T.; Kimble, J. A.; Saba, J. L. R.
2012-01-01
We use high-resolution spectral emission line data obtained by the SERTS instrument during three rocket flights to demonstrate a new approach for constraining electron densities of solar active region plasma.We apply differential emission measure (DEM) forward-fitting techniques to characterize the multithermal solar plasma producing the observed EUV spectra, with constraints on the high-temperature plasma from the Yohkoh Soft X-ray Telescope. In this iterative process, we compare line intensities predicted by an input source distribution to observed line intensities for multiple iron ion species, and search a broad range of densities to optimize chi-square simultaneously for the many available density-sensitive lines. This produces a density weighted by the DEM, which appears to be useful for characterizing the bulk of the emitting plasma over a significant range of temperature. This "DEM-weighted density" technique is complementary to the use of density-sensitive line ratios and less affected by uncertainties in atomic data and ionization fraction for any specific line. Once the DEM shape and the DEM-weighted density have been established from the iron lines, the relative elemental abundances can be determined for other lines in the spectrum. We have also identified spectral lines in the SERTS wavelength range that may be problematic
DERIVING PLASMA DENSITIES AND ELEMENTAL ABUNDANCES FROM SERTS DIFFERENTIAL EMISSION MEASURE ANALYSIS
Schmelz, J. T.; Kimble, J. A.; Saba, J. L. R.
2012-09-20
We use high-resolution spectral emission line data obtained by the SERTS instrument during three rocket flights to demonstrate a new approach for constraining electron densities of solar active region plasma. We apply differential emission measure (DEM) forward-fitting techniques to characterize the multithermal solar plasma producing the observed EUV spectra, with constraints on the high-temperature plasma from the Yohkoh Soft X-ray Telescope. In this iterative process, we compare line intensities predicted by an input source distribution to observed line intensities for multiple iron ion species, and search a broad range of densities to optimize {chi}{sup 2} simultaneously for the many available density-sensitive lines. This produces a density weighted by the DEM, which appears to be useful for characterizing the bulk of the emitting plasma over a significant range of temperature. This 'DEM-weighted density' technique is complementary to the use of density-sensitive line ratios and less affected by uncertainties in atomic data and ionization fraction for any specific line. Once the DEM shape and the DEM-weighted density have been established from the iron lines, the relative elemental abundances can be determined for other lines in the spectrum. We have also identified spectral lines in the SERTS wavelength range that may be problematic.
NASA Astrophysics Data System (ADS)
Alvarez, G.
2009-09-01
The purpose of this paper is (i) to present a generic and fully functional implementation of the density-matrix renormalization group (DMRG) algorithm, and (ii) to describe how to write additional strongly-correlated electron models and geometries by using templated classes. Besides considering general models and geometries, the code implements Hamiltonian symmetries in a generic way and parallelization over symmetry-related matrix blocks. Program summaryProgram title: DMRG++ Catalogue identifier: AEDJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDJ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: See file LICENSE No. of lines in distributed program, including test data, etc.: 15 795 No. of bytes in distributed program, including test data, etc.: 83 454 Distribution format: tar.gz Programming language: C++, MPI Computer: PC, HP cluster Operating system: Any, tested on Linux Has the code been vectorized or parallelized?: Yes RAM: 1 GB (256 MB is enough to run included test) Classification: 23 External routines: BLAS and LAPACK Nature of problem: Strongly correlated electrons systems, display a broad range of important phenomena, and their study is a major area of research in condensed matter physics. In this context, model Hamiltonians are used to simulate the relevant interactions of a given compound, and the relevant degrees of freedom. These studies rely on the use of tight-binding lattice models that consider electron localization, where states on one site can be labeled by spin and orbital degrees of freedom. The calculation of properties from these Hamiltonians is a computational intensive problem, since the Hilbert space over which these Hamiltonians act grows exponentially with the number of sites on the lattice. Solution method: The DMRG is a numerical variational technique to study quantum many body Hamiltonians. For one-dimensional and quasi one-dimensional systems, the
NASA Astrophysics Data System (ADS)
Gates, S. James; Guyton, Forrest; Harmalkar, Siddhartha; Kessler, David S.; Korotkikh, Vadim; Meszaros, Victor A.
