A Hartree-Fock-Bogoliubov mass formula
Samyn, M; Heenen, P H; Pearson, J M; Tondeur, F
2002-01-01
In order to have more reliable predictions of nuclear masses at the neutron drip line, we here go beyond the recent mass formula HFBCS-1 and present a new mass formula, HFB-1, based on the Hartree-Fock-Bogoliubov method. As with the HFBCS-1 mass formula, we use a 10-parameter Skyrme force along with a 4-parameter delta-function pairing force and a 2-parameter phenomenological Wigner term. However, with the original HFBCS-1 Skyrme force (MSk7), the rms error becomes unacceptably large and a new force fit is required. With the isoscalar and isovector effective masses constrained to be equal, the remaining 15 degrees of freedom are fitted to the masses of all the 1754 measured nuclei with A>=16, |N-Z|>2 given in the 1995 Audi-Wapstra compilation. The rms error with respect to the masses of all the 1888 measured nuclei with Z,N>=8 is 0.764 MeV. A complete mass table, HFB-1 (available on the Web), has been constructed, giving all nuclei lying between the two drip lines over the range Z,N>=8 and Z<=120. A compar...
Relativistic Hartree-Fock-Bogoliubov model for deformed nuclei
Ebran, J -P; Arteaga, D Pena; Vretenar, D
2010-01-01
The Relativistic Hartree-Fock-Bogoliubov model for axially deformed nuclei (RHFBz) is introduced. The model is based on an effective Lagrangian with density-dependent meson-nucleon couplings in the particle-hole channel, and the pairing part of the Gogny force is used in the pairing channel. The RHFBz quasiparticle equations are solved by expansion in the basis of a deformed harmonic oscillator. Illustrative RHFBz calculations are performed for Carbon, Neon and Magnesium isotopes. The effect of the explicitly including the pion field is investigated for binding energies, deformation parameters, and charge radii.
The Gogny-Hartree-Fock-Bogoliubov nuclear-mass model
Goriely, S. [Universite Libre de Bruxelles, Institut d' Astronomie et d' Astrophysique, CP-226, Brussels (Belgium); Hilaire, S.; Girod, M.; Peru, S. [CEA, DAM, DIF, Arpajon (France)
2016-07-15
We present the Gogny-Hartree-Fock-Bogoliubov model which reproduces nuclear masses with an accuracy comparable with the best mass formulas. In contrast to the Skyrme-HFB nuclear-mass models, an explicit and self-consistent account of all the quadrupole correlation energies is included within the 5D collective Hamiltonian approach. The final rms deviation with respect to the 2353 measured masses is 789 keV in the 2012 atomic mass evaluation. In addition, the D1M Gogny force is shown to predict nuclear and neutron matter properties in agreement with microscopic calculations based on realistic two- and three-body forces. The D1M properties and its predictions of various observables are compared with those of D1S and D1N. (orig.)
On the solution of the Hartree-Fock-Bogoliubov equations by the conjugate gradient method
Egido, J.L. [Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica; Lessing, J. [Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica; Martin, V. [Analisis Numerico, Facultad de Informatica, Universidad Politecnica de Madrid, E-28660 Boadilla del Monte, Madrid (Spain); Robledo, L.M. [Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica
1995-11-06
The conjugate gradient method is formulated in the Hilbert space for density and non-density dependent Hamiltonians. We apply it to the solution of the Hartree-Fock-Bogoliubov equations with constraints. As a numerical application we show calculations with the finite range density dependent Gogny force. The number of iterations required to reach convergence is reduced by a factor of three to four as compared with the standard gradient method. (orig.).
Superdeformed rotational bands in the mercury region. A cranked Skyrme-Hartree-Fock-Bogoliubov study
Gall, B. (Centre de Spectrometrie Nucleaire et de Spectrometrie de Masse, 91 Orsay (France)); Bonche, P. (Service de Physique Theorique, DSM, CE Saclay, 91 Gif-sur-Yvette (France)); Dobaczewski, J. (Inst. of Theoretical Physics, Warsaw Univ., Warsaw (Poland)); Flocard, H. (Div. de Physique Theorique, Inst. de Physique Nucleaire, 91 Orsay (France)); Heenen, P.H. (Physique Nucleaire Theorique, Univ. Libre de Bruxelles (Belgium))
1994-05-01
A study of rotational properties of the ground superdeformed bands in [sup 190]Hg, [sup 192]Hg, [sup 194]Hg, and [sup 194]Pb is presented. We use the cranked Hartree-Fock-Bogoliubov method with the SkM* parametrization of the Skyrme force in the particle-hole channel and a seniority interaction in the pairing channel. An approximate particle number projection is performed by means of the Lipkin-Nogami prescription. We analyze the proton and neutron quasiparticle routhians in connection with the present information on about thirty presently observed superdeformed bands in nuclei close neighbours of [sup 192]Hg (orig.)
Superdeformed rotational bands in the mercury region; a cranked Skyrme-Hartree-Fock-Bogoliubov study
Gall, B.; Bonche, P.; Dobaczewski, J.; Flocard, H.; Heenen, P. -H.
1994-01-01
URL: http://www-spht.cea.fr/articles/T94/011 http://fr.arxiv.org/abs/nucl-th/9312011; International audience; A study of rotational properties of the ground superdeformed bands in $ ^{190} {\\rm Hg,} $ $ ^{192} {\\rm Hg,} $ $ ^{194} {\\rm Hg,} $ and $ ^{194} {\\rm Pb} $ is presented. We use the cranked Hartree-Fock-Bogoliubov method with the SkM$ ^\\ast $ parametrization of the Skyrme force in the particle-hole channel and a seniority interaction in the pairing channel. An approximate particle num...
Superdeformed rotational bands in the mercury region. A cranked Skyrme-Hartree-Fock-Bogoliubov study
Gall, B.; Bonche, P.; Dobaczewski, J.; Flocard, H.; Heenen, P.-H.
1994-09-01
A study of rotational properties of the ground superdeformed bands in190Hg,192Hg,194Hg, and194Pb is presented. We use the cranked Hartree-Fock-Bogoliubov method with the SkM* parametrization of the Skyrme force in the particle-hole channel and a seniority interaction in the pairing channel. An approximate particle number projection is performed by means of the Lipkin-Nogami prescription. We analyze the proton and neutron quasiparticle routhians in connection with the present information on about thirty presently observed superdeformed bands in nuclei close neighbours of192Hg.
Olshanii, Maxim; Pricoupenko, Ludovic
2001-05-01
We introduce a novel one-parametric family of zero-range pseudopotentials hatV^Λ(r) = g_Λ δ(r) [ partialr + Λ ] (r \\cdot ) with g_Λ = fracg_01-Λ a and g0 = 4πhbar^2 a/m , whose scattering length a does not depend on the free parameter Λ. No exact (after the zero-range approximation has been made) many-body observable depends on it, although approximate treatments differ for different Λ (M. Olshanii and L. Pricoupenko, mat/0101275>). We incorporate these pseudopotentials in the Hartree-Fock-Bogoliubov variational formalism, whose conventional (Λ=0) version is known to exhibit UV-divergencies, inconsistencies with both Hugenholtz-Pines theorem and many-body T-matrix calculations, and inability to develop an energy minimum for the atomic condensate leading to a molecular condensate instead. Using Λ as a new variational parameter we resolve all inconsistencies of the Hartree-Fock-Bogoliubov formalism known so far, with no ad hoc modifications of the theory.
Pairing phase transition: A Finite-Temperature Relativistic Hartree-Fock-Bogoliubov study
Li, Jia Jie; Long, Wen Hui; Van Giai, Nguyen
2015-01-01
Background: The relativistic Hartree-Fock-Bogoliubov (RHFB) theory has recently been developed and it provides a unified and highly predictive description of both nuclear mean field and pairing correlations. Ground state properties of finite nuclei can accurately be reproduced without neglecting exchange (Fock) contributions. Purpose: Finite-temperature RHFB (FT-RHFB) theory has not yet been developed, leaving yet unknown its predictions for phase transitions and thermal excitations in both stable and weakly bound nuclei. Method: FT-RHFB equations are solved in a Dirac Woods-Saxon (DWS) basis considering two kinds of pairing interactions: finite or zero range. Such a model is appropriate for describing stable as well as loosely bound nuclei since the basis states have correct asymptotic behaviour for large spatial distributions. Results: Systematic FT-RH(F)B calculations are performed for several semi-magic isotopic/isotonic chains comparing the predictions of a large number of Lagrangians, among which are PK...
GUO Lu; ZHAO En-Guang; SAKATA Fumihiko
2003-01-01
Ground-state.properties of C, O, and Ne isotopes are described in the framework of Hartree-FockBogoliubov theory with density-dependent finite-range Gogny interaction D1S. We include all the contributions to the Hartree-Fock and pairing field arising from Gogny and Coulomb interaction as well as the center of mass correction in the numerical calculations. These ground-state properties of C, O, and Ne isotopes are compared with available experimental results, Hartree-Fock plus BCS, shell model and relativistic Hartree-Bogoliubov calculations. The agreement between experiments and our theoretical results is pretty well. The predicted drip-line is dependent strongly on the model and effective interaction due to their sensitivity to various theoretical details. The calculations predict no evidence for halo structure predicted for C, O, and Ne isotopes in a previous RHB study.
GUOLu; ZHAOEn-Guang; SAKATAFumihiko
2003-01-01
Ground-state properties of C, O, and Ne isotopes are described in the framework of Hartree-Fock-Bogoliubov theory with density-dependent finite-range Gogny interaction D1S. We include all the contributions to the Hartree-Fock and pairing feld arising from Gogny and Coulomb interaction as well as the center of mass correction in the numerical calcu/ations. These ground-state properties of C, O, and Ne isotopes are compared with available experimental results, Hartree-Fock plus BCS, shell model and relativistic Hartree--Bogoliubov calculations. The agreement between experiments and our theoretical results is pretty well. The predicted drip-line is dependent strongly on the model and effective interaction due to their sensitivity to various theoretical details. The calculations predict no evidence for halo structure predicted for C,O, and Ne isotopes in a previous RHB study.
Quasi-particle Continuum and Resonances in the Hartree-Fock-Bogoliubov Theory
Pei, J. C. [University of Tennessee, Knoxville (UTK) & Oak Ridge National Laboratory (ORNL); Kruppa, Andras Tibor [ORNL; Nazarewicz, Witold [ORNL
2011-01-01
The quasi-particle energy spectrum of the Hartree-Fock-Bogoliubov (HFB) equations contains discrete bound states, resonances, and non-resonant continuum states. We study the structure of the unbound quasi-particle spectrum of weakly bound nuclei within several methods that do not rely on imposing scattering or outgoing boundary conditions. Various approximations are examined to estimate resonance widths. It is shown that the stabilization method works well for all HFB resonances except for very narrow ones. The Thomas-Fermi approximation to the non-resonant continuum has been shown to be very effective, especially for coordinate-space HFB calculations in large boxes that involve huge amounts of discretized quasi-particle continuum states.
Quasiparticle continuum and resonances in the Hartree-Fock-Bogoliubov theory
Pei, Junchen [ORNL; Kruppa, A. T. [Joint Institute for Heavy Ion Research, Oak Ridge; Nazarewicz, W. [University of Tennessee, Knoxville (UTK) & Oak Ridge National Laboratory (ORNL)
2011-01-01
The quasi-particle energy spectrum of the Hartree-Fock-Bogoliubov (HFB) equations contains discrete bound states, resonances, and non-resonant continuum states. We study the structure of the unbound quasi-particle spectrum of weakly bound nuclei within several methods that do not rely on imposing scattering or outgoing boundary conditions. Various approximations are examined to estimate resonance widths. It is shown that the stabilization method works well for all HFB resonances except for very narrow ones. The Thomas-Fermi approximation to the non-resonant continuum has been shown to be very effective, especially for coordinate-space HFB calculations in large boxes that involve huge amounts of discretized quasi-particle continuum states.
Ebran, J-P [CEA/DAM/DIF, F-91297 Arpajon (France); Khan, E; Arteaga, D Pena [Institut de Physique Nucleaire, University Paris-Sud, IN2P3-CNRS, F-91406 Orsay Cedex (France); Vretenar, D, E-mail: jean-paul.ebran@cea.fr [Physics Department, Faculty of Science, University of Zagreb, 10000 Zagreb (Croatia)
2011-09-16
The Relativistic Hartree-Fock-Bogoliubov model for axially deformed nuclei (RHFBz) is presented. The model involves a phenomenological Lagrangian with density-dependent meson-nucleon couplings in the particle-hole channel and the central part of the Gogny force in the particle-particle channel. The RHFBz equations are solved by expansion in the basis of a deformed harmonic oscillator. Illustrative RHFBz calculations are performed for Neon isotopes.
Generalized Hartree-Fock-Bogoliubov description of the Fröhlich polaron
Kain, Ben; Ling, Hong Y.
2016-07-01
We adapt the generalized Hartree-Fock-Bogoliubov (HFB) method to an interacting many-phonon system free of impurities. The many-phonon system is obtained from applying the Lee-Low-Pine (LLP) transformation to the Fröhlich model which describes a mobile impurity coupled to noninteracting phonons. We specialize our general HFB description of the Fröhlich polaron to Bose polarons in quasi-one-dimensional cold-atom mixtures. The LLP-transformed many-phonon system distinguishes itself with an artificial phonon-phonon interaction which is very different from the usual two-body interaction. We use the quasi-one-dimensional model, which is free of an ultraviolet divergence that exists in higher dimensions, to better understand how this unique interaction affects polaron states and how the density and pair correlations inherent to the HFB method conspire to create a polaron ground state with an energy in good agreement with and far closer to the prediction from Feynman's variational path integral approach than mean-field theory where HFB correlations are absent.
Coordinate-Space Hartree-Fock-Bogoliubov Solvers for Superfluid Fermi Systems in Large Boxes
Pei, J. C. [University of Tennessee (UTK) and Oak Ridge National Laboratory (ORNL); Fann, George I [ORNL; Harrison, Robert J [ORNL; Nazarewicz, W. [University of Tennessee (UTK) and Oak Ridge National Laboratory (ORNL); Hill, Judith C [ORNL; Galindo, Diego A [ORNL; Jia, Jun [ORNL
2012-01-01
The self-consistent Hartree-Fock-Bogoliubov problem in large boxes can be solved accurately in the coordinate space with the recently developed solvers HFB-AX (2D) and MADNESS-HFB (3D). This is essential for the description of superfluid Fermi systems with complicated topologies and significant spatial extend, such as fissioning nuclei, weakly-bound nuclei, nuclear matter in the neutron star rust, and ultracold Fermi atoms in elongated traps. The HFB-AX solver based on B-spline techniques uses a hybrid MPI and OpenMP programming model for parallel computation for distributed parallel computation, within a node multi-threaded LAPACK and BLAS libraries are used to further enable parallel calculations of large eigensystems. The MADNESS-HFB solver uses a novel multi-resolution analysis based adaptive pseudo-spectral techniques to enable fully parallel 3D calculations of very large systems. In this work we present benchmark results for HFB-AX and MADNESS-HFB on ultracold trapped fermions.
Bassem, Y El
2016-01-01
In a previous work [Int. J. Mod. Phys. E 24, 1550073 (2015)], hereafter referred as paper I, we have investigated the ground-state properties of Nd, Ce and Sm isotopes within Hartree-Fock-Bogoliubov method with SLy5 skyrme force in which the pairing strength has been generalized with a new proposed formula. However, that formula is more appropriate for the region of Nd. In this work, we have studied the ground-state properties of both even-even and odd Mo and Ru isotopes. For this, we have used Hartree- Fock-Bogoliubov method with SLy4 skyrme force, and a new formula of the pairing strength which is more accurate for this region of nuclei. The results have been compared with available experimental data, the results of Hartree-Fock-Bogoliubov calculations based on the D1S Gogny effective nucleon-nucleon interaction and predictions of some nuclear models such as Finite Range Droplet Model (FRDM) and Relativistic Mean Field (RMF) theory.
Adaptive multi-resolution 3D Hartree-Fock-Bogoliubov solver for nuclear structure
Pei, J. C.; Fann, G. I.; Harrison, R. J.; Nazarewicz, W.; Shi, Yue; Thornton, S.