2017-06-01
We examine values of the Adinkra Holoraumy-induced Gadget representation space metric over all possible four-color, four-open node, and four-closed node adinkras. Of the 1,358,954,496 gadget matrix elements, only 226,492,416 are non-vanishing and take on one of three values: -1/3, 1/3, or 1 and thus a subspace isomorphic to a description of a body-centered tetrahedral molecule emerges.
NASA Astrophysics Data System (ADS)
Vanfleteren, Diederik; Van Neck, Dimitri; Bultinck, Patrick; Ayers, Paul W.; Waroquier, Michel
2012-01-01
A previously introduced partitioning of the molecular one-electron density matrix over atoms and bonds [D. Vanfleteren et al., J. Chem. Phys. 133, 231103 (2010)] is investigated in detail. Orthogonal projection operators are used to define atomic subspaces, as in Natural Population Analysis. The orthogonal projection operators are constructed with a recursive scheme. These operators are chemically relevant and obey a stockholder principle, familiar from the Hirshfeld-I partitioning of the electron density. The stockholder principle is extended to density matrices, where the orthogonal projectors are considered to be atomic fractions of the summed contributions. All calculations are performed as matrix manipulations in one-electron Hilbert space. Mathematical proofs and numerical evidence concerning this recursive scheme are provided in the present paper. The advantages associated with the use of these stockholder projection operators are examined with respect to covalent bond orders, bond polarization, and transferability.
Sweany, M.; Marleau, P.
2016-07-08
In this paper, we present the design and expected performance of a proof-of-concept 32 channel material identification system. Our system is based on the energy-dependent attenuation of fast neutrons for four elements: hydrogen, carbon, nitrogen and oxygen. We describe a new approach to obtaining a broad range of neutron energies to probe a sample, as well as our technique for reconstructing the molar densities within a sample. The system's performance as a function of time-of-flight energy resolution is explored using a Geant4-based Monte Carlo. Our results indicate that, with the expected detector response of our system, we will be able to determine the molar density of all four elements to within a 20–30% accuracy in a two hour scan time. In many cases this error is systematically low, thus the ratio between elements is more accurate. This degree of accuracy is enough to distinguish, for example, a sample of water from a sample of pure hydrogen peroxide: the ratio of oxygen to hydrogen is reconstructed to within 8±0.5% of the true value. Lastly, with future algorithm development that accounts for backgrounds caused by scattering within the sample itself, the accuracy of molar densities, not ratios, may improve to the 5–10% level for a two hour scan time.
NASA Astrophysics Data System (ADS)
Sweany, M.; Marleau, P.
2016-10-01
We present the design and expected performance of a proof-of-concept 32 channel material identification system. Our system is based on the energy-dependent attenuation of fast neutrons for four elements: hydrogen, carbon, nitrogen and oxygen. We describe a new approach to obtaining a broad range of neutron energies to probe a sample, as well as our technique for reconstructing the molar densities within a sample. The system's performance as a function of time-of-flight energy resolution is explored using a Geant4-based Monte Carlo. Our results indicate that, with the expected detector response of our system, we will be able to determine the molar density of all four elements to within a 20-30% accuracy in a two hour scan time. In many cases this error is systematically low, thus the ratio between elements is more accurate. This degree of accuracy is enough to distinguish, for example, a sample of water from a sample of pure hydrogen peroxide: the ratio of oxygen to hydrogen is reconstructed to within 8±0.5% of the true value. Finally, with future algorithm development that accounts for backgrounds caused by scattering within the sample itself, the accuracy of molar densities, not ratios, may improve to the 5-10% level for a two hour scan time.
Sweany, M.; Marleau, P.
2016-07-08
In this paper, we present the design and expected performance of a proof-of-concept 32 channel material identification system. Our system is based on the energy-dependent attenuation of fast neutrons for four elements: hydrogen, carbon, nitrogen and oxygen. We describe a new approach to obtaining a broad range of neutron energies to probe a sample, as well as our technique for reconstructing the molar densities within a sample. The system's performance as a function of time-of-flight energy resolution is explored using a Geant4-based Monte Carlo. Our results indicate that, with the expected detector response of our system, we will be able to determine the molar density of all four elements to within a 20–30% accuracy in a two hour scan time. In many cases this error is systematically low, thus the ratio between elements is more accurate. This degree of accuracy is enough to distinguish, for example, a sample of water from a sample of pure hydrogen peroxide: the ratio of oxygen to hydrogen is reconstructed to within 8±0.5% of the true value. Lastly, with future algorithm development that accounts for backgrounds caused by scattering within the sample itself, the accuracy of molar densities, not ratios, may improve to the 5–10% level for a two hour scan time.
Sweany, M.; Marleau, P.
2016-07-08
In this paper, we present the design and expected performance of a proof-of-concept 32 channel material identification system. Our system is based on the energy-dependent attenuation of fast neutrons for four elements: hydrogen, carbon, nitrogen and oxygen. We describe a new approach to obtaining a broad range of neutron energies to probe a sample, as well as our technique for reconstructing the molar densities within a sample. The system's performance as a function of time-of-flight energy resolution is explored using a Geant4-based Monte Carlo. Our results indicate that, with the expected detector response of our system, we will be ablemore » to determine the molar density of all four elements to within a 20–30% accuracy in a two hour scan time. In many cases this error is systematically low, thus the ratio between elements is more accurate. This degree of accuracy is enough to distinguish, for example, a sample of water from a sample of pure hydrogen peroxide: the ratio of oxygen to hydrogen is reconstructed to within 8±0.5% of the true value. Lastly, with future algorithm development that accounts for backgrounds caused by scattering within the sample itself, the accuracy of molar densities, not ratios, may improve to the 5–10% level for a two hour scan time.« less
NASA Astrophysics Data System (ADS)
Khokhar, Zahid R.; Ashcroft, Ian A.; Silberschmidt, Vadim V.
2011-02-01
Two main damage mechanisms of laminates—matrix cracking and inter-ply delaminationare closely linked together (Joshi and Sun 1). This paper is focussed on interaction between matrix cracking and delamination failure mechanisms in CFRP cross-ply laminates under quasi-static tensile loading. In the first part of the work, a transverse crack is introduced in 90o layers of the cross-ply laminate [01/904/01], and the stresses and strains that arise due to tensile loading are analyzed. In the second part, the cohesive zone modelling approach where the constitutive behaviour of the cohesive elements is governed by traction-displacement relationship is employed to deal with the problem of delamination initiation from the matrix crack introduced in the 90o layers of the laminate specimen. Additionally, the effect of microstructural randomness, exhibited by CFRP laminates on the damage behaviour of these laminates is also accounted for in simulations. This effect is studied in numerical finite-element simulations by introducing stochastic cohesive zone elements. The proposed damage modelling effectively simulated the interaction between the matrix crack and delamination and the variations in the stresses, damage and crack lengths of the laminate specimen due to the microstructural randomness.
Superheavy Elements from r-Process Calculations with an Energy-Density Mass Formula
NASA Astrophysics Data System (ADS)
Brueckner, K. A.; Chirico, J. H.; Jorna, S.; Meldner, H. W.; Schramm, D. N.; Seeger, P. A.
1973-05-01
Astrophysical superheavy-element synthesis by rapid neutron capture is studied by utilizing nuclear masses from energy-density functional calculations and a new β-decay formula in a modified r-process code. We find reduced abundances for elements with large atomic numbers relative to those predicted by conventional mass formulas. Calculations have been performed with fission barriers corresponding to both large and small values of the surface-symmetry contribution to the deformation energy. Our results, based on a different mass-formula parametrization, show that it is possible to synthesize superheavy elements in the r process even for very large surface-symmetry contributions if certain mass-formula terms are modified. Also, a more realistic formula for β-decay rates yields r-process fission-cycle times which are about 1 order of magnitude shorter than previous values.