2014-08-01
Background: Complex many-body systems, such as triaxial and reflection-asymmetric nuclei, weakly bound halo states, cluster configurations, nuclear fragments produced in heavy-ion fusion reactions, cold Fermi gases, and pasta phases in neutron star crust, are all characterized by large sizes and complex topologies in which many geometrical symmetries characteristic of ground-state configurations are broken. A tool of choice to study such complex forms of matter is an adaptive multi-resolution wavelet analysis. This method has generated much excitement since it provides a common framework linking many diversified methodologies across different fields, including signal processing, data compression, harmonic analysis and operator theory, fractals, and quantum field theory. Purpose: To describe complex superfluid many-fermion systems, we introduce an adaptive pseudospectral method for solving self-consistent equations of nuclear density functional theory in three dimensions, without symmetry restrictions. Methods: The numerical method is based on the multi-resolution and computational harmonic analysis techniques with a multi-wavelet basis. The application of state-of-the-art parallel programming techniques include sophisticated object-oriented templates which parse the high-level code into distributed parallel tasks with a multi-thread task queue scheduler for each multi-core node. The internode communications are asynchronous. The algorithm is variational and is capable of solving coupled complex-geometric systems of equations adaptively, with functional and boundary constraints, in a finite spatial domain of very large size, limited by existing parallel computer memory. For smooth functions, user-defined finite precision is guaranteed. Results: The new adaptive multi-resolution Hartree-Fock-Bogoliubov (HFB) solver madness-hfb is benchmarked against a two-dimensional coordinate-space solver hfb-ax that is based on the B-spline technique and a three-dimensional solver
Superdeformed rotational bands in the Mercury region. A cranked Skyrme-Hartree-Fock-Bogoliubov study
Gall, B. [Paris-11 Univ., 91 - Orsay (France). Centre de Spectrometrie Nucleaire et de Spectrometrie de Masse; Bonche, P. [CEA Centre d`Etudes de Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique; Dobaczewski, J. [Warsaw Univ. (Poland). Inst. Fizyki Teoretycznej; Heenen, P.H. [Universite Libre de Bruxelles (Belgium). Physique Nucleaire Theorique; Flocard, H.
1993-12-17
A study of rotational properties of the ground superdeformed bands in {sup 190}Hg, {sup 192}Hg, {sup 194}Hg, and {sup 194}Pb is presented. The cranked Hartree-Fock-Bogolyubov method is used with the SkM* parametrization of the Skyrme force in the particle-hole channel and a seniority interaction in the pairing channel. An approximate particle number projection is performed by means of the Lipkin-Nogami prescription. The proton and neutron quasiparticle rhouthians are analyzed in connection with the present information on about thirty presently observed superdeformed bands in nuclei close neighbours of {sup 192}Hg. (authors). 53 refs., 14 figs.
Zhang, Ying; Meng, Jie
2010-01-01
The neutron pair correlation in nuclei near the neutron drip-line is investigated using the selfconsistent continuum Skyrme-Hartree-Fock-Bogoliubov theory formulated with the coordinate-space Green's function technique. Numerical analysis is performed for even-even N = 86 isotones in the Mo-Sn region, where the 3p3/2 and 3p1/2 orbits lying near the Fermi energy are either weakly bound or unbound. The quasiparticle states originating from the l = 1 orbits form resonances with large widths, which are due to the low barrier height and the strong continuum coupling caused by the pair potential. Analyzing in detail the pairing properties and roles of the quasiparticle resonances, we found that the l = 1 broad quasiparticle resonances persist to feel the pair potential and contribute to the pair correlation even when their widths are comparable with the resonance energy.
Ground state properties of even-even and odd Nd,Ce and Sm isotopes in Hartree-Fock-Bogoliubov method
Bassem, Younes El
2015-01-01
In this work, we have studied ground-state properties of both even-even and odd Nd isotopes within Hartree-Fock-Bogoliubov method with SLy5 Skyrme force in which the pairing strength has been generalized with a new proposed formula. We calculated bind- ing energies, two-neutron separation energies, quadrupole deformation, charge, neutron and proton radii. Similar calculations have been carried out for Ce and Sm in order to verify the validity of our pairing strength formula. The results have been compared with available experimental data, the results of Hartree-Fock-Bogoliubov calculations based on the D1S Gogny effective nucleon-nucleon interaction and predictions of some nuclear models such as Finite Range Droplet Model (FRDM) and Relativistic Mean Field (RMF) theory.
Goriely, S.; Chamel, N.; Pearson, J. M.
2016-03-01
Extending our earlier work, a new family of three Hartree-Fock-Bogoliubov (HFB) mass models, labeled HFB-30, HFB-31, and HFB-32, is presented, along with their underlying interactions, BSk30, BSk31, and BSk32, respectively. The principle new feature is a purely phenomenological pairing term that depends on the density gradient. This enables us to have a bulk pairing term that is fitted to realistic nuclear-matter calculations in which for the first time the self-energy corrections are included, while the behavior of the nucleon effective masses in asymmetric homogeneous nuclear matter is significantly improved. Furthermore, in the particle-hole channel all the highly realistic constraints of our earlier work are retained. In particular, the unconventional Skyrme forces containing t4 and t5 terms are still constrained to fit realistic equations of state of neutron matter stiff enough to support the massive neutron stars PSR J1614-2230 and PSR J0348+0432. All unphysical long-wavelength spin and spin-isospin instabilities of nuclear matter, including the unphysical transition to a polarized state in neutron-star matter, are eliminated. Our three interactions are characterized by values of the symmetry coefficient J of 30, 31, and 32 MeV, respectively. The best fit to the database of 2353 nuclear masses is found for model HFB-31 (J =31 MeV ) with a model error of 0.561 MeV. This model also fits the charge-radius data with an root-mean-square error of 0.027 fm.
Ebata, Shuichiro; Inakura, Tsunenori
2014-01-01
Systematic investigations of the electric dipole (E1) modes of excitation are performed using the canonical-basis time-dependent Hartree-Fock-Bogoliubov (Cb-TDHFB) theory. The Cb-TDHFB is able to describe dynamical pairing correlations in excited states of nuclear systems. We apply the method to the real-time calculation of linear response in even-even nuclei with Skyrme functionals. Effects of shell structure, neutron skin, deformation, and neutron chemical potential (separation energy) are studied in a systematic way. This reveals a number of characteristic features of the low-energy E1 modes. We also find a universal behavior in the low-energy E1 modes for heavy neutron-rich isotopes, which suggests the emergence of decoupled E1 peaks beyond N = 82.
On Blowup for time-dependent generalized Hartree-Fock equations
Hainzl, Christian; Lewin, Mathieu; Schlein, Benjamin
2009-01-01
We prove finite-time blowup for spherically symmetric and negative energy solutions of Hartree-Fock and Hartree-Fock-Bogoliubov type equations, which describe the evolution of attractive fermionic systems (e. g. white dwarfs). Our main results are twofold: First, we extend the recent blowup result of [Hainzl and Schlein, Comm. Math. Phys. \\textbf{287} (2009), 705--714] to Hartree-Fock equations with infinite rank solutions and a general class of Newtonian type interactions. Second, we show the existence of finite-time blowup for spherically symmetric solutions of a Hartree-Fock-Bogoliubov model, where an angular momentum cutoff is introduced. We also explain the key difficulties encountered in the full Hartree-Fock-Bogoliubov theory.
Relativistic Hartree-Bogoliubov description of the halo nuclei
Meng, J.; Ring, P. [Universitaet Muenchen, Garching (Germany)
1996-12-31
Here the authors report the development of the relativistic Hartree-Bogoliubov theory in coordinate space. Pairing correlations are taken into account by both density dependent force of zero range and finite range Gogny force. As a primary application the relativistic HB theory is used to describe the chain of Lithium isotopes reaching from {sup 6}Li to {sup 11}Li. In contrast to earlier investigations within a relativistic mean field theory and a density dependent Hartree Fock theory, where the halo in {sup 11}Li could only be reproduced by an artificial shift of the 1p{sub 1/2} level close to the continuum limit, the halo is now reproduced in a self-consistent way without further modifications using the scattering of Cooper pairs to the 2s{sub 1/2} level in the continuum. Excellent agreement with recent experimental data is observed.
Stoitsov, M. V.; Schunck, N.; Kortelainen, M.; Michel, N.; Nam, H.; Olsen, E.; Sarich, J.; Wild, S.
2013-06-01
We describe the new version 2.00d of the code HFBTHO that solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogoliubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the modified Broyden method for non-linear problems, (ii) optional breaking of reflection symmetry, (iii) calculation of axial multipole moments, (iv) finite temperature formalism for the HFB method, (v) linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations, (vi) blocking of quasi-particles in the Equal Filling Approximation (EFA), (vii) framework for generalized energy density with arbitrary density-dependences, and (viii) shared memory parallelism via OpenMP pragmas. Program summaryProgram title: HFBTHO v2.00d Catalog identifier: ADUI_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUI_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 167228 No. of bytes in distributed program, including test data, etc.: 2672156 Distribution format: tar.gz Programming language: FORTRAN-95. Computer: Intel Pentium-III, Intel Xeon, AMD-Athlon, AMD-Opteron, Cray XT5, Cray XE6. Operating system: UNIX, LINUX, WindowsXP. RAM: 200 Mwords Word size: 8 bits Classification: 17.22. Does the new version supercede the previous version?: Yes Catalog identifier of previous version: ADUI_v1_0 Journal reference of previous version: Comput. Phys. Comm. 167 (2005) 43 Nature of problem: The solution of self-consistent mean-field equations for weakly-bound paired nuclei requires a correct description of the asymptotic properties of nuclear quasi-particle wave functions. In the present implementation, this is achieved by using the single-particle wave functions
Misfits in Skyrme-Hartree-Fock
Erler, J; Reinhard, P -G
2010-01-01
We address very briefly five critical points in the context of the Skyrme-Hartree-Fock (SHF) scheme: 1) the impossibility to consider it as an interaction, 2) a possible inconsistency of correlation corrections as, e.g., the center-of-mass correction, 3) problems to describe the giant dipole resonance (GDR) simultaneously in light and heavy nuclei, 4) deficiencies in the extrapolation of binding energies to super-heavy elements (SHE), and 5) a yet inappropriate trend in fission life-times when going to the heaviest SHE. While the first two points have more a formal bias, the other three points have practical implications and wait for solution.
Koopmans' theorem in statistical Hartree-Fock theory
Pain, Jean-Christophe
2011-01-01
In this short paper, the validity of Koopmans' theorem in the Hartree-Fock theory at non-zero temperature (Hartree-Fock statistical theory) is investigated. It is shown that Koopmans' theorem does not apply in the grand-canonical ensemble, due to a missing contribution to the energy proportional to the interaction between two electrons belonging to the same orbital. Hartree-Fock statistical theory has also been applied in the canonical ensemble [Blenski et al., Phys. Rev. E 55, R4889 (1997)] for the purpose of photo-absorption calculations. In that case, the Hartree-Fock self-consistent-field equations are derived in the super-configuration approximation. It is shown that Koopmans' theorem does not hold in the canonical ensemble, but that a restricted version of the theorem can be obtained, by assuming that a particular quantity multiplying the interaction matrix element in the expression of the energy does not change during the removal of an electron.
Relativistic Brueckner-Hartree-Fock theory for finite nuclei
Shen, Shihang; Liang, Haozhao; Meng, Jie; Ring, Peter; Zhang, Shuangquan
2016-01-01
Starting with a bare nucleon-nucleon interaction, for the first time the full relativistic Brueckner-Hartree-Fock equations are solved for finite nuclei in a Dirac-Woods-Saxon basis. No free parameters are introduced to calculate the ground-state properties of finite nuclei. The nucleus $^{16}$O is investigated as an example. The resulting ground-state properties, such as binding energy and charge radius, are considerably improved as compared with the non-relativistic Brueckner-Hartree-Fock results and much closer to the experimental data. This opens the door for \\emph{ab initio} covariant investigations of heavy nuclei.
Constrained Hartree-Fock and quasi-spin projection
Cambiaggio, M. C.; Plastino, A.; Szybisz, L.
1980-08-01
The constrained Hartree-Fock approach of Elliott and Evans is studied in detail with reference to two quasi-spin models, and their predictions compared with those arising from a projection method. It is found that the new approach works fairly well, although limitations to its applicability are encountered.
2-D Hartee-Fock-Bogoliubov Calculations For Exotic Deformed Nuclei
Blazkiewicz, Artur; Oberacker, Volker E.; Umar, Sait A.; Teran, Edgar
2003-10-01
We solve the Hartree-Fock-Bogoliubov (HFB) equations in coordinate space; the computational method has been specifically designed to study ground state properties of nuclei near the neutron and proton drip lines teref1. The unique feature of our code is that it takes into account the strong coupling to high-energy continuum states, up to an equivalent single-particle energy of 60 MeV or higher. We solve the HFB equations for deformed, axially symmetric even-even nuclei in coordinate space on a 2-D lattice with Basis-Spline methods. For the p-h channel, the Skyrme (SLy4) effective N-N interaction is utilized, and for the p-p and h-h channel we use a delta interaction. Results teref2,ref3 are presented for binding energies, deformations, normal densities and pairing densities, Fermi levels, and pairing gaps. In particular, we calculate the properties of two light isotope chains up to the two-neutron dripline: oxygen (^22-28O) and sulfur (^40-52S). For some of the sulfur isotopes we found the "shape coexistence" what was also confirmed by RMF calculations of P. Ring and G.A. Lalazissis teref4. Furthermore, we study the strongly deformed heavy systems zirconium (^102,104Zr), cerium (^152Ce), and samarium (^158Sm).We are also planning to study other isotopes by running our new parallel MPI version of HFB code. Comparison with relativistic mean field theory and with experimental data is given whenever available. This work has been supported by the U.S. Department of Energy under grant No. DE-FG02-96ER40963 with Vanderbilt University. The numerical calculations were carried out on the IBM-RS/6000 SP supercomputer at NERSC in Berkeley and on our local "Beowulf" Vampire computer at Vanderbilt University. 99 ref1 Axially Symmetric Hartee-Fock-Bogoliubov calculations for nuclei near the drip lines,E. Teran, V.E. Oberacker and A.S. Umar, Phys. Rev. C 67, (June 2003) ref2 Half lives of isomeric states from SF of ^252Cf and large deformations in ^104Zr and ^158Sm, J.K. Hwang, A
Accurate Hartree-Fock energy of extended systems using large Gaussian basis sets
Paier, Joachim; Diaconu, Cristian V.; Scuseria, Gustavo E.; Guidon, Manuel; Vandevondele, Joost; Hutter, Jürg
2009-11-01
Calculating highly accurate thermochemical properties of condensed matter via wave-function-based approaches (such as, e.g., Hartree-Fock or hybrid functionals) has recently attracted much interest. We here present two strategies providing accurate Hartree-Fock energies for solid LiH in a large Gaussian basis set and applying periodic boundary conditions. The total energies were obtained using two different approaches, namely, a supercell evaluation of Hartree-Fock exchange using a truncated Coulomb operator and an extrapolation toward the full-range Hartree-Fock limit of a Padé fit to a series of short-range screened Hartree-Fock calculations. These two techniques agreed to significant precision. We also present the Hartree-Fock cohesive energy of LiH (converged to within sub-millielectron volt) at the experimental equilibrium volume as well as the Hartree-Fock equilibrium lattice constant and bulk modulus.
Qualitative breakdown of the unrestricted Hartree-Fock energy
Mori-Sánchez, Paula, E-mail: paula.mori@uam.es [Departamento de Química and Instituto de Física de la Materia Condensada (IFIMAC), Universidad Autónoma de Madrid, 28049 Madrid (Spain); Cohen, Aron J., E-mail: ajc54@cam.ac.uk [Department of Chemistry, Lensfield Road, University of Cambridge, Cambridge CB2 1EW (United Kingdom)
2014-10-28
The stretching of closed-shell molecules is a qualitative problem for restricted Hartree-Fock that is usually circumvented by the use of unrestricted Hartree-Fock (UHF). UHF is well known to break the spin symmetry at the Coulson-Fischer point, leading to a discontinuous derivative in the potential energy surface and incorrect spin density. However, this is generally not considered as a major drawback. In this work, we present a set of two electron molecules which magnify the problem of symmetry breaking and lead to drastically incorrect potential energy surfaces with UHF. These molecules also fail with unrestricted density-functional calculations where a functional such as B3LYP gives both symmetry breaking and an unphysically low energy due to the delocalization error. The implications for density functional theory are also discussed.