NASA Astrophysics Data System (ADS)
Sturtz, Timothy M.
Source apportionment models attempt to untangle the relationship between pollution sources and the impacts at downwind receptors. Two frameworks of source apportionment models exist: source-oriented and receptor-oriented. Source based apportionment models use presumed emissions and atmospheric processes to estimate the downwind source contributions. Conversely, receptor based models leverage speciated concentration data from downwind receptors and apply statistical methods to predict source contributions. Integration of both source-oriented and receptor-oriented models could lead to a better understanding of the implications sources have on the environment and society. The research presented here investigated three different types of constraints applied to the Positive Matrix Factorization (PMF) receptor model within the framework of the Multilinear Engine (ME-2): element ratio constraints, spatial separation constraints, and chemical transport model (CTM) source attribution constraints. PM10-2.5 mass and trace element concentrations were measured in Winston-Salem, Chicago, and St. Paul at up to 60 sites per city during two different seasons in 2010. PMF was used to explore the underlying sources of variability. Information on previously reported PM10-2.5 tire and brake wear profiles were used to constrain these features in PMF by prior specification of selected species ratios. We also modified PMF to allow for combining the measurements from all three cities into a single model while preserving city-specific soil features. Relatively minor differences were observed between model predictions with and without the prior ratio constraints, increasing confidence in our ability to identify separate brake wear and tire wear features. Using separate data, source contributions to total fine particle carbon predicted by a CTM were incorporated into the PMF receptor model to form a receptor-oriented hybrid model. The level of influence of the CTM versus traditional PMF was
Density matrix embedding theory studies of the two-dimensional Hubbard model
NASA Astrophysics Data System (ADS)
Zheng, Bo-Xiao
Density matrix embedding theory (DMET) provides a quantum embedding framework to compute the electronic structure in strongly correlated lattice systems. It has been applied to various model Hamiltonians and ab initio systems. In this talk, I will review the results obtained in the two-dimensional one-band Hubbard model using DMET. Over the last years, we mapped a calibrated ground-state phase diagram of the two-dimensional Hubbard model, concerning magnetic, superconducting and various inhomogeneous phases. Based on the results from this work, as well as the consistent data from other numerical methods, we are able to conclude that many parts of the Hubbard phase diagram is already settled up to an accurate energy scale of 0.001t. Recently, by using large-scale auxiliary-field quantum Monte Carlo (AFQMC) in the impurity problem, we are able to treat much larger embedded clusters at half-filling (and with the constrained path approximation at non-half-filling), which provides a deeper understanding on the finite-size effects of energy and observables in both quantum embedding and finite cluster numerical methods. Finally, we systematically investigated the putative inhomogeneous phases in the underdoped, strong coupling Hubbard model, proposing new inhomogeneous patterns as strong candidates for the ground state. Reference: [1] Bo-Xiao Zheng, Garnet K.-L. Chan, arXiv:1504.01784 [2] J.P.F. Leblanc, Andrey E. Antipov, et al., arXiv:1505.02290 We acknowledge funding from the US Department of Energy, Office of Science, through DE-SC0008624 and DE-SC0010530. This work was also performed as part of the Simons Collaboration on the Many Electron Problem, sponsored by the Simons Foundation.
Dissipative quantum molecular dynamics in gases and condensed media: A density matrix treatment
NASA Astrophysics Data System (ADS)
Leathers, Andrew S.