Particle unstable nuclei in the Hartree-Fock theory
Kruppa, A.T. [Magyar Tudomanyos Akademia, Debrecen (Hungary). Atommag Kutato Intezete; Heenen, P.H. [Brussels Univ. (Belgium). Service de Physique Nucleaire Theorique; Flocard, H. [Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire; Liotta, R.J. [Manne Siegbahn Inst. of Physics, Stockholm (Sweden)
1997-12-31
Ground state energies and decay widths of particle unstable nuclei are calculated within the Hartree-Fock approximation by performing a complex scaling of the many-body Hamiltonian. Through this transformation, the wave functions of the resonant state become square integrable. The method is implemented with Skyrme effective interactions. Several Skyrme parametrizations are tested on four unstable nuclei: {sup 10}He, {sup 12}O, {sup 26}O and {sup 28}O. (author). 24 refs.
Potential Energy Surface in Hartree-Fock Theory:Adiabatic or Configuration-Constrained?
GUO Lu; Sakata Fumihiko; ZHAO En-Guang
2004-01-01
Validity of adiabatic assumption is discussed within the constrained Hartree-Fock theory for self-conjugate nucleus 72Kr. It is shown that the adiabatic assumption does not provide a correct description for the nature of nucleus when a configuration change is involved. The excited Hartree-Fock states and the continuously-connected constrained Hartree-Fock states are given for the first time by applying the configuration dictated constrained Hartree-Fock theory with Gogny force. The importance of self-consistency between the mean-field and the single particle wave functions is emphasized even when a small number of nucleons are involved in the configuration change.
Properties of the periodic Hartree-Fock minimizer
Ghimenti, Marco
2008-01-01
We study the periodic Hartree-Fock model used for the description of electrons in a crystal. The existence of a minimizer was previously shown by Catto, Le Bris and Lions (Ann. Inst. H. Poincare Anal. Non Lineaire} 18 (2001), no.6, 687--760). We prove in this paper that any minimizer is necessarily a projector and that it solves a certain nonlinear equation, similarly to the atomic case. In particular we show that the Fermi level is either empty or totally filled.
Ground state properties of graphene in Hartree-Fock theory
Hainzl, Christian; Sparber, Christof
2012-01-01
We study the Hartree-Fock approximation of graphene in infinite volume, with instantaneous Coulomb interactions. First we construct its translation-invariant ground state and we recover the well-known fact that, due to the exchange term, the effective Fermi velocity is logarithmically divergent at zero momentum. In a second step we prove the existence of a ground state in the presence of local defects and we discuss some properties of the linear response to an external electric field. All our results are non perturbative.
Hellweg, Arnim
2016-01-01
Hartree--Fock theory is one of the most ancient methods of computational chemistry, but up to the present day quantum chemical calculations on Hartree--Fock level or with hybrid density functional theory can be excessively time consuming. We compare three currently available techniques to reduce the computational demands of such calculations in terms of timing and accuracy.
Extreme Exotic Calcium Lambda Hypernuclei in the Relativistic Continuum Hartree-Bogoliubov Theory
L(U) Hong-Feng
2008-01-01
Exotic calcium lambda hypernuclei properties with the neutron number of 20-400 by a step of 20 are discussed by employing the relativistic continuum Hartree-Bogoliubov theory with a zero range pairing interaction. The Bethe-Weizs(a)cker mass formula of a multi-strange system and the Woods-Saxon-type potential of larnbda need to be modified for exotic calcium hypernuclei with unusual number of neutrons and lambdas. The possible neutron and lambda limits of exotic Ca larnbda hypernuclei are also investigated.
Evolution of $N = 28$ shell closure in relativistic continuum Hartree-Bogoliubov theory
Xia, Xuewei
2015-01-01
The $N = 28$ shell gap in sulfur, argon, calcium and titanium isotopes is investigated in the framework of relativistic continuum Hartree-Bogoliubov (RCHB) theory. The evolutions of neutron shell gap, separation energy, single particle energy and pairing energy are analyzed, and it is found that $N = 28$ shell gap is quenched in sulfur isotopes but persists in argon, calcium and titanium isotopes. The evolution of $N = 28$ shell gap in $N = 28$ isotonic chain is discussed, and the erosion of $N = 28$ shell gap is understood with the evolution of potential with proton number.
Error estimates for the Skyrme-Hartree-Fock model
Erler, J
2014-01-01
There are many complementing strategies to estimate the extrapolation errors of a model which was calibrated in least-squares fits. We consider the Skyrme-Hartree-Fock model for nuclear structure and dynamics and exemplify the following five strategies: uncertainties from statistical analysis, covariances between observables, trends of residuals, variation of fit data, dedicated variation of model parameters. This gives useful insight into the impact of the key fit data as they are: binding energies, charge r.m.s. radii, and charge formfactor. Amongst others, we check in particular the predictive value for observables in the stable nucleus $^{208}$Pb, the super-heavy element $^{266}$Hs, $r$-process nuclei, and neutron stars.
Computational Nuclear Physics and Post Hartree-Fock Methods
Lietz, Justin; Jansen, Gustav R; Hagen, Gaute; Hjorth-Jensen, Morten
2016-01-01
We present a computational approach to infinite nuclear matter employing Hartree-Fock theory, many-body perturbation theory and coupled cluster theory. These lectures are closely linked with those of chapters 9, 10 and 11 and serve as input for the correlation functions employed in Monte Carlo calculations in chapter 9, the in-medium similarity renormalization group theory of dense fermionic systems of chapter 10 and the Green's function approach in chapter 11. We provide extensive code examples and benchmark calculations, allowing thereby an eventual reader to start writing her/his own codes. We start with an object-oriented serial code and end with discussions on strategies for porting the code to present and planned high-performance computing facilities.
Semiempirical Hartree-Fock calculations for $KNbO_{3}$
Eglitis, R I; Borstel, G
1996-01-01
In applying the semiempirical intermediate neglect of differential overlap (INDO) method based on the Hartree-Fock formalism to a cubic perovskite-based ferroelectric material KNbO3, it was demonstrated that the accuracy of the method is sufficient for adequately describing the small energy differences related to the ferroelectric instability. The choice of INDO parameters has been done for a system containing Nb. Based on the parametrization proposed, the electronic structure, equilibrium ground state structure of the orthorhombic and rhombohedral phases, and Gamma-TO phonon frequencies in cubic and rhombohedral phases of KNbO3 were calculated and found to be in good agreement with the experimental data and with the first-principles calculations available.
Using Hartree-Fock pseudopotentials in GW calculations
Hamann, D. R.; Vanderbilt, David
2010-03-01
The issue of including shallow ``semi-core'' states as valence has recently resurfaced in the context of self-consistent GW calculations.footnotetextF. Bruneval et al., Phys. Rev. Lett. 97, 267601 (2006). Supposing that semi-core-valence exchange is the dominant process necessitating the inclusion of semi-cores, we have investigated whether the use Hartree-Fock pseudopotentialsfootnotetextW. A. Al-Saidi, E. J. Walter, and A. M. Rappe, Phys. Rev. B 77, 075122 (2008). instead of density-functional psp's might obviate the need for semi-cores. The answers to this question appear to be ``yes'' for the case of CuCl (filled d shell), and ``semi-cores don't matter anyway'' for ScN (empty d shell). Opportunity permitting, additional examples will be discussed.
Correlated Electron Calculations with Hartree-Fock Scaling
Gebauer, Ralph; Car, Roberto
2013-01-01
We introduce an energy functional for ground-state electronic structure calculations with fundamental variables the natural spin orbitals and their joint occupation probabilities in an implied many-body trial wave function. We use a controlled approximation for the two-particle density matrix that greatly extends the accuracy compared to current functionals of the one-particle density matrix only. Algebraic scaling of computational cost with electron number is achieved in general, and Hartree-Fock scaling in the seniority-zero version of the theory. We present results obtained with the latter version for saturated small molecular systems for which highly accurate quantum chemical computations are available for comparison. The results are variational, capturing most of the correlation energy from equilibrium to dissociation.
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.
A collisional extension of time-dependent Hartree-Fock
Lacombe, L.; Reinhard, P.-G.; Dinh, P. M.; Suraud, E.
2016-12-01
We propose a collisional extension of time-dependent mean-field theories on the basis of a recently proposed stochastic extension of mean-field dynamics (stochastic time-dependent Hartree-Fock, STDHF). The latter theory is unfortunately too involved to envision practical applications in realistic systems in the near future and is thus bound to model systems. It is also hard to explore moderate to low energies with STDHF, because of vanishing transition probabilities that are impossible to sample properly. For such moderately excited situations covering small fluctuations, we compactify sampling by employing the same average mean field for all STDHF trajectories. The new approach, coined average STDHF (ASTDHF), ignores the fluctuations of the mean field but still accounts correctly for the collisional correlations responsible for dissipative features on top of mean-field dynamics. We detail the main features of the new approach in relation to existing equations, in particular quantum kinetic theories. The new theory is directly connected to STDHF, both formally and practically. We thus discuss in detail how the two approaches are related to each other. We apply the new scheme to illustrative examples taking as benchmark STDHF dynamics in 1D. ASTDHF provides results that are in remarkable agreement with the more elaborate STDHF. It makes it a promising approach to deal with dissipative dynamics in finite quantum systems, because of its moderate cost allowing applications in realistic systems and the possibility of exploring any excitation energy range where collisional correlations are expected to play a role.
The neutron halo structure of 17B studied with the relativistic Hartree-Bogoliubov theory
JI Juan-Xia; LI Jia-Xing; HAN Rui; WANG Jian-Song; HU Qiang
2012-01-01
The properties of neutron-rich boron isotopes are studied in the relativistic continuum HartreeBogoliubov theory in coordinate space with NL-SH,PK1 and TM2 effective interactions.Pairing corrections are taken into account by a density dependent force of zero range.The binding energies calculated for these nuclei agree with the experimental data quite well.The neutron-rich nucleus 17B has been predicted to have a two-neutron halo structure in its ground state.The halo structure of 17B is reproduced in a self-consistent way,and this halo is shown to be formed by the valence neutron level 2s1/2.
A relativistic continuum Hartree-Bogoliubov theory description of N=3 isotones
HAN Rui; JI Juan-Xia; LI Jia-Xing
2011-01-01
The ground-state properties of N=3 isotones and mirror nuclei have been investigated in the Rrelativistic Continuum Hartree-Bogoliubov theory with the NLSH effective interaction.Pairing correlations are taken into account by a density-dependent δ-force.The calculations show that the proton density distributions of 8B and 9C have a long tail,the core has an increasing tendency of 9C and the paired off valence protons make the halo distribution shrink.The cross sections for the 8B(9C)+12C reaction which are consistent with the experimental data are calculated using the Glauber model.On the whole,we think that 8B is a one-proton halo nucleus and 9C is a two-proton halo nucleus.
Multidimensionally-constrained relativistic Hartree-Bogoliubov study of nuclear spontaneous fission
Zhao, Jie; Niksic, Tamara; Vretenar, Dario
2015-01-01
Recent microscopic studies, based on the theoretical framework of nuclear energy density functionals, have analyzed dynamic (least action) and static (minimum energy) fission paths, and it has been shown that in addition to the important role played by nonaxial and/or octupole collective degrees of freedom, fission paths crucially depend on the approximations adopted in calculating the collective inertia. The dynamics of spontaneous fission of $^{264}$Fm and $^{250}$Fm is explored. The fission paths, action integrals and the corresponding half-lives predicted by the functionals PC-PK1 and DD-PC1 are compared and, in the case of $^{264}$Fm, discussed in relation with recent results obtained using the HFB model based on the Skyrme functional SkM$^*$ and a density dependent mixed pairing interaction. Deformation energy surfaces, collective potentials, and perturbative and nonperturbative cranking collective inertia tensors are calculated using the multidimensionally-constrained relativistic Hartree-Bogoliubov (M...
Momentum distribution of relativistic nuclei with Hartree-Fock mesonic correlations
Amaro, J.E. [Departamento de Fisica Moderna, Universidad de Granada, E-18071 Granada (Spain); Barbaro, M.B. [Dipartimento di Fisica Teorica, Universita di Torino and INFN, Sezione di Torino, Via P. Giuria 1, 10125 Torino (Italy); Departamento de Fisica Atomica, Molecular y Nuclear Universidad de Sevilla, Apdo. 1065, E-41080 Sevilla (Spain); Caballero, J.A. [Departamento de Fisica Atomica, Molecular y Nuclear Universidad de Sevilla, Apdo. 1065, E-41080 Sevilla (Spain); Donnelly, T.W. [Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Molinari, A. [Dipartimento di Fisica Teorica, Universita di Torino and INFN, Sezione di Torino, Via P. Giuria 1, 10125 Torino (Italy)
2002-12-01
The impact of Hartree-Fock correlations on the nuclear momentum distribution is studied in a fully relativistic one-boson-exchange model. Hartree-Fock equations are exactly solved to first order in the coupling constants. The renormalization of the Dirac spinors in the medium is shown to affect the momentum distribution, as opposed to what happens in the non-relativistic case. The unitarity of the model is shown to be preserved by the present renormalization procedure. (orig.)
Restricted Closed Shell Hartree Fock Roothaan Matrix Method Applied to Helium Atom Using Mathematica
Acosta, César R.; Tapia, J. Alejandro; Cab, César
2014-01-01
Slater type orbitals were used to construct the overlap and the Hamiltonian core matrices; we also found the values of the bi-electron repulsion integrals. The Hartree Fock Roothaan approximation process starts with setting an initial guess value for the elements of the density matrix; with these matrices we constructed the initial Fock matrix.…
CASTRO EUSTÁQUIO V. R. DE
2001-01-01
Full Text Available The generator coordinate Hartree-Fock method is used to generate adapted Gaussian basis sets for the atoms from Li (Z=3 through Xe (Z=54. In this method the Griffin-Hill-Wheeler-Hartree-Fock equations are integrated through the integral discretization technique. The wave functions generated in this work are compared with the widely used Roothaan-Hartree-Fock wave functions of Clementi and Roetti (1974, and with other basis sets reported in the literature. For all atoms studied, the errors in our total energy values relatively to the numerical Hartree-Fock limits are always less than 7.426 mhartree.
Thermal resonating Hartree-Bogoliubov theory based on the projection method
Nishiyama, Seiya; Ohnishi, Hiromasa
2013-01-01
We propose a rigorous thermal resonating mean-field theory (Res-MFT). A state is approximated by superposition of multiple MF wavefunctions (WFs) composed of non-orthogonal Hartree-Bogoliubov (HB) WFs. We adopt a Res-HB subspace spanned by Res-HB ground and excited states. A partition function (PF) in a SO(2N) coherent state representation |g> (N:Number of single-particle states) is expressed as Tr(e^{-\\beta H})=2^{N-1} \\int dg (\\beta=1/k_BT). Introducing a projection operator P to the Res-HB subspace, the PF in the Res-HB subspace is given as Tr(Pe^{-\\beta H}), which is calculated within the Res-HB subspace by using the Laplace transform of e^{-\\beta H} and the projection method. The variation of the Res-HB free energy is made, which leads to a thermal HB density matrix W_{Res}^{thermal} expressed in terms of a thermal Res-FB operator F_{Res}^{thermal} as W_{Res}^{thermal}={1_{2N}+exp(\\beta F_{Res}^{thermal})}^{-1}. A calculation of the PF by an infinite matrix continued fraction is cumbersome and a procedur...
Projected Hartree Fock Theory as a Polynomial Similarity Transformation Theory of Single Excitations
Qiu, Yiheng; Scuseria, Gustavo E
2016-01-01
Spin-projected Hartree-Fock is introduced as a particle-hole excitation ansatz over a symmetry-adapted reference determinant. Remarkably, this expansion has an analytic expression that we were able to decipher. While the form of the polynomial expansion is universal, the excitation amplitudes need to be optimized. This is equivalent to the optimization of orbitals in the conventional projected Hartree-Fock framework of non-orthogonal determinants. Using the inverse of the particle-hole expansion, we similarity transform the Hamiltonian in a coupled-cluster style theory. The left eigenvector of the non-hermitian Hamiltonian is constructed in a similar particle-hole expansion fashion, and we show that to numerically reproduce variational projected Hartree-Fock results, one needs as many pair excitations in the bra as the number of strongly correlated entangled pairs in the system. This single-excitation polynomial similarity transformation theory is an alternative to our recently presented double excitation the...
A finite-temperature Hartree-Fock code for shell-model Hamiltonians
Bertsch, G. F.; Mehlhaff, J. M.
2016-10-01
The codes HFgradZ.py and HFgradT.py find axially symmetric minima of a Hartree-Fock energy functional for a Hamiltonian supplied in a shell model basis. The functional to be minimized is the Hartree-Fock energy for zero-temperature properties or the Hartree-Fock grand potential for finite-temperature properties (thermal energy, entropy). The minimization may be subjected to additional constraints besides axial symmetry and nucleon numbers. A single-particle operator can be used to constrain the minimization by adding it to the single-particle Hamiltonian with a Lagrange multiplier. One can also constrain its expectation value in the zero-temperature code. Also the orbital filling can be constrained in the zero-temperature code, fixing the number of nucleons having given Kπ quantum numbers. This is particularly useful to resolve near-degeneracies among distinct minima.
Application of Fourth Order Vibrational Perturbation Theory with Analytic Hartree-Fock Force Fields
Gong, Justin Z.; Matthews, Devin A.; Stanton, John F.
2014-06-01
Fourth-Order Rayleigh-Schrodinger Perturbation Theory (VPT4) is applied to a series of small molecules. The quality of results have been shown to be heavily dependent on the quality of the quintic and sextic force constants used and that numerical sextic force constants converge poorly and are unreliable for VPT4. Using analytic Hartree-Fock force constants, it is shown that these analytic higher-order force constants are comparable to corresponding force constants from numerical calculations at a higher level of theory. Calculations show that analytic Hartree-Fock sextic force constants are reliable and can provide good results with Fourth-Order Rayleigh-Schrodinger Perturbation Theory.
Excess Charge for Pseudo-relativistic Atoms in Hartree-Fock Theory
Dall'Acqua, Anna; Solovej, Jan Philip
2010-01-01
We prove within the Hartree-Fock theory of pseudo-relativistic atoms that the maximal negative ionization charge and the ionization energy of an atom remain bounded independently of the nuclear charge $Z$ and the fine structure constant $\\alpha$ as long as $Z\\alpha$ is bounded.......We prove within the Hartree-Fock theory of pseudo-relativistic atoms that the maximal negative ionization charge and the ionization energy of an atom remain bounded independently of the nuclear charge $Z$ and the fine structure constant $\\alpha$ as long as $Z\\alpha$ is bounded....
Excess Charge for Pseudo-relativistic Atoms in Hartree-Fock Theory
Dall'Acqua, Anna; Solovej, Jan Philip
2010-01-01
We prove within the Hartree-Fock theory of pseudo-relativistic atoms that the maximal negative ionization charge and the ionization energy of an atom remain bounded independently of the nuclear charge $Z$ and the fine structure constant $\\alpha$ as long as $Z\\alpha$ is bounded.......We prove within the Hartree-Fock theory of pseudo-relativistic atoms that the maximal negative ionization charge and the ionization energy of an atom remain bounded independently of the nuclear charge $Z$ and the fine structure constant $\\alpha$ as long as $Z\\alpha$ is bounded....
Hartree-Fock Cluster Study of Interstitial Transition Metals in Silicon
Broer, R.; Aissing, G.; Nieuwpoort, W.C.; Feiner, L.F.
1986-01-01
Results are presented of a Hartree-Fock cluster study of interstitial Ti, V, Cr, and Mn impurities in silicon. A Si10 cluster models the nearest Si atoms around a tetrahedral interstitial site in crystalline Si. The dangling bonds of the Si atoms are saturated by hydrogens. The effect of the Si core
Method of renormalization potential for one model of Hartree-Fock-Slater type
Zasorin, Y V
2002-01-01
A new method of the potential renormalization for the quasiclassical model of the Hartree-Fock-Slater real potential is proposed. The method makes it possible to easily construct the wave functions and contrary to the majority od similar methods it does not require the knowledge of the real-type potential
Robust Periodic Hartree-Fock Exchange for Large-Scale Simulations Using Gaussian Basis Sets.
Guidon, Manuel; Hutter, Jürg; VandeVondele, Joost
2009-11-10
Hartree-Fock exchange with a truncated Coulomb operator has recently been discussed in the context of periodic plane-waves calculations [Spencer, J.; Alavi, A. Phys. Rev. B: Solid State, 2008, 77, 193110]. In this work, this approach is extended to Gaussian basis sets, leading to a stable and accurate procedure for evaluating Hartree-Fock exchange at the Γ-point. Furthermore, it has been found that standard hybrid functionals can be transformed into short-range functionals without loss of accuracy. The well-defined short-range nature of the truncated exchange operator can naturally be exploited in integral screening procedures and makes this approach interesting for both condensed phase and gas phase systems. The presented Hartree-Fock implementation is massively parallel and scales up to ten thousands of cores. This makes it feasible to perform highly accurate calculations on systems containing thousands of atoms or ten thousands of basis functions. The applicability of this scheme is demonstrated by calculating the cohesive energy of a LiH crystal close to the Hartree-Fock basis set limit and by performing an electronic structure calculation of a complete protein (rubredoxin) in solution with a large and flexible basis set.
Koopmans' theorem in the statistical Hartree-Fock theory
Pain, Jean-Christophe, E-mail: jean-christophe.pain@cea.fr [CEA, DAM, DIF, F-91297 Arpajon (France)
2011-07-28
In this short paper, the validity of Koopmans' theorem in the Hartree-Fock theory at non-zero temperature (Hartree-Fock statistical theory) is investigated. It is shown that Koopmans' theorem does not apply in the grand-canonical ensemble, due to a missing contribution to the energy proportional to the interaction between two electrons belonging to the same orbital. The Hartree-Fock statistical theory has also been applied in the canonical ensemble (Blenski et al 1997 Phys. Rev. E 55 R4889) for the purpose of photo-absorption calculations. In that case, the Hartree-Fock self-consistent field equations are derived in the super-configuration approximation. It is shown that Koopmans' theorem does not hold in the canonical ensemble, but a restricted version of the theorem can be obtained by assuming that a particular quantity multiplying the interaction matrix element in the expression of the energy does not change during the removal of an electron.
Qiu, Yiheng; Henderson, Thomas M.; Scuseria, Gustavo E.
2016-09-01
Spin-projected Hartree-Fock is written as a particle-hole excitation ansatz over a symmetry-adapted reference determinant. Remarkably, this expansion has an analytic expression that we were able to decipher. While the form of the polynomial expansion is universal, the excitation amplitudes need to be optimized. This is equivalent to the optimization of orbitals in the conventional projected Hartree-Fock framework of non-orthogonal determinants. Using the inverse of the particle-hole expansion, we similarity transform the Hamiltonian in a coupled-cluster style theory. The left eigenvector of the non-Hermitian Hamiltonian is constructed in a similar particle-hole expansion fashion, and we show that to numerically reproduce variational projected Hartree-Fock results, one needs as many pair excitations in the bra as the number of strongly correlated entangled pairs in the system. This single-excitation polynomial similarity transformation theory is an alternative to our recently presented double excitation theory, but supports projected Hartree-Fock and coupled cluster simultaneously rather than interpolating between them.
Hartree-Fock Cluster Study of Interstitial Transition Metals in Silicon
Broer, R.; Aissing, G.; Nieuwpoort, W.C.; Feiner, L.F.
Results are presented of a Hartree-Fock cluster study of interstitial Ti, V, Cr, and Mn impurities in silicon. A Si10 cluster models the nearest Si atoms around a tetrahedral interstitial site in crystalline Si. The dangling bonds of the Si atoms are saturated by hydrogens. The effect of the Si core
Perturbative calculation of the Sternheimer anti-shielding factor with Hartree-Fock atomic orbitals
2012-01-01
We report a calculation of the Sternheimer anti-shielding factor, \\gamma, by means of first order perturbation theory. In quality of basis functions, we use Hartree-Fock electronic orbitals, expanded on hydrogenic atomic states. The computed \\gamma(r) for Fe^{3+} and Cu^{1+} inner electronic cores are reported and compared with literature values, obtained from alternative methodologies.
New Multithreaded Hybrid CPU/GPU Approach to Hartree-Fock.
Asadchev, Andrey; Gordon, Mark S
2012-11-13
In this article, a new multithreaded Hartree-Fock CPU/GPU method is presented which utilizes automatically generated code and modern C++ techniques to achieve a significant improvement in memory usage and computer time. In particular, the newly implemented Rys Quadrature and Fock Matrix algorithms, implemented as a stand-alone C++ library, with C and Fortran bindings, provides up to 40% improvement over the traditional Fortran Rys Quadrature. The C++ GPU HF code provides approximately a factor of 17.5 improvement over the corresponding C++ CPU code.
Fission dynamics within time-dependent Hartree-Fock: boost-induced fission
Goddard, P M; Rios, A
2015-01-01
Background: Nuclear fission is a complex large-amplitude collective decay mode in heavy nuclei. Microscopic density functional studies of fission have previously concentrated on adiabatic approaches based on constrained static calculations ignoring dynamical excitations of the fissioning nucleus, and the daughter products. Purpose: To explore the ability of dynamic mean-field methods to describe induced fission processes, using quadrupole boosts in the nuclide $^{240}$Pu as an example. Methods: Quadrupole constrained Hartree-Fock calculations are used to create a potential energy surface. An isomeric state and a state beyond the second barrier peak are excited by means of instantaneous as well as temporally extended gauge boosts with quadrupole shapes. The subsequent deexcitation is studied in a time-dependent Hartree-Fock simulation, with emphasis on fissioned final states. The corresponding fission fragment mass numbers are studied. Results: In general, the energy deposited by the quadrupole boost is quickl...
Multiconfiguration hartree-fock theory for pseudorelativistic systems: The time-dependent case
Hajaiej, Hichem
2014-03-01
In [Setting and analysis of the multi-configuration time-dependent Hartree-Fock equations, Arch. Ration. Mech. Anal. 198 (2010) 273-330] the third author has studied in collaboration with Bardos, Catto and Mauser the nonrelativistic multiconfiguration time-dependent Hartree-Fock system of equations arising in the modeling of molecular dynamics. In this paper, we extend the previous work to the case of pseudorelativistic atoms. We show the existence and the uniqueness of global-in-time solution to the underlying system under technical assumptions on the energy of the initial data and the charge of the nucleus. Moreover, we prove that the result can be extended to the case of neutron stars when the number of electrons is less than a critical number N cr. © 2014 World Scientific Publishing Company.
Brueckner-Hartree-Fock and its renormalized calculations for finite nuclei
Hu, B S; Ma, Y Z; Wu, Q; Sun, Z H
2016-01-01
We have performed self-consistent Brueckner-Hartree-Fock (BHF) and its renormalized theory to the structure calculations of finite nuclei. The $G$-matrix is calculated within the BHF basis, and the exact Pauli exclusion operator is determined by the BHF spectrum. Self-consistent occupation probabilities are included in the renormalized Brueckner-Hartree-Fock (RBHF). Various systematics and convergences are studies. Good results are obtained for the ground-state energy and radius. RBHF can give a more reasonable single-particle spectrum and radius. We present a first benchmark calculation with other {\\it ab initio} methods using the same effective Hamiltonian. We find that the BHF and RBHF results are in good agreement with other $\\it{ab}$ $\\it{initio}$ methods.
RONG; Jian; MA; Zhongyu
2004-01-01
The relativistic microscopic optical potential in the asymmetric nuclear matter is studied in the framework of the Dirac Brueckner-Hartree-Fock method. A new decomposition of the Dirac structure of the nuclear self-energy in nuclear matter is adopted. The self-energy of a nucleon with E＞ 0 in nuclear matter is calculated with the G matrix in the Hartree-Fock approach. The optical potential of a nucleon in the nuclear medium is identified with the nucleon self-energy. The energy and asymmetric parameter dependence of the relativistic optical potentials for proton and neutron are discussed. The resulting Schroedinger equivalent potentials have reasonable behaviors of the energy dependence. The asymmetric parameter dependence of relativistic optical potentials and Schroedinger potentials are emphasized.
Fission dynamics within time-dependent Hartree-Fock: deformation-induced fission
Goddard, P M; Rios, A
2015-01-01
Background: Nuclear fission is a complex large-amplitude collective decay mode in heavy nuclei. Microscopic density functional studies of fission have previously concentrated on adiabatic approaches based on constrained static calculations ignoring dynamical excitations of the fissioning nucleus, and the daughter products. Purpose: To explore the ability of dynamic mean-field methods to describe fast fission processes beyond the fission barrier, using the nuclide $^{240}$Pu as an example. Methods: Time-dependent Hartree-Fock calculations based on the Skyrme interaction are used to calculate non-adiabatic fission paths, beginning from static constrained Hartree-Fock calculations. The properties of the dynamic states are interpreted in terms of the nature of their collective motion. Fission product properties are compared to data. Results: Parent nuclei constrained to begin dynamic evolution with a deformation less than the fission barrier exhibit giant-resonance-type behaviour. Those beginning just beyond the ...
Hartree-Fock and Random Phase Approximation theories in a many-fermion solvable model
Co', Giampaolo
2016-01-01
We present an ideal system of interacting fermions where the solutions of the many-body Schroedinger equation can be obtained without making approximations. These exact solutions are used to test the validity of two many-body effective approaches, the Hartree-Fock and the Random Phase Approximation theories. The description of the ground state done by the effective theories improves with increasing number of particles.
Mazurek, A. P.; Sadlej-Sosnowska, N.
2000-11-01
A comparison of the ab initio quantum chemical methods: Hartree-Fock (HF) and hybrid density functional theory (DFT)/B3LYP for the treatment of tautomeric equilibria both in the gas phase and in the solution is made. The solvent effects were investigated in terms of the self-consistent reaction field (SCRF). Ionization potentials (IP), calculated by DFT/B3LYP, are also compared with those calculated previously within the HF frame.
Fractional Electron Loss in Approximate DFT and Hartree-Fock Theory.
Peach, Michael J G; Teale, Andrew M; Helgaker, Trygve; Tozer, David J
2015-11-10
Plots of electronic energy vs electron number, determined using approximate density functional theory (DFT) and Hartree-Fock theory, are typically piecewise convex and piecewise concave, respectively. The curves also commonly exhibit a minimum and maximum, respectively, in the neutral → anion segment, which lead to positive DFT anion HOMO energies and positive Hartree-Fock neutral LUMO energies. These minima/maxima are a consequence of using basis sets that are local to the system, preventing fractional electron loss. Ground-state curves are presented that illustrate the idealized behavior that would occur if the basis set were to be modified to enable fractional electron loss without changing the description in the vicinity of the system. The key feature is that the energy cannot increase when the electron number increases, so the slope cannot be anywhere positive, meaning frontier orbital energies cannot be positive. For the convex (DFT) case, the idealized curve is flat beyond a critical electron number such that any additional fraction of an electron added to the system is unbound. The anion HOMO energy is zero. For the concave (Hartree-Fock) case, the idealized curve is flat up to some critical electron number, beyond which it curves down to the anion energy. A minimum fraction of an electron is required before any binding occurs, but beyond that, the full fraction abruptly binds. The neutral LUMO energy is zero. Approximate DFT and Hartree-Fock results are presented for the F → F(-) segment, and results approaching the idealized behavior are recovered for highly diffuse basis sets. It is noted that if a DFT calculation using a highly diffuse basis set yields a negative LUMO energy then a fraction of an electron must bind and the electron affinity must be positive, irrespective of whether an electron binds experimentally. This is illustrated by calculations on Ne → Ne(-).