We present a study of dissipative quantum molecular dynamics, covering several different methods of treating the dissipation. We use a reduced density matrix framework, which leads to coupled integro-differential equations in time. We then develop a numerical algorithm for solving these equations. This algorithm is tested by comparing the results to a solved model. The method is then applied to the vibrational relaxation of adsorbates on metal surfaces. We also use this model to test approximations which transform the integro-differential equations into simpler integral equations. Our results compare well to experiment, and demonstrate the need for a full treatment without approximations. This model is then expanded to allow for electronic relaxation, as well as excitation by a light pulse. The electronic relaxation occurs on a different time scale, and is treated differently than the vibrational relaxation. Our method is shown to be general enough to handle both cases. Our next model is light-induced electron transfer in a metal cluster on a semiconductor surface. We consider both direct electronic excitation causing electron transfer, as well as indirect transfer, where there is excitation to an intermediate state which is coupled to the electron transferred state. Our results indicate vibrational relaxation plays a small role in the direct transfer dynamics, but is still important in the indirect case. Finally, we present a mixed quantum-classical study of the effect of initial conditions, with the goal of moving towards a method capable of treating dissipation in both quantum and mixed quatum-classical systems. (Full text of this dissertation may be available via the University of Florida Libraries web site. Please check http://www.uflib.ufl.edu/etd.html)
Harris, Travis V.; Morokuma, Keiji; Kurashige, Yuki; Yanai, Takeshi
2014-02-07
The applicability of ab initio multireference wavefunction-based methods to the study of magnetic complexes has been restricted by the quickly rising active-space requirements of oligonuclear systems and dinuclear complexes with S > 1 spin centers. Ab initio density matrix renormalization group (DMRG) methods built upon an efficient parameterization of the correlation network enable the use of much larger active spaces, and therefore may offer a way forward. Here, we apply DMRG-CASSCF to the dinuclear complexes [Fe{sub 2}OCl{sub 6}]{sup 2−} and [Cr{sub 2}O(NH{sub 3}){sub 10}]{sup 4+}. After developing the methodology through systematic basis set and DMRG M testing, we explore the effects of extended active spaces that are beyond the limit of conventional methods. We find that DMRG-CASSCF with active spaces including the metal d orbitals, occupied bridging-ligand orbitals, and their virtual double shells already capture a major portion of the dynamic correlation effects, accurately reproducing the experimental magnetic coupling constant (J) of [Fe{sub 2}OCl{sub 6}]{sup 2−} with (16e,26o), and considerably improving the smaller active space results for [Cr{sub 2}O(NH{sub 3}){sub 10}]{sup 4+} with (12e,32o). For comparison, we perform conventional MRCI+Q calculations and find the J values to be consistent with those from DMRG-CASSCF. In contrast to previous studies, the higher spin states of the two systems show similar deviations from the Heisenberg spectrum, regardless of the computational method.
Matrix elements of the electromagnetic operator between kaon and pion states
Baum, I.; Lubicz, V.; Martinelli, G.; Orifici, L.; Simula, S.
2011-10-01
We compute the matrix elements of the electromagnetic operator sF{sub {mu}{nu}}{sigma}{sup {mu}{nu}}d between kaon and pion states, using lattice QCD with maximally twisted-mass fermions and two flavors of dynamical quarks (N{sub f}=2). The operator is renormalized nonperturbatively in the RI'/MOM scheme and our simulations cover pion masses as light as 270 MeV and three values of the lattice spacing from {approx_equal}0.07 up to {approx_equal}0.1 fm. At the physical point our result for the corresponding tensor form factor at zero-momentum transfer is f{sub T}{sup K{pi}}(0)=0.417(14{sub stat})(5{sub syst}), where the systematic error does not include the effect of quenching the strange and charm quarks. Our result differs significantly from the old quenched result f{sub T}{sup K{pi}}(0)=0.78(6) obtained by the SPQ{sub cd}R Collaboration with pion masses above 500 MeV. We investigate the source of this difference and conclude that it is mainly related to the chiral extrapolation. We also study the tensor charge of the pion and obtain the value f{sub T}{sup {pi}{pi}}(0)=0.195(8{sub stat})(6{sub syst}) in good agreement with, but more accurate than the result f{sub T}{sup {pi}{pi}}(0)=0.216(34) obtained by the QCDSF Collaboration using higher pion masses.