Generalization of Cramer's rule and its application to the projection of Hartree-Fock wave function
Hage-Hassan, Mehdi
2009-01-01
We generalize the Cramer's rule of linear algebra. We apply it to calculate the spectra of nucleus by applying Hill-Wheeler projection operator to Hartree-Fock wave function, and to derive L\\"owdin formula and Thouless theorem. We derive by an elementary method the infinitesimal or L\\"owdin projection operators and its integral representation to be useful for the projection of Slater determinant.
The Dielectric Permittivity of Crystals in the reduced Hartree-Fock approximation
Cancès, Eric
2009-01-01
In a recent article (Canc\\`es, Deleurence and Lewin, Commun. Math. Phys., 281 (2008), pp. 129-177), we have rigorously derived, by means of bulk limit arguments, a new variational model to describe the electronic ground state of insulating or semiconducting crystals in the presence of local defects. In this so-called reduced Hartree-Fock model, the ground state electronic density matrix is decomposed as $\\gamma = \\gamma^0_{\\rm per} + Q_{\
Can X-ray constrained Hartree-Fock wavefunctions retrieve electron correlation?
Genoni, Alessandro; Dos Santos, Leonardo H R; Meyer, Benjamin; Macchi, Piero
2017-03-01
The X-ray constrained wavefunction (XC-WF) method proposed by Jayatilaka [Jayatilaka & Grimwood (2001) ▸, Acta Cryst. A57, 76-86] has attracted much attention because it represents a possible third way of theoretically studying the electronic structure of atoms and molecules, combining features of the more popular wavefunction- and DFT-based approaches. In its original formulation, the XC-WF technique extracts statistically plausible wavefunctions from experimental X-ray diffraction data of molecular crystals. A weight is used to constrain the pure Hartree-Fock solution to the observed X-ray structure factors. Despite the wavefunction being a single Slater determinant, it is generally assumed that its flexibility could guarantee the capture, better than any other experimental model, of electron correlation effects, absent in the Hartree-Fock Hamiltonian but present in the structure factors measured experimentally. However, although the approach has been known for long time, careful testing of this fundamental hypothesis is still missing. Since a formal demonstration is impossible, the validation can only be done heuristically and, to accomplish this task, X-ray constrained Hartree-Fock calculations have been performed using structure factor amplitudes computed at a very high correlation level (coupled cluster) for selected molecules in isolation, in order to avoid the perturbations due to intermolecular interactions. The results show that a single-determinant XC-WF is able to capture the electron correlation effects only partially. The largest amount of electron correlation is extracted when: (i) a large external weight is used (much larger than what has normally been used in XC-WF calculations using experimental data); and (ii) the high-order reflections, which carry less information on the electron correlation, are down-weighted (or even excluded), otherwise they would bias the fitting towards the unconstrained Hartree-Fock wavefunction.
On the NP-completeness of the Hartree-Fock method for translationally invariant systems
Whitfield, James D
2014-01-01
The self-consistent field method utilized for solving the Hartree-Fock (HF) problem and the closely related Kohn-Sham problem, is typically thought of as one of the cheapest methods available to quantum chemists. This intuition has been developed from the numerous applications of the self-consistent field method to a large variety of molecular systems. However, in terms of its worst-case computational complexity, the HF problem is NP-complete. In this work, we investigate how far one can push the boundaries of the NP-completeness by investigating restricted instances of HF. We have constructed two new NP-complete variants of the problem. The first is a set of Hamiltonians whose translationally invariant Hartree-Fock solutions are trivial, but whose broken symmetry solutions are NP-complete. Second, we demonstrate how to embed instances of spin glasses into translationally invariant Hartree-Fock instances and provide a numerical example. These findings are the first steps towards understanding in which cases t...
Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.
Khoromskaia, Venera; Khoromskij, Boris N
2015-12-21
We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, first appeared as an accurate tensor calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in O(n log n) complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D n × n × n Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D "density fitting" scheme, which yield an almost irreducible number of product basis functions involved in the 3D convolution integrals, depending on a threshold ε > 0. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excitation energies, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is towards the tensor-based Hartree-Fock numerical scheme for finite lattices, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a L × L × L lattice manifests the linear in L computational work, O(L), instead of the usual O(L(3) log L) scaling by the Ewald-type approaches.
Xu, Ruirui; Ma, Zhongyu; Zhang, Yue; Tian, Yuan; van Dalen, E. N. E.; Müther, H.
2016-09-01
Background: For the study of exotic nuclei it is important to have an optical model potential that is reliable not only for stable nuclei but can also be extrapolated to nuclear systems with exotic numbers of protons and neutrons. An efficient way to obtain such a potential is to develop a microscopic optical potential (MOP) based on a fundamental theory with a minimal number of free parameters, which are adjusted to describe stable nuclei all over the nuclide chart. Purpose: The choice adopted in the present work is to develop the MOP within a relativistic scheme which provides a natural and consistent relation between the spin-orbit part and the central part of the potential. The Dirac-Brueckner-Hartree-Fock (DBHF) approach provides such a microscopic relativistic scheme, which is based on a realistic nucleon-nucleon interaction and reproduces the saturation properties of symmetric nuclear matter without any adjustable parameter. Its solution using the projection technique within the subtracted T -matrix representation provides a reliable extension to asymmetric nuclear matter, which is important to describe the features of isospin asymmetric nuclei. The present work performs a global analysis of the isospin dependent nucleon-nucleus MOP based on the DBHF calculation in symmetric and asymmetric nuclear matter. Methods: The DBHF approach is used to evaluate the relativistic structure of the nucleon self-energies in nuclear matter at various densities and asymmetries. The Schrödinger equivalent potentials of finite nuclei are derived from these Dirac components by a local density approximation (LDA). The density distributions of finite nuclei are taken from the Hartree-Fock-Bogoliubov approach with Gogny D1S force. An improved LDA approach (ILDA) is employed to get a better prediction of the scattering observables. A χ2 assessment system based on the global simulated annealing algorithm is developed to optimize the very few free components in this study. Results
Zhang, Lin-Feng; Xia, Xue-Wei
2016-05-01
The α-decay energies (Q α ) are systematically investigated with the nuclear masses for 10 ⩽ Z ⩽ 120 isotopes obtained by the relativistic continuum Hartree-Bogoliubov (RCHB) theory with the covariant density functional PC-PK1, and compared with available experimental values. It is found that the α-decay energies deduced from the RCHB results present a similar pattern to those from available experiments. Owing to the large predicted Q α values (⩾ 4 MeV), many undiscovered heavy nuclei in the proton-rich side and super-heavy nuclei may have large possibilities for α-decay. The influence of nuclear shell structure on α-decay energies is also analysed. Supported by Major State 973 Program of China (2013CB834400), National Natural Science Foundation of China (11175002, 11335002, 11375015, 11461141002), Research Fund for the Doctoral Program of Higher Education (20110001110087) and National Undergraduate Innovation Training Programs of Peking University.
Bouguettoucha, A.
1996-06-14
A possible effects of the C{sub 4}-symmetry in the superdeformed nuclei of the A {approx}150 mass range has been studied microscopically using cranking Strutinsky method with the deformed Woods-Saxon potential and the Hartree-Fock approach with the Skyrme interaction. If the existence of such a symmetry is judged by the moments Q{sub 44}, the results of the calculation indicate a very weak effect of this kind. Four new superdeformed bands in the {sup 148}Gd nucleus have been studied in reaction to the recent experimental observations (Eurogam Phase 2): a backbending has been tentatively observed at very high rotational frequency in the third excited band. One of the other bands exhibits a J{sup (2)} moment very similar to that of the yrast band in {sup 152}Dy, and this is the first example of identical bands which differ by four mass units. Calculations with the methods mentioned above have been used to analyse the band structure in terms of the nucleonic configurations. Calculation have been performed for some nuclear configurations predicted to involve the exotic octupole deformations (Y{sub 30-}`pear shapes`; Y{sub 31-}`banana mode`; Y{sub 32-}`T{sub d}-symmetry` and Y{sub 33-}`C{sub 3}-symmetry`). While the previous calculations based on the Strutinsky method could not treat the coupling between those modes, the Hartree-Fock approach allows to see for the first time in which propositions the various modes couple. (author). 116 refs.
Zhao, Jie; Zhao, En-Guang; Zhou, Shan-Gui
2016-01-01
We develop a multidimensionally-constrained relativistic Hartree-Bogoliubov (MDC-RHB) model in which the pairing correlations are taken into account by making the Bogoliubov transformation. In this model, the nuclear shape is assumed to be invariant under the reversion of $x$ and $y$ axes, i.e., the intrinsic symmetry group is $V_4$ and all shape degrees of freedom $\\beta_{\\lambda\\mu}$ with even $\\mu$ are included self-consistently. The RHB equation is solved in an axially deformed harmonic oscillator basis. A separable pairing force of finite range is adopted in the MDC-RHB model. The potential energy curves of neutron-rich even-even Zr isotopes are calculated. The ground state shapes of $^{108-112}$Zr are predicted to be tetrahedral with both functionals DD-PC1 and PC-PK1 and $^{106}$Zr is also predicted to have a tetrahedral ground state with the functional PC-PK1. The tetrahedral ground states are caused by large energy gaps at $Z=40$ and $N=70$ when $\\beta_{32}$ deformation is included. Although the incl...
Veeraraghavan, Srikant; Mazziotti, David A
2014-03-28
We present a density matrix approach for computing global solutions of restricted open-shell Hartree-Fock theory, based on semidefinite programming (SDP), that gives upper and lower bounds on the Hartree-Fock energy of quantum systems. While wave function approaches to Hartree-Fock theory yield an upper bound to the Hartree-Fock energy, we derive a semidefinite relaxation of Hartree-Fock theory that yields a rigorous lower bound on the Hartree-Fock energy. We also develop an upper-bound algorithm in which Hartree-Fock theory is cast as a SDP with a nonconvex constraint on the rank of the matrix variable. Equality of the upper- and lower-bound energies guarantees that the computed solution is the globally optimal solution of Hartree-Fock theory. The work extends a previously presented method for closed-shell systems [S. Veeraraghavan and D. A. Mazziotti, Phys. Rev. A 89, 010502-R (2014)]. For strongly correlated systems the SDP approach provides an alternative to the locally optimized Hartree-Fock energies and densities with a certificate of global optimality. Applications are made to the potential energy curves of C2, CN, Cr2, and NO2.
Veeraraghavan, Srikant; Mazziotti, David A., E-mail: damazz@uchicago.edu [Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 (United States)
2014-03-28
We present a density matrix approach for computing global solutions of restricted open-shell Hartree-Fock theory, based on semidefinite programming (SDP), that gives upper and lower bounds on the Hartree-Fock energy of quantum systems. While wave function approaches to Hartree-Fock theory yield an upper bound to the Hartree-Fock energy, we derive a semidefinite relaxation of Hartree-Fock theory that yields a rigorous lower bound on the Hartree-Fock energy. We also develop an upper-bound algorithm in which Hartree-Fock theory is cast as a SDP with a nonconvex constraint on the rank of the matrix variable. Equality of the upper- and lower-bound energies guarantees that the computed solution is the globally optimal solution of Hartree-Fock theory. The work extends a previously presented method for closed-shell systems [S. Veeraraghavan and D. A. Mazziotti, Phys. Rev. A 89, 010502–R (2014)]. For strongly correlated systems the SDP approach provides an alternative to the locally optimized Hartree-Fock energies and densities with a certificate of global optimality. Applications are made to the potential energy curves of C{sub 2}, CN, Cr {sub 2}, and NO {sub 2}.
Complete equation of state for neutron stars using the relativistic Hartree-Fock approximation
Miyatsu, Tsuyoshi; Cheoun, Myung-Ki [Department of Physics, Soongsil University, Seoul 156-743 (Korea, Republic of); Yamamuro, Sachiko; Nakazato, Ken' ichiro [Department of Physics, Faculty of Science and Technology, Tokyo University of Science (TUS), Noda 278-8510 (Japan)
2014-05-02
We construct the equation of state in a wide-density range for neutron stars within relativistic Hartree-Fock approximation. The properties of uniform and nonuniform nuclear matter are studied consistently. The tensor couplings of vector mesons to baryons due to exchange contributions (Fock terms) are included, and the change of baryon internal structure in matter is also taken into account using the quark-meson coupling model. The Thomas-Fermi calculation is adopted to describe nonuniform matter, where the lattice of nuclei and the neutron drip out of nuclei are considered. Even if hyperons exist in the core of a neutron star, we obtain the maximum neutron-star mass of 1.95M{sub ⊙}, which is consistent with the recently observed massive pulsar, PSR J1614-2230. In addition, the strange vector (φ) meson also plays a important role in supporting a massive neutron star.
Time-dependent Hartree-Fock studies of the dynamical fusion threshold
Nakatsukasa Takashi
2012-12-01
Full Text Available A microscopic description of dynamical fusion threshold in heavy ion collisions is performed in the framework of time-dependent Hartree-Fock (TDHF theory using Skyrme energy density functional (EDF. TDHF fusion threshold is in a better agreement with experimental fusion barrier. We find that the onset of extra push lies at the effective fissility 33, which is consistent with the prediction of Swiateckis macroscopic model. The extra push energy in our TDHF simulation is systematically smaller than the prediction in macroscopic model. The important dynamical effects and the way to fit the parameter might be responsible for the different results.
Projected gradient algorithms for Hartree-Fock and density matrix functional theory calculations
Cancès, Eric; Pernal, Katarzyna
2008-04-01
We present projected gradient algorithms designed for optimizing various functionals defined on the set of N-representable one-electron reduced density matrices. We show that projected gradient algorithms are efficient in minimizing the Hartree-Fock or the Müller-Buijse-Baerends functional. On the other hand, they converge very slowly when applied to the recently proposed BBk (k =1,2,3) functionals [O. Gritsenko et al., J. Chem. Phys. 122, 204102 (2005)]. This is due to the fact that the BBk functionals are not proper functionals of the density matrix.
Nuclear relativistic Hartree-Fock calculations including pions interacting with a scalar field
Marcos, S.; Lopez-Quelle, M.; Niembro, R.; Savushkin, L. N. [Departamento de Fisica Moderna, Universidad de Cantabria, Santander (Spain); Departamento de Fisica Aplicada, Universidad de Cantabria, Santander (Spain); Departamento de Fisica Moderna, Universidad de Cantabria, Santander (Spain); Department of Physics, St. Petersburg University for Telecommunications, St. Petersburg (Russian Federation)
2012-10-20
The effect of pions on the nuclear shell structure is analyzed in a relativistic Hartree-Fock approximation (RHFA). The Lagrangian includes, in particular, a mixture of {pi}N pseudoscalar (PS) and pseudovector (PV) couplings, self-interactions of the scalar field {sigma} and a {sigma} - {pi} interaction that dresses pions with an effective mass (m*{sub {pi}}). It is found that an increase of m*{sub {pi}} strongly reduces the unrealistic effect of pions, keeping roughly unchanged their contribution to the total binding energy.
Adaptive Multi-resolution 3D Hartree-Fock-Bogoliubov Solver for Nuclear Structure
Pei, Junchen; Harrison, Robert; Nazarewicz, Witold; Shi, Yue; Thornton, Scott
2014-01-01
Complex many-body systems, such as triaxial and reflection-asymmetric nuclei, weakly-bound halo states, cluster configurations, nuclear fragments produced in heavy-ion fusion reactions, cold Fermi gases, and pasta phases in neutron star crust, they are all characterized by large sizes and complex topologies, in which many geometrical symmetries characteristic of ground-state configurations are broken. A tool of choice to study such complex forms of matter is an adaptive multi-resolution wavelet analysis. This method has generated much excitement since it provides a common framework linking many diversified methodologies across different fields, including signal processing, data compression, harmonic analysis and operator theory, fractals, and quantum field theory. To describe complex superfluid many-fermion systems, we introduce an adaptive pseudo-spectral method for solving self-consistent equations of nuclear density functional theory in three dimensions, without symmetry restrictions. The new adaptive mult...
Δ (1232 ) effects in density-dependent relativistic Hartree-Fock theory and neutron stars
Zhu, Zhen-Yu; Li, Ang; Hu, Jin-Niu; Sagawa, Hiroyuki
2016-10-01
The density-dependent relativistic Hartree-Fock (DDRHF) theory is extended to include Δ isobars for the study of dense nuclear matter and neutron stars. To this end, we solve the Rarita-Schwinger equation for spin-3/2 particle. Both the direct and exchange terms of the Δ isobars' self-energies are evaluated in detail. In comparison with the relativistic mean field theory (Hartree approximation), a weaker parameter dependence is found for DDRHF. An early appearance of Δ isobars is recognized at ρB˜0.28 fm-3, comparable with that of hyperons. Also, we find that the Δ isobars' softening of the equation of state is mainly due to the reduced Fock contributions from the coupling of the isoscalar mesons, while the pion contributions are negligibly small. We finally conclude that with typical parameter sets, neutron stars with Δ isobars in their interiors could be as heavy as the two massive pulsars whose masses are precisely measured, with slightly smaller radii than normal neutron stars.
$\\Delta$ (1232) effects in density-dependent relativistic Hartree-Fock theory and neutron stars
Zhu, Zhen-Yu; Hu, Jin-Niu; Sagawa, Hiroyuki
2016-01-01
The density-dependent relativistic Hartree-Fock (DDRHF) theory is extended to include $\\Delta$-isobars for the study of dense nuclear matter and neutron stars. To this end, we solve the Rarita-Schwinger equation for spin-3/2 particle. Both the direct and exchange terms of the $\\Delta$-isobars' self-energies are evaluated in details. In comparison with the relativistic mean field theory (Hartree approximation), a weaker parameter dependence is found for DDRHF. An early appearance of $\\Delta$-isobars is recognized at $\\rho_B\\sim0.27$fm$^{-3}$, comparable with that of hyperons. Also, we find that the $\\Delta$-isobars' softening of the equation of state is found to be mainly due to the reduced Fock contributions from the coupling of the isoscalar mesons, while the pion contributions are found negligibly small. We finally conclude that with typical parameter sets, neutron stars with $\\Delta$-isobars in their interiors could be as heavy as the two massive pulsars whose masses are precisely measured, with slightly s...
Hu, Jinniu; Shen, Hong
2016-01-01
We study the properties of nuclear matter with lattice nucleon-nucleon ($NN$) potential in the relativistic Brueckner-Hartree-Fock (RBHF) theory. To use this potential in such a microscopic many-body theory, we firstly have to construct a one-boson-exchange potential (OBEP) based on the latest lattice $NN$ potential. Three mesons, pion, $\\sigma$ meson, and $\\omega$ meson, are considered. Their coupling constants and cut-off momenta are determined by fitting the on-shell behaviors and phase shifts of the lattice force, respectively. Therefore, we obtain two parameter sets of the OBEP potential (named as LOBEP1 and LOBEP2) with these two fitting ways. We calculate the properties of symmetric and pure neutron matter with LOBEP1 and LOBEP2. In non-relativistic Brueckner-Hartree-Fock case, the binding energies of symmetric nuclear matter are around $-3$ and $-5$ MeV at saturation densities, while it becomes $-8$ and $-12$ MeV in relativistic framework with $^1S_0,~^3S_1,$ and $^3D_1$ channels using our two paramet...
A divide and conquer real space finite-element Hartree-Fock method
Alizadegan, R.; Hsia, K. J.; Martinez, T. J.
2010-01-01
Since the seminal contribution of Roothaan, quantum chemistry methods are traditionally expressed using finite basis sets comprised of smooth and continuous functions (atom-centered Gaussians) to describe the electronic degrees of freedom. Although this approach proved quite powerful, it is not well suited for large basis sets because of linear dependence problems and ill conditioning of the required matrices. The finite element method (FEM), on the other hand, is a powerful numerical method whose convergence is also guaranteed by variational principles and can be achieved systematically by increasing the number of degrees of freedom and/or the polynomial order of the shape functions. Here we apply the real-space FEM to Hartree-Fock calculations in three dimensions. The method produces sparse, banded Hermitian matrices while allowing for variable spatial resolution. This local-basis approach to electronic structure theory allows for systematic convergence and promises to provide an accurate and efficient way toward the full ab initio analysis of materials at larger scales. We introduce a new acceleration technique for evaluating the exchange contribution within FEM and explore the accuracy and robustness of the method for some selected test atoms and molecules. Furthermore, we applied a divide-and-conquer (DC) method to the finite-element Hartree-Fock ab initio electronic-structure calculations in three dimensions. This DC approach leads to facile parallelization and should enable reduced scaling for large systems.
Barbosa, Rugles Cesar
2002-07-01
The present thesis is divided into two parts. The first part describes the many kind of the formalisms of the Generator Coordinate Hartree-Fock method (GCHFM) and second part describes the computational aspect applied to the GCHFM formalism in its discreet form. The major aim of this work is the development of an alternative method to non-linear parameters optimization (basis set) and later uses these optimized parameters to adjust the weight function into GCHFM method. The study of the weight function when N {yields} {infinity} (or for large N), where N represents the number of mesh, is important since the GCHFM theory in its continuous form depend on understanding of such behavior. In this thesis, a detailed study is carried out about the methodologies of the self-consistent solution of the GCHFM and some methodology aspects of non-linear parameters optimization. This work shows that the Generator Coordinate Hartree-Fock method is general and it has as particular case the Hartree-Fock Roothaan method. Some possible variations or combinations around of the characteristics of the GCHFM and a comparison with conventional SCF procedure are reported in this thesis. The piecewise weight function method developed in this work shows to be very good for collective parameter optimizations of the Generator Coordinate (GC). The GCHFM calculations are necessary restrict (GCM-RHF), especially when the calculated value energies approach of its numerical values or Hartree-Fock limit. In the optimization methods of state functions for atomic electronic systems is very common the application of the gradient method and its efficacy is not contested. However, the method describes above allow us to obtain results as good as the gradient method. The basis set generated using the piecewise weight function method for Gaussian type function were used in the Restrict Hartree-Fock (RHF) calculations to obtain the total energies for some atomic electronic systems, such as neutron atoms and
Amour, Laurent; Nourrigat, Jean
2011-01-01
We study the Wick symbol of a solution of the time dependent Hartree Fock equation, under weaker hypotheses than those needed for the Weyl symbol in the first paper with thesame title. With similar, we prove some kind of Ehrenfest theorem for observables that are not pseudo-differential operators.
Jiménez-Hoyos, Carlos A; Scuseria, Gustavo E
2013-01-01
Recent work from our research group has demonstrated that symmetry-projected Hartree--Fock (HF) methods provide a compact representation of molecular ground state wavefunctions based on a superposition of non-orthogonal Slater determinants. The symmetry-projected ansatz can account for static correlations in a computationally efficient way. Here we present a variational extension of this methodology applicable to excited states of the same symmetry as the ground state. Benchmark calculations on the C$_2$ dimer with a modest basis set, which allows comparison with full configuration interaction results, indicate that this extension provides a high quality description of the low-lying spectrum for the entire dissociation profile. We apply the same methodology to obtain the full low-lying vertical excitation spectrum of formaldehyde, in good agreement with available theoretical and experimental data, as well as to a challenging model $C_{2v}$ insertion pathway for BeH$_2$. The variational excited state methodolo...
Constrained Hartree-Fock Theory and Study of Deformed Structures of Closed Shell Nuclei
Praharaj, Choudhury
2016-03-01
We have studied some N or Z = 50 nuclei in a microscopic model with effective interaction in a reasonably large shell model space. Excitation of particles across 50 shell closure leads to well-deformed excited prolate configurations. The potential energy surfaces of nuclei are studied using Hartree-Fock theory with quadrupole constraint to explore the various deformed configurations of N = 50 nuclei 82Ge , 84Se and 86Kr . Energy spectra are calculated from various intrinsic states using Peierls-Yoccoz angular momentum projection technique. Results of spectra and electromagnetic moments and transitions will be presented for N = 50 nuclei and for Z = 50 114Sn nucleus. Supported by Grant No SB/S2/HEP-06/2013 of DST.
Twist-averaged boundary conditions for nuclear pasta Hartree-Fock calculations
Schuetrumpf, B
2015-01-01
Background: Nuclear pasta phases, present in the inner crust of neutron stars, are associated with nucleonic matter at sub-saturation densities arranged in regular shapes. Those complex phases, residing in a layer which is approximately 100 m thick, impact many features of neutron stars. Theoretical quantum-mechanical simulations of nuclear pasta are usually carried out in finite 3D boxes assuming periodic boundary conditions (PBC). The resulting solutions are affected by spurious finite-size effects. Purpose: In order to remove spurious finite-size effects, it is convenient to employ twist-averaged boundary conditions (TABC) used in condensed matter, nuclear matter, and lattice QCD applications. In this work, we study the effectiveness of TABC in the context of pasta phases simulations within nuclear density functional theory. Methods: We perform Skyrme-Hartree-Fock calculations in three dimensions by implementing Bloch boundary conditions. The TABC averages are obtained by means of Gauss-Legendre integratio...
A New Decomposition Approach of Dirac Brueckner Hartree-Fock G Matrix for Asymmetric Nuclear Matter
刘玲; 马中玉
2002-01-01
Asymmetric nuclear matter is investigated by the Dirac Brueckner Hartree-Fock (DBHF) approach with a new decomposition of the Dirac structure of nucleon self-energy from the G matrix. It is found that the isospin dependence of the scalar and vector potentials is relatively weak, although both potentials for neutron (proton)become deep (shallow) in the neutron-rich nuclear matter. The results in asymmetric nuclear matter are rather different from those obtained by a simple method, where the nucleon self-energy is deduced from the single-particle energy. The nuclear binding energy as a function of the asymmetry parameter fulfils the empirical parabolic law up to very extreme isospin asymmetric nuclear matter in the DBHF approach. The behaviour of the density dependence of the asymmetry energy is different from that obtained by non-relativistic approaches, although both give similar asymmetry energy at the nuclear saturation density.
Time-Dependent Hartree-Fock Approach to Nuclear Pasta at Finite Temperature
Schuetrumpf, Bastian; Iida, Kei; Maruhn, Joachim; Mecke, Klaus; Reinhard, Paul-Gerhard
2013-01-01
We present simulations of neutron-rich matter at subnuclear densities, like supernova matter, with the time-dependent Hartree-Fock approximation at temperatures of several MeV. The initial state consists of $\\alpha$ particles randomly distributed in space that have a Maxwell-Boltzmann distribution in momentum space. Adding a neutron background initialized with Fermi distributed plane waves the calculations reflect a reasonable approximation of astrophysical matter. This matter evolves into spherical, rod-like, and slab-like shapes and mixtures thereof. The simulations employ a full Skyrme interaction in a periodic three-dimensional grid. By an improved morphological analysis based on Minkowski functionals, all eight pasta shapes can be uniquely identified by the sign of only two valuations, namely the Euler characteristic and the integral mean curvature.
Pion tensor force and nuclear binding energy in the relativistic Hartree-Fock formalism
Marcos, S.; López-Quelle, M.; Niembro, R.; Savushkin, L. N.
2014-03-01
The binding energies of several isotopic families are studied within the relativistic Hartree-Fock approximation with the pseudovector coupling for the πN vertex, to find out a suitable strength for the effective pion tensor force (EPTF). An approximation for determining separately the contributions of the central and tensor forces generated by pion is considered. The results for heavy nuclei indicate that a realistic strength for the EPTF is smaller than a half of that appearing in the OPEP. This conclusion also applies to the results for the single-particle energies. Besides, it has been found that there is a genuine relativistic contribution of the EPTF in nuclear matter which is small but significant.
Hartree-Fock mean-field theory for trapped dirty bosons
Khellil, Tama; Pelster, Axel
2016-06-01
Here we work out in detail a non-perturbative approach to the dirty boson problem, which relies on the Hartree-Fock theory and the replica method. For a weakly interacting Bose gas within a trapped confinement and a delta-correlated disorder potential at finite temperature, we determine the underlying free energy. From it we determine via extremization self-consistency equations for the three components of the particle density, namely the condensate density, the thermal density, and the density of fragmented local Bose-Einstein condensates within the respective minima of the random potential landscape. Solving these self-consistency equations in one and three dimensions in two other publications has revealed how these three densities change for increasing disorder strength.
Spiral magnetic phases on the Kondo Lattice Model: A Hartree-Fock approach
Costa, N. C.; Lima, J. P.; dos Santos, Raimundo R.
2017-02-01
We study the Kondo Lattice Model (KLM) on a square lattice through a Hartree-Fock approximation in which the local spins are treated semi-classically, in the sense that their average values are modulated by a magnetic wavevector Q while they couple with the conduction electrons through fermion operators. In this way, we obtain a ground state phase diagram in which spiral magnetic phases (in which the wavevector depends on the coupling constants and on the density) interpolate between the low-density ferromagnetic phase and the antiferromagnetic phase at half filling; within small regions of the phase diagram commensurate magnetic phases can coexist with Kondo screening. We have also obtained 'Doniach-like' diagrams, showing the effect of temperature on the ground state phases, and established that for some ranges of the model parameters (the exchange coupling and conduction electron density) the magnetic wavevector changes with temperature, either continuously or abruptly (e.g., from spiral to ferromagnetic).
Self-consistent Hartree-Fock RPA calculations in 208Pb
Taqi, Ali H.; Ali, Mohammed S.
2017-07-01
The nuclear structure of 208Pb is studied in the framework of the self-consistent random phase approximation (SCRPA). The Hartree-Fock mean field and single particle states are used to implement a completely SCRPA with Skyrme-type interactions. The Hamiltonian is diagonalised within a model space using five Skyrme parameter sets, namely LNS, SkI3, SkO, SkP and SLy4. In view of the huge number of the existing Skyrme-force parameterizations, the question remains which of them provide the best description of data. The approach attempts to accurately describe the structure of the spherical even-even nucleus 208Pb. To illustrate our approach, we compared the binding energy, charge density distribution, excitation energy levels scheme with the available experimental data. Moreover, we calculated isoscalar and isovector monopole, dipole, and quadrupole transition densities and strength functions.
Pseudospin symmetry in finite nuclei within the relativistic Hartree-Fock framework
Lopez-Quelle, M [Departamento de Fisica Aplicada, Universidad de Cantabria, E-39005 Santander (Spain); Savushkin, L N [Department of Physics, St Petersburg University for Telecommunications, 191186 St Petersburg (Russian Federation); Marcos, S [Departamento de Fisica Moderna, Universidad de Cantabria, E-39005 Santander (Spain); Niembro, R [Departamento de Fisica Moderna, Universidad de Cantabria, E-39005 Santander (Spain)
2005-10-01
In the present work, we analyse the behaviour of the pseudospin symmetry (PSS) in heavy nuclei ({sup 208}Pb) in the framework of the relativistic Hartree-Fock approximation (RHFA). The quasidegeneracy of the pseudospin partners and the similarity of the small F components of their respective Dirac spinors have a somewhat lower degree of accuracy than in the relativistic mean field approximation (RMFA). Both properties improve when the number of nodes of the small component increases, as happens in the RMFA. The behaviour of the single-particle potentials appearing in the Dirac equation of the pseudospin partners is analysed. There is no dominance of the pseudocentrifugal barrier (PCB) compared to the pseudospin-orbit potential (PSOP). In the RHFA, the PSS is an approximately satisfied symmetry in nuclei and its dynamical character is reinforced with respect to the RMFA.
Phase structure of the massive chiral Gross-Neveu model from Hartree-Fock
Boehmer, Christian; Kraus, Sebastian; Thies, Michael
2008-01-01
The phase diagram of the massive chiral Gross-Neveu model (the massive Nambu-Jona-Lasinio model in 1+1 dimensions) is constructed. In the large N limit, the Hartree-Fock approach can be used. We find numerically a chiral crystal phase separated from a massive Fermi gas phase by a 1st order transition. Using perturbation theory, we also construct the critical sheet where the homogeneous phase becomes unstable in a 2nd order transition. A tricritical curve is located. The phase diagram is mapped out as a function of fermion mass, chemical potential and temperature and compared with the one of the discrete chiral Gross-Neveu model. As a by-product, we illustrate the crystal structure of matter at zero temperature for various densities and fermion masses.