Streubel, A; Siepmann, J; Bodmeier, R
2003-01-01
The aim of this study was to develop and physicochemically characterize single unit, floating controlled drug delivery systems consisting of (i). polypropylene foam powder, (ii). matrix-forming polymer(s), (iii). drug, and (iv). filler (optional). The highly porous foam powder provided low density and, thus, excellent in vitro floating behavior of the tablets. All foam powder-containing tablets remained floating for at least 8 h in 0.1 N HCl at 37 degrees C. Different types of matrix-forming polymers were studied: hydroxypropyl methylcellulose (HPMC), polyacrylates, sodium alginate, corn starch, carrageenan, gum guar and gum arabic. The tablets eroded upon contact with the release medium, and the relative importance of drug diffusion, polymer swelling and tablet erosion for the resulting release patterns varied significantly with the type of matrix former. The release rate could effectively be modified by varying the "matrix-forming polymer/foam powder" ratio, the initial drug loading, the tablet geometry (radius and height), the type of matrix-forming polymer, the use of polymer blends and the addition of water-soluble or water-insoluble fillers (such as lactose or microcrystalline cellulose). The floating behavior of the low density drug delivery systems could successfully be combined with accurate control of the drug release patterns.
Diarra, Harona; Mazel, Vincent; Busignies, Virginie; Tchoreloff, Pierre
2015-09-30
Finite elements method was used to study the influence of tablet thickness and punch curvature on the density distribution inside convex faced (CF) tablets. The modeling of the process was conducted on 2 pharmaceutical excipients (anhydrous calcium phosphate and microcrystalline cellulose) by using Drucker-Prager Cap model in Abaqus(®) software. The parameters of the model were obtained from experimental tests. Several punch shapes based on industrial standards were used. A flat-faced (FF) punch and 3 convex faced (CF) punches (8R11, 8R8 and 8R6) with a diameter of 8mm were chosen. Different tablet thicknesses were studied at a constant compression force. The simulation of the compaction of CF tablets with increasing thicknesses showed an important change on the density distribution inside the tablet. For smaller thicknesses, low density zones are located toward the center. The density is not uniform inside CF tablets and the center of the 2 faces appears with low density whereas the distribution inside FF tablets is almost independent of the tablet thickness. These results showed that FF and CF tablets, even obtained at the same compression force, do not have the same density at the center of the compact. As a consequence differences in tensile strength, as measured by diametral compression, are expected. This was confirmed by experimental tests. Copyright © 2015 Elsevier B.V. All rights reserved.
Sinka, I C; Cunningham, J C; Zavaliangos, A
2004-08-01
A Drucker-Prager/cap constitutive model, where the elastic and plastic model parameters are expressed as a function of relative density (RD), was presented in a companion article together with experimental calibration procedures. Here, we examine the RD distribution in curved-faced tablets with special reference to the die wall lubrication conditions. The compaction of powders is examined using finite element analysis, which involves the following factors: constitutive behavior of powder, friction between powder and tooling, geometry of die and punches, sequence of punch motions, and initial conditions that result from die fill. The predictions of the model are validated using experimental RD maps. It is shown that different die wall lubrication conditions induce opposite density distribution trends in identical tablets (weight, height, and material). The importance of the internal tablet structure is illustrated with respect to break force, failure mode, and friability: it is demonstrated that for a given average tablet density the break force and failure mode are not unique. Also, tablet regions having lower density locally have higher propensity for damage. The applicability of finite element analysis for optimizations of formulation design, process development, tablet image, and tool design is discussed. Copyright 2004 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 93:2040-2053, 2004
Measurements of continuum lowering in solid-density plasmas created from elements and compounds
Ciricosta, O.; Vinko, S. M.; Barbrel, B.; Rackstraw, D. S.; Preston, T. R.; Burian, T.; Chalupský, J.; Cho, B. I.; Chung, H. -K.; Dakovski, G. L.; Engelhorn, K.; Hájková, V.; Heimann, P.; Holmes, M.; Juha, L.; Krzywinski, J.; Lee, R. W.; Toleikis, S.; Turner, J. J.; Zastrau, U.; Wark, J. S.
2016-01-01
The effect of a dense plasma environment on the energy levels of an embedded ion is usually described in terms of the lowering of its continuum level. For strongly coupled plasmas, the phenomenon is intimately related to the equation of state; hence, an accurate treatment is crucial for most astrophysical and inertial-fusion applications, where the case of plasma mixtures is of particular interest. Here we present an experiment showing that the standard density-dependent analytical models are inadequate to describe solid-density plasmas at the temperatures studied, where the reduction of the binding energies for a given species is unaffected by the different plasma environment (ion density) in either the element or compounds of that species, and can be accurately estimated by calculations only involving the energy levels of an isolated neutral atom. The results have implications for the standard approaches to the equation of state calculations. PMID:27210741
Measurements of continuum lowering in solid-density plasmas created from elements and compounds.
Ciricosta, O; Vinko, S M; Barbrel, B; Rackstraw, D S; Preston, T R; Burian, T; Chalupský, J; Cho, B I; Chung, H-K; Dakovski, G L; Engelhorn, K; Hájková, V; Heimann, P; Holmes, M; Juha, L; Krzywinski, J; Lee, R W; Toleikis, S; Turner, J J; Zastrau, U; Wark, J S
2016-05-23
The effect of a dense plasma environment on the energy levels of an embedded ion is usually described in terms of the lowering of its continuum level. For strongly coupled plasmas, the phenomenon is intimately related to the equation of state; hence, an accurate treatment is crucial for most astrophysical and inertial-fusion applications, where the case of plasma mixtures is of particular interest. Here we present an experiment showing that the standard density-dependent analytical models are inadequate to describe solid-density plasmas at the temperatures studied, where the reduction of the binding energies for a given species is unaffected by the different plasma environment (ion density) in either the element or compounds of that species, and can be accurately estimated by calculations only involving the energy levels of an isolated neutral atom. The results have implications for the standard approaches to the equation of state calculations.
Measurements of continuum lowering in solid-density plasmas created from elements and compounds
Ciricosta, O.; Vinko, S. M.; Barbrel, B.; Rackstraw, D. S.; Preston, T. R.; Burian, T.; Chalupský, J.; Cho, B. I.; Chung, H. -K.; Dakovski, G. L.; Engelhorn, K.; Hájková, V.; Heimann, P.; Holmes, M.; Juha, L.; Krzywinski, J.; Lee, R. W.; Toleikis, S.; Turner, J. J.; Zastrau, U.; Wark, J. S.
2016-05-23
The effect of a dense plasma environment on the energy levels of an embedded ion is usually described in terms of the lowering of its continuum level. For strongly coupled plasmas, the phenomenon is intimately related to the equation of state; hence, an accurate treatment is crucial for most astrophysical and inertial-fusion applications, where the case of plasma mixtures is of particular interest. In this study, we present an experiment showing that the standard density-dependent analytical models are inadequate to describe solid-density plasmas at the temperatures studied, where the reduction of the binding energies for a given species is unaffected by the different plasma environment (ion density) in either the element or compounds of that species, and can be accurately estimated by calculations only involving the energy levels of an isolated neutral atom. Lastly, the results have implications for the standard approaches to the equation of state calculations.
Measurements of continuum lowering in solid-density plasmas created from elements and compounds
Ciricosta, O.; Vinko, S. M.; Barbrel, B.; ...
2016-05-23
The effect of a dense plasma environment on the energy levels of an embedded ion is usually described in terms of the lowering of its continuum level. For strongly coupled plasmas, the phenomenon is intimately related to the equation of state; hence, an accurate treatment is crucial for most astrophysical and inertial-fusion applications, where the case of plasma mixtures is of particular interest. In this study, we present an experiment showing that the standard density-dependent analytical models are inadequate to describe solid-density plasmas at the temperatures studied, where the reduction of the binding energies for a given species is unaffectedmore » by the different plasma environment (ion density) in either the element or compounds of that species, and can be accurately estimated by calculations only involving the energy levels of an isolated neutral atom. Lastly, the results have implications for the standard approaches to the equation of state calculations.« less
NASA Astrophysics Data System (ADS)
Ito, Fumiyuki
2010-12-01
The supermolecule approach has been used to model molecules embedded in solid argon matrix, wherein interaction between the guest and the host atoms in the first solvation shell is evaluated with the use of density functional calculations. Structural stability and simulated spectra have been obtained for formic acid dimer (FAD)-Arn (n = 21-26) clusters. The calculations at the B971/6-31++G(3df,3pd) level have shown that the tetrasubstitutional site on Ar(111) plane is likely to incorporate FAD most stably, in view of consistency with the matrix shifts available experimentally.