Comparative study of metal cluster fission in Hartree-Fock and LDA
Lyalin, A; Greiner, W; Lyalin, Andrey; Solov'yov, Andrey; Greiner, Walter
2001-01-01
Fission of doubly charged metal clusters is studied using the open-shell two-center deformed jellium Hartree-Fock model and Local Density Approximation. Results of calculations of the electronic structure and fission barriers for the symmetric and asymmetric channels associated with the following processes Na_{10}^{2+} --> Na_{7}^{+} + Na_{3}^{+}, Na_{18}^{2+} --> Na_{15}^{+} + Na_{3}^{+} and Na_{18}^{2+} --> 2 Na_{9}^{+} are presented. The role of the exact exchange and many-body correlation effects in metal clusters fission is analysed. It is demonstrated that the influence of many-electron correlation effects on the height of the fission barrier is more profound if the barrier arises nearby or beyond the scission point. The importance of cluster deformation effects in the fission process is elucidated with the use of the overlapping-spheroids shape parametrization allowing one an independent variation of deformations in the parent and daughter clusters.
Ab-initio Hartree-Fock study of tritium desorption from Li{sub 2}O
Taniguchi, Masaki; Tanaka, Satoru [Tokyo Univ. (Japan). Faculty of Engineering
1998-03-01
Dissociative adsorption of hydrogen on Li{sub 2}O (110) surface has been investigated with ab-initio Hartree-Fock quantum chemical calculation technique. Heat of adsorption and potential energy surface for H{sub 2} dissociative adsorption was evaluated by calculating the total energy of the system. Calculation results on adsorption heat indicated that H{sub 2} adsorption is endothermic. However, when oxygen vacancy exists adjacent to the adsorption sites, heat of adsorption energy became less endothermic and the activation energy required to dissociate the H-H bonding was smaller than that for the terrace site. This is considered to be caused by the excess charge localized near the defect. (author)
Parallel and Low-Order Scaling Implementation of Hartree-Fock Exchange Using Local Density Fitting.
Köppl, Christoph; Werner, Hans-Joachim
2016-07-12
Calculations using modern linear-scaling electron-correlation methods are often much faster than the necessary reference Hartree-Fock (HF) calculations. We report a newly implemented HF program that speeds up the most time-consuming step, namely, the evaluation of the exchange contributions to the Fock matrix. Using localized orbitals and their sparsity, local density fitting (LDF), and atomic orbital domains, we demonstrate that the calculation of the exchange matrix scales asymptotically linearly with molecular size. The remaining parts of the HF calculation scale cubically but become dominant only for very large molecular sizes or with many processing cores. The method is well parallelized, and the speedup scales well with up to about 100 CPU cores on multiple compute nodes. The effect of the local approximations on the accuracy of computed HF and local second-order Møller-Plesset perturbation theory energies is systematically investigated, and default values are established for the parameters that determine the domain sizes. Using these values, calculations for molecules with hundreds of atoms in combination with triple-ζ basis sets can be carried out in less than 1 h, with just a few compute nodes. The method can also be used to speed up density functional theory calculations with hybrid functionals that contain HF exchange.
On the problem of representability and the Bogolyubov-Hartree-Fock theory
Knoerr, Hans Konrad
2013-11-22
The general topic of this thesis is an approximation of the ground state energy for many-particle quantum systems. In particular the Bogolyubov-Hartree-Fock theory and the representability of one- and two-particle density matrices are studied. After an introductory chapter we specify some basic notation of many-body quantum mechanics in Chapter 2. In Chapter 3 we consider boson, as well as fermion systems. We first tackle the question of representability for bosons, i.e., the question which conditions a one- and a two-particle operator must satisfy to ensure that they are the one- and the two-particle density matrix of a state. For a particle number-conserving system, the representability conditions up to second order for bosons are well-known and called admissibility, P-, and G-conditions. Since, however, most physical systems consisting of bosons are not particle number-conserving, we give an alternative for such systems: Generalizing the two-particle density matrix, we observe that the representability conditions up to second order hold if and only if this generalized two-particle density matrix is positive semi-definite and the one- and the two-particle density matrices fulfill trace class and symmetry conditions. Moreover, we study the Bogolyubov-Hartree-Fock energy of boson and fermion systems. We generalize Lieb's variational principle which in its original formulation holds for purely repulsive particle interactions for fermions only. Our second main result is the following: for bosons, as well as for fermions the infimum of the energy for a variation over pure quasifree states coincides with the one for a variation over all quasifree states under the assumption that the Hamiltonian is bounded below. In the last section of Chapter 3 we specify the relation between centered quasifree states and their corresponding generalized one-particle density matrix, which finds an application in the variational process in the Bogolyubov-Hartree-Fock theory. It is
On the problem of representability and the Bogolyubov-Hartree-Fock theory
Knoerr, Hans Konrad
2013-11-22
The general topic of this thesis is an approximation of the ground state energy for many-particle quantum systems. In particular the Bogolyubov-Hartree-Fock theory and the representability of one- and two-particle density matrices are studied. After an introductory chapter we specify some basic notation of many-body quantum mechanics in Chapter 2. In Chapter 3 we consider boson, as well as fermion systems. We first tackle the question of representability for bosons, i.e., the question which conditions a one- and a two-particle operator must satisfy to ensure that they are the one- and the two-particle density matrix of a state. For a particle number-conserving system, the representability conditions up to second order for bosons are well-known and called admissibility, P-, and G-conditions. Since, however, most physical systems consisting of bosons are not particle number-conserving, we give an alternative for such systems: Generalizing the two-particle density matrix, we observe that the representability conditions up to second order hold if and only if this generalized two-particle density matrix is positive semi-definite and the one- and the two-particle density matrices fulfill trace class and symmetry conditions. Moreover, we study the Bogolyubov-Hartree-Fock energy of boson and fermion systems. We generalize Lieb's variational principle which in its original formulation holds for purely repulsive particle interactions for fermions only. Our second main result is the following: for bosons, as well as for fermions the infimum of the energy for a variation over pure quasifree states coincides with the one for a variation over all quasifree states under the assumption that the Hamiltonian is bounded below. In the last section of Chapter 3 we specify the relation between centered quasifree states and their corresponding generalized one-particle density matrix, which finds an application in the variational process in the Bogolyubov-Hartree-Fock theory. It is
The classical limit of the time dependent Hartree-Fock equation. I. The Weyl symbol of the solution
Amour, Laurent; Nourrigat, Jean
2011-01-01
We study the time evolution of the Weyl symbol of a solution of the time dependent Hartree Fock equation, assuming that for t=0, it has a Weyl symbol which is integrable in the phase space, such as all its derivatives. We prove that the solution has the same property for all t, and we give an asymptotic expansion, in L1 sense, of this Weyl symbol.
Systematic study of even-even nuclei with Hartree-Fock+BCS method using Skyrme SIII force
Tajima, Naoki; Takahara, Satoshi; Onishi, Naoki [Tokyo Univ. (Japan). Coll. of Arts and Sciences
1997-03-01
We have applied the Hartree-Fock+BCS method with Skyrme SIII force formulated in a three-dimensional Cartesian-mesh representation to even-even nuclei with 2 {<=} Z {<=} 114. We discuss the results concerning the atomic masses, the quadrupole (m=0, 2) and hexadecapole (m=0, 2, 4) deformations, the skin thicknesses, and the halo radii. We also discuss the energy difference between oblate and prolate solutions and the shape difference between protons and neutrons. (author)
Fischer, C F
1977-11-01
This technical report contains a listing of a general program for multi-configuration Hartree--Fock (MCHF) calculations, including its documentation. Several examples are given showing how the program may be used. Typical output for several cases is also presented. This program has been tested over an extended period of time for a large variety of cases. This program is written for the IBM 360 or 370 in double-precision arithmetic.
General technique for analytical derivatives of post-projected Hartree-Fock
Tsuchimochi, Takashi; Ten-no, Seiichiro
2017-02-01
In electronic structure theory, the availability of an analytical derivative is one of the desired features for a method to be useful in practical applications, as it allows for geometry optimization as well as computation of molecular properties. With the recent advances in the development of symmetry-projected Hartree-Fock (PHF) methods, we here aim at further extensions by devising the analytic gradients of post-PHF approaches with a special focus on spin-extended (spin-projected) configuration interaction with single and double substitutions (ECISD). Just like standard single-reference methods, the mean-field PHF part does not require the corresponding coupled-perturbed equation to be solved, while the correlation energy term needs the orbital relaxation effect to be accounted for, unless the underlying molecular orbitals are variationally optimized in the presence of the correlation energy. We present a general strategy for post-PHF analytical gradients, which closely parallels that for single-reference methods, yet addressing the major difference between them. The similarity between ECISD and multi-reference CI not only in the energy but also in the optimized geometry is clearly demonstrated by the numerical examples of ozone and cyclobutadiene.
Exploration of (super-)heavy elements using the Skyrme-Hartree-Fock model
Erler, Jochen
2011-01-31
Motivated by the steadily increasing number of known nuclei and nuclear properties, theories of nuclear structure are presently a field of intense research. This work concentrates on the self-consistent description of nuclei in terms of the Skyrme-Hartree-Fock (SHF) approach. The extrapolation of nuclear shell structure to the region of super-heavy elements (SHE) using the SHF model, the dependence on different parameterization and the influence of collective correlation will be studied. The general scope of this work are large scale calculation for a global survey of properties of SHE like binding energies, separation energies and decay characteristics and lifetimes. These calculations were done in a collaboration with the theory group of the GSI in Darmstadt and have the aim to develop a database of lifetimes and reaction rates for {alpha}, {beta}-decay and spontaneous fission in a very wide range with proton numbers 86 {<=} Z {<=} 120 and neutron numbers up to N {approx} 260 relevant for the astrophysical r-process. The results of this study for example predictions of a possible islands of very stable nuclei and information of favored decay mode for each nuclei are also applicable in the recent experimental synthesis of exotic SHE. For these calculation a framework to calculate {beta}-decay half-lives within the SHF model has been developed and the existing axial SHF code has been extended to compute {beta}-transition matrix elements and so to provide an estimation of half-lives. (orig.)
The Hartree-Fock exchange effect on the CO adsorption by the boron nitride nanocage
Vessally, E.; Soleimani-Amiri, S.; Hosseinian, A.; Edjlali, L.; Bekhradnia, A.
2017-03-01
We studied the effect of Hartree-Fock (HF) exchange percentage of a density functional on the adsorption properties and electronic sensitivity of the B12N12 nanocluster to CO molecule. It was found that by an increase in the %HF, the LUMO level is nearly constant while the HOMO level is strongly stabilized, expanding the HOMO-LUMO gap (Eg). Also, the volume of the all structures decreased and the sensitivity of the B12N12 is slightly increased to CO molecule. For the pristine B12N12 cluster, the B66 and B64 bonds are about 1.43 and 1.49 Å at 10% HF, and 1.23 and 1.26 Å at 100% HF, respectively. The HF exchange between 10-20% may predict an accurate Eg for the B12N12 system. We concluded that functionals with a large %HF such as M06-HF, and M06-2X may significantly overestimate the Eg, and bond strength. We obtained a parabolic relationship between the %HF and the adsorption energy of CO molecule on the B12N12 cluster. Also, an increase in the %HF predicts a larger charge transfer from the CO molecule to the cage.
Exact exchange potential evaluated solely from occupied Kohn-Sham and Hartree-Fock solutions
Cinal, M
2011-01-01
The reported new algorithm determines the exact exchange potential v_x in a iterative way using energy and orbital shifts (ES, OS) obtained - with finite-difference formulas - from the solutions (occupied orbitals and their energies) of the Hartree-Fock-like equation and the Kohn-Sham-like equation, the former used for the initial approximation to v_x and the latter - for increments of ES and OS due to subsequent changes of v_x. Thus, solution of the differential equations for OS, used by Kummel and Perdew (KP) [Phys. Rev. Lett. 90, 043004 (2003)], is avoided. The iterated exchange potential, expressed in terms of ES and OS, is improved by modifying ES at odd iteration steps and OS at even steps. The modification formulas are related to the OEP equation (satisfied at convergence) written as the condition of vanishing density shift (DS) - they are obtained, respectively, by enforcing its satisfaction through corrections to approximate OS and by determining optimal ES that minimize the DS norm. The proposed met...
Angular-momentum projection for Hartree-Fock and RPA with realistic interactions
Erler, Bastian; Roth, Robert [Institut fuer Kernphysik, TU Darmstadt (Germany)
2012-07-01
Hartree-Fock (HF) with a Hamiltonian constructed from similarity transformed realistic NN potentials plus 3N contact interactions provides a good starting point for the description of closed shell nuclei. In conjunction with Many-Body-Perturbation-Theory, experimental ground-state energies and radii are well reproduced. To describe collective excitations, the Random-Phase-Approximation (RPA) is the method of choice. Beyond closed shells, e.g. in the sd-shell region, ground-states might exhibit intrinsic deformation, resulting in HF states where angular-momentum ceases to be a good quantum number. Lab-frame observables, like ground-state energies or rotational bands can be recovered from the intrinsic states via angular-momentum projection. We study axially deformed even-even sd-shell nuclei, namely {sup 20}Ne, {sup 28}Si and {sup 32}S. Starting from a HF ground state obtained by exact angular-momentum projection, we use the RPA to study collective excitations. The transition strengths obtained from the RPA are projected to good angular momentum in an exact formalism, without resorting to popular approximations. We investigate the effect of deformed intrinsic states on giant resonances.
Aryal, M. M.; Maharjan, N. B.; Paudyal, D. D.; Mishra, D. R.; Byahut, S. R.; Scheicher, R. H.; Badu, S. R.; Jeong, J.; Chow, Lee; Das, T. P.
2008-03-01
Using the first-principles Hartree-Fock Cluster Procedure, we have studied the electronic structures of pure chain like Selenium and Tellurium, pure ring structured Selenium, Tellurium impurity in chain and ring-structured Selenium and Selenium impurity in chain-structured Tellurium chain. For our investigations in all the systems we have carried out convergence studies with respect to variational basis set sizes,sizes of clusters and electron correlation effects using many-body perturbation theory. Using our calculated electronic field-gradient parameters q in the pure chain systems and employing the experimental quadrupole coupling constants (e^2qQ), the values Q(^77Se)=(0.50±0.04) 10-28 m^2 and Q(^125Te)=-(0.2±0.02) 10-28m^2. Results will also be presented for the asymmetry parameters η for the pure chain systems and the e^2qQ and η for ^77Se in selenium ring. Our calculated values for e^2qQ and η for the impurity systems will also be presented and compared with available experimental data and earlier theoretical results.
Hartree-Fock Many-Body Perturbation Theory for Nuclear Ground-States
Tichai, Alexander; Binder, Sven; Roth, Robert
2016-01-01
We investigate the order-by-order convergence behavior of many-body perturbation theory (MBPT) as a simple and efficient tool to approximate the ground-state energy of closed-shell nuclei. To address the convergence properties directly, we explore perturbative corrections up to 30th order and highlight the role of the partitioning for convergence. The use of a simple Hartree-Fock solution to construct the unperturbed basis leads to a convergent MBPT series for soft interactions, in contrast to, e.g., a harmonic oscillator basis. For larger model spaces and heavier nuclei, where a direct high-order MBPT calculation in not feasible, we perform third-order calculation and compare to advanced ab initio coupled-cluster calculations for the same interactions and model spaces. We demonstrate that third-order MBPT provides ground-state energies for nuclei up into tin isotopic chain that are in excellent agreement with the best available coupled-cluster results at a fraction of the computational cost.
Madsen, Lars Bojer; Jensen, Frank; Dnestryan, Andrey I.; Tolstikhin, Oleg I.