Nakatani, Naoki; Chan, Garnet Kin-Lic
2013-04-07
We investigate tree tensor network states for quantum chemistry. Tree tensor network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states encode a one-dimensional entanglement structure, tree tensor network states encode a tree entanglement structure, allowing for a more flexible description of general molecules. We describe an optimal tree tensor network state algorithm for quantum chemistry. We introduce the concept of half-renormalization which greatly improves the efficiency of the calculations. Using our efficient formulation we demonstrate the strengths and weaknesses of tree tensor network states versus matrix product states. We carry out benchmark calculations both on tree systems (hydrogen trees and π-conjugated dendrimers) as well as non-tree molecules (hydrogen chains, nitrogen dimer, and chromium dimer). In general, tree tensor network states require much fewer renormalized states to achieve the same accuracy as matrix product states. In non-tree molecules, whether this translates into a computational savings is system dependent, due to the higher prefactor and computational scaling associated with tree algorithms. In tree like molecules, tree network states are easily superior to matrix product states. As an illustration, our largest dendrimer calculation with tree tensor network states correlates 110 electrons in 110 active orbitals.
Poelmans, Ward; Van Raemdonck, Mario; Verstichel, Brecht; De Baerdemacker, Stijn; Torre, Alicia; Lain, Luis; Massaccesi, Gustavo E; Alcoba, Diego R; Bultinck, Patrick; Van Neck, Dimitri
2015-09-08
We perform a direct variational determination of the second-order (two-particle) density matrix corresponding to a many-electron system, under a restricted set of the two-index N-representability P-, Q-, and G-conditions. In addition, we impose a set of necessary constraints that the two-particle density matrix must be derivable from a doubly occupied many-electron wave function, i.e., a singlet wave function for which the Slater determinant decomposition only contains determinants in which spatial orbitals are doubly occupied. We rederive the two-index N-representability conditions first found by Weinhold and Wilson and apply them to various benchmark systems (linear hydrogen chains, He, N2, and CN(-)). This work is motivated by the fact that a doubly occupied many-electron wave function captures in many cases the bulk of the static correlation. Compared to the general case, the structure of doubly occupied two-particle density matrices causes the associate semidefinite program to have a very favorable scaling as L(3), where L is the number of spatial orbitals. Since the doubly occupied Hilbert space depends on the choice of the orbitals, variational calculation steps of the two-particle density matrix are interspersed with orbital-optimization steps (based on Jacobi rotations in the space of the spatial orbitals). We also point to the importance of symmetry breaking of the orbitals when performing calculations in a doubly occupied framework.
NASA Astrophysics Data System (ADS)
Whiting, Daniel J.; Keaveney, James; Adams, Charles S.; Hughes, Ifan G.
2016-04-01
Applying large magnetic fields to gain access to the hyperfine Paschen-Back regime can isolate three-level systems in a hot alkali metal vapors, thereby simplifying usually complex atom-light interactions. We use this method to make the first direct measurement of the |<5 P ||e r ||5 D >| matrix element in 87Rb. An analytic model with only three levels accurately models the experimental electromagnetically induced transparency spectra and extracted Rabi frequencies are used to determine the dipole matrix element. We measure |<5 P3 /2||e r ||5 D5 /2>| =(2.290 ±0 .002stat±0 .04syst) e a0 , which is in excellent agreement with the theoretical calculations of Safronova, Williams, and Clark [Phys. Rev. A 69, 022509 (2004), 10.1103/PhysRevA.69.022509].