2017-07-01
In the leading-order approximation of the weak-field asymptotic theory (WFAT), the dependence of the tunneling ionization rate of a molecule in an electric field on its orientation with respect to the field is determined by the structure factor of the ionizing molecular orbital. The WFAT yields an expression for the structure factor in terms of a local property of the orbital in the asymptotic region. However, in general quantum chemistry approaches molecular orbitals are expanded in a Gaussian basis which does not reproduce their asymptotic behavior correctly. This hinders the application of the WFAT to polyatomic molecules, which are attracting increasing interest in strong-field physics. Recently, an integral-equation approach to the WFAT for tunneling ionization of one electron from an arbitrary potential has been developed. The structure factor is expressed in an integral form as a matrix element involving the ionizing orbital. The integral is not sensitive to the asymptotic behavior of the orbital, which resolves the difficulty mentioned above. Here, we extend the integral representation for the structure factor to many-electron systems treated within the Hartree-Fock method and show how it can be implemented on the basis of standard quantum chemistry software packages. We validate the methodology by considering noble-gas atoms and the CO molecule, for which accurate structure factors exist in the literature. We also present benchmark results for CO2 and for NH3 in the pyramidal and planar geometries.
Nuclear Pasta at Finite Temperature with the Time-Dependent Hartree-Fock Approach
Schuetrumpf, B.; Klatt, M. A.; Iida, K.; Maruhn, J. A.; Mecke, K.; Reinhard, P.-G.
2016-01-01
We present simulations of neutron-rich matter at sub-nuclear densities, like supernova matter. With the time-dependent Hartree-Fock approximation we can study the evolution of the system at temperatures of several MeV employing a full Skyrme interaction in a periodic three-dimensional grid [1]. The initial state consists of α particles randomly distributed in space that have a Maxwell-Boltzmann distribution in momentum space. Adding a neutron background initialized with Fermi distributed plane waves the calculations reflect a reasonable approximation of astrophysical matter. The matter evolves into spherical, rod-like, connected rod-like and slab-like shapes. Further we observe gyroid-like structures, discussed e.g. in [2], which are formed spontaneously choosing a certain value of the simulation box length. The ρ-T-map of pasta shapes is basically consistent with the phase diagrams obtained from QMD calculations [3]. By an improved topological analysis based on Minkowski functionals [4], all observed pasta shapes can be uniquely identified by only two valuations, namely the Euler characteristic and the integral mean curvature. In addition we propose the variance in the cell-density distribution as a measure to distinguish pasta matter from uniform matter.
Hassaneen, Khaled; Mansour, Hesham
2017-02-01
The single-particle potentials and other properties at absolute zero temperature in isospin asymmetric nuclear matter are investigated in the frame of an extended Brueckner theory. Also thermal quantities are calculated in asymmetric nuclear matter using CD-Bonn potential and the Urbana three-body forces (3BF). Also, the effects of the hole-hole contributions are investigated within the self-consistent Greens function approach. The inclusion of 3BF or the hole-hole contributions improves the predicted saturation property of symmetric nuclear matter within the Brueckner-Hartree-Fock approach and it leads to a significant stiffening of the density dependence of symmetry energy at high densities but the exact saturation point is not reproduced. This is of great importance in astrophysical calculation. A phenomenological term simulating the three-body interaction is introduced to assure the empirical saturation property. The hot properties of asymmetric nuclear matter such as the internal energy and the pressure are analyzed using T2-approximation method at low temperatures.
A simple and efficient dispersion correction to the Hartree-Fock theory.
Yoshida, Tatsusada; Mashima, Akira; Sasahara, Katsunori; Chuman, Hiroshi
2014-02-15
One of the most challenging problems in computational chemistry and in drug discovery is the accurate prediction of the binding energy between a ligand and a protein receptor. It is well known that the binding energy calculated with the Hartree-Fock molecular orbital theory (HF) lacks the dispersion interaction energy that significantly affects the accuracy of the total binding energy of a large molecular system. We propose a simple and efficient dispersion energy correction to the HF theory (HF-Dtq). The performance of HF-Dtq was compared with those of several recently proposed dispersion corrected density functional theory methods (DFT-Ds) as to the binding energies of 68 small non-covalent complexes. The overall performance of HF-Dtq was found to be nearly equivalent to that of more sophisticated B3LYP-D3. HF-Dtq will thus be a useful and powerful method for accurately predicting the binding energy between a ligand and a protein, albeit it is a simple correction procedure based on HF.
Cho, Daeheum; Ko, Kyoung Chul; Lee, Jin Yong, E-mail: jinylee@skku.edu [Department of Chemistry, Sungkyunkwan University, Suwon 440-746 (Korea, Republic of); Ikabata, Yasuhiro; Wakayama, Kazufumi; Yoshikawa, Takeshi [Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555 (Japan); Nakai, Hiromi, E-mail: nakai@waseda.jp [Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555 (Japan); Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555 (Japan); CREST, Japan Science and Technology Agency, Tokyo 102-0075 (Japan); Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520 (Japan)
2015-01-14
The intramolecular magnetic coupling constant (J) of diradical systems linked with five- or six-membered aromatic rings was calculated to obtain the scaling factor (experimental J/calculated J ratio) for various density functional theory (DFT) functionals. Scaling factors of group A (PBE, TPSSh, B3LYP, B97-1, X3LYP, PBE0, and BH and HLYP) and B (M06-L, M06, M06-2X, and M06-HF) were shown to decrease as the amount of Hartree-Fock exact exchange (HFx) increases, in other words, overestimation of calculated J becomes more severe as the HFx increases. We further investigated the effect of HFx fraction of DFT functional on J value, spin contamination, and spin density distributions by comparing the B3LYP analogues containing different amount of HFx. It was revealed that spin contamination and spin densities at each atom increases as the HFx increases. Above all, newly developed BLYP-5 functional, which has 5% of HFx, was found to have the scaling factor of 1.029, indicating that calculated J values are very close to that of experimental values without scaling. BLYP-5 has potential to be utilized for accurate evaluation of intramolecular magnetic coupling constant (J) of diradicals linked by five- or six-membered aromatic ring couplers.
Basis set effects on the Hartree-Fock description of confined many-electron atoms
Garza, Jorge; Hernández-Pérez, Julio M.; Ramírez, José-Zeferino; Vargas, Rubicelia
2012-01-01
In this work, the basis sets designed by Clementi, Bunge and Thakkar, for atomic systems, have been used to obtain the electronic structure of confined many-electron atoms by using Roothaan's approach in the Hartree-Fock context with a new code written in C, which uses the message-passing interface library. The confinement was imposed as Ludeña suggested to simulate walls with infinity potential. For closed-shell atoms, the Thakkar basis set functions give the best total energies (TE) as a function of the confinement radius, obtaining the following ordering: TE(Thakkar) Clementi). However, for few open-shell atoms this ordering is not preserved and a trend, for the basis sets, is not observed. Although there are differences between the TE predicted by these basis set functions, the corresponding pressures are similar to each other; it means that changes in the total energy are described almost in the same way by using any of these basis sets. By analysing the total energy as a function of the inverse of the volume we propose an equation of state; for regions of small volumes, this equation predicts that the pressure is inversely proportional to the square of the volume.
Brueckner-Hartree-Fock calculations for finite nuclei with renormalized realistic forces
Hu, B. S.; Xu, F. R.; Wu, Q.; Ma, Y. Z.; Sun, Z. H.
2017-03-01
One can adopt two-step G -matrix approximations for the Brueckner-Hartree-Fock (BHF) calculations. The first G matrix is to soften the bare force, and the second one is to include the high-order correlations of the interaction in medium. The first G -matrix calculation for two-nucleon interaction should be done in the center-of-mass coordinate. As another alternative BHF approach, we have adopted the Vlow-k technique to soften the interaction and used the G matrix to include high-order correlations. The Vlow-k renormalization leads to high-momentum and low-momentum components of the interaction decoupled. With the Vlow-k potential, we have performed the BHF calculations for finite nuclei. The G -matrix elements with exact Pauli exclusions are calculated in the self-consistent BHF basis. To see effects from further possible correlations beyond BHF, we have simultaneously performed renormalized BHF (RBHF) calculations with the same potential. In RBHF, the mean field derived from realistic forces is modified by introducing the particle-occupation depletion resulting from many-body correlations. The ground-state energies and radii of the closed-shell nuclei, 4He, 16O, and 40Ca, have been investigated. The convergences of the BHF and RBHF calculations have been discussed and compared with other ab initio calculations with the same potential.
Rayka, Milad; Shahbazian, Shant
2016-01-01
In this communication, an effective set of the Hartree-Fock equations are derived only for electrons of the muonic systems, i.e., molecules containing a positively charged muon, conceiving the muon as a quantum oscillator. In these equations, a non-Coulombic potential is added to the orthodox coulomb and exchange potential energy terms, which describes the interaction of the muon and electrons effectively. The explicit form of the effective potential depends on the nature of muon vibrations and is derived for a combination of Cartesian Gaussian functions that are used to expand the muonic spatial orbital. The resulting effective Hartree-Fock equations are implemented computationally and used successfully, as a proof of concept, in the case of MuCN molecule, which results from replacing the proton of HCN molecule with a muon. The developed effective Hartree-Fock theory is quite general and in principle can be used for any muonic system while it is the starting point for a general effective electronic structure...
Nishiyama, Seiya; da Providência, João
2015-02-01
In this paper we present the induced representation of SO(2N) canonical transformation group and introduce (SO(2N))/(U(N)) coset variables. We give a derivation of the time-dependent Hartree-Bogoliubov (TDHB) equation on the Kähler coset space (G)/(H) = (SO(2N))/(U(N)) from the Euler-Lagrange equation of motion for the coset variables. The TDHB wave function represents the TD behavior of Bose condensate of fermion pairs. It is a good approximation for the ground state of the fermion system with a pairing interaction, producing the spontaneous Bose condensation. To describe the classical motion on the coset manifold, we start from the local equation of motion. This equation becomes a Riccati-type equation. After giving a simple two-level model and a solution for a coset variable, we can get successfully a general solution of time-dependent Riccati-Hartree-Bogoliubov equation for the coset variables. We obtain the Harish-Chandra decomposition for the SO(2N) matrix based on the nonlinear Möbius transformation together with the geodesic flow on the manifold.
Quiney, HM; Glushkov, VN; Wilson, S
2002-01-01
Using basis sets of distributed s-type Gaussian functions with positions and exponents optimized so as to support Hartree-Fock total energies with an accuracy approaching the sub-muHartree level, Dirac-Hartree-Fock-Coulomb calculations are reported for the ground states of the H-2, LiH, and BH molec
Study of superdeformation at zero spin with Skyrme-Hartree-Fock method
Takahara, S.; Tajima, N.; Onishi, N. [Tokyo Univ. (Japan)
1998-03-01
Superdeformed (SD) bands have been studied extensively both experimentally and theoretically in the last decade. Since the first observation in {sup 152}Dy in 1986, SD bands have been found in four mass regions, i.e., A {approx} 80, 130, 150 and 190. While these SD bands have been observed only at high spins so far, they may also be present at zero spin like fission isomers in actinide nuclei: The familiar generic argument on the strong shell effect at axis ratio 2:1 does not assume rotations. If non-fissile SD isomers exist at zero spin, they may be utilized to develop new experimental methods to study exotic states, in a similar manner as short-lived high-spin isomers are planned to be utilized as projectiles of fusion reactions in order to populate very high-spin near-yrast states. They will also be useful to test theoretical models whether the models can describe correctly the large deformations of rare-earth nuclei without further complications due to rotations. In this report, we employ the Skyrme-Hartree-Fock method to study the SD states at zero spin. First, we compare various Skyrme force parameter sets to test whether they can reproduce the extrapolated excitation energy of the SD band head of {sup 194}Hg. Second, we systematically search large-deformation solutions with the SkM{sup *} force. The feature of our calculations is that the single-particle wavefunctions are expressed in a three-dimensional-Cartesian-mesh representation. This representation enables one to obtain solutions of various shapes (including SD) without preparing a basis specific to each shape. Solving the mean-field equations in this representation requires, however, a large amount of computation which can be accomplished only with present supercomputers. (author)
Ragot, Sébastien
2008-04-01
The ground-state Hartree-Fock (HF) wavefunction of Hooke's atom is not known in closed form, contrary to the exact solution. The single HF orbital involved has thus far been studied using expansion techniques only, leading to slightly disparate energies. Therefore, the present letter aims at proposing alternative definitions of the HF wavefunction. First, the HF limit is ascertained using a simple expansion, which makes it possible to formulate explicit expressions of HF properties. The resulting energy, 2.038 438 871 8 Eh, is found stable at the tenth digit. Second and more instructive, an analysis of the Hartree equation makes it possible to infer a remarkably simple and accurate HF orbital, i.e., φHF(r)=nHFe-αr2√r2+β2, leading to an energy exceeding by 5.76×10-7 Eh only the above HF limit. This orbital makes it possible to obtain (near) Hartree-Fock properties in closed form, which in turn enables handy comparisons with exact quantities.
Staker, Joshua T
2013-01-01
We make numerical comparison of spectra from angular-momentum projection on Hartree-Fock states with spectra from configuration-interaction nuclear shell-model calculations, all carried out in the same model spaces (in this case the sd, lower pf, and p-sd_5/2 shells) and using the same input Hamiltonians. We find, unsurprisingly, that the low-lying excitation spectra for rotational nuclides are well reproduced, but the spectra for vibrational nuclides, and more generally the complex specta for odd-A and odd-odd nuclides are less well reproduced in detail.
Miyasita, Mitiyasu, E-mail: miyasita.mitiyasu@gmail.com [Graduate School of Science and Engineering, Shinshu University, Ueda 386-8567 (Japan); Higuchi, Katsuhiko [Graduate School of Advanced Science of Matter, Hiroshima University, Higashi-Hiroshima 739-8527 (Japan); Higuchi, Masahiko [Department of Physics, Faculty of Science, Shinshu University, Matsumoto 390-8621 (Japan)
2012-07-15
We present an alternative scheme for calculating the unrestricted Hartree-Fock (HF) equation. The scheme is based on the variational method utilizing the sophisticated basis functions that include no adjustable parameters. The validity of the present scheme is confirmed by actual calculations of the boron and neon atoms. The total energy of the present scheme is lower than that of the conventional restrictive HF equation, but higher than that of the CI method. Also, the resultant wave function satisfies the electron-nucleus cusp condition.
Thermal Bogoliubov transformation in nuclear structure theory
Vdovin, A I
2010-01-01
Thermal Bogoliubov transformation is an essential ingredient of the thermo field dynamics -- the real time formalism in quantum field and many-body theories at finite temperatures developed by H. Umezawa and coworkers. The approach to study properties of hot nuclei which is based on the extension of the well-known Quasiparticle-Phonon Model to finite temperatures employing the TFD formalism is presented. A distinctive feature of the QPM-TFD combination is a possibility to go beyond the standard approximations like the thermal Hartree-Fock or the thermal RPA ones.
Small, David W; Sundstrom, Eric J; Head-Gordon, Martin
2015-01-14
Restricted Hartree Fock using complex-valued orbitals (cRHF) is studied. We introduce an orbital pairing theorem, with which we obtain a concise connection between cRHF and real-valued RHF, and use it to uncover the close relationship between cRHF, unrestricted Hartree Fock, and generalized valence bond perfect pairing. This enables an intuition for cRHF, contrasting with the generally unintuitive nature of complex orbitals. We also describe an efficient computer implementation of cRHF and its corresponding stability analysis. By applying cRHF to the Be + H2 insertion reaction, a Woodward-Hoffmann violating reaction, and a symmetry-driven conical intersection, we demonstrate in genuine molecular systems that cRHF is capable of removing certain potential energy surface singularities that plague real-valued RHF and related methods. This complements earlier work that showed this capability in a model system. We also describe how cRHF is the preferred RHF method for certain radicaloid systems like singlet oxygen and antiaromatic molecules. For singlet O2, we show that standard methods fail even at the equilibrium geometry. An implication of this work is that, regardless of their individual efficacies, cRHF solutions to the HF equations are fairly commonplace.
Kupka, T.; Ruscic, B.; Botto, R. E.; Chemistry
2003-05-01
The nuclear shielding anisotropy and shielding tensor components calculated using the hybrid density functional B3PW91 are reported for a model set of compounds comprised of N{sub 2}, NH{sub 3}, CH{sub 4}, C{sub 2}H{sub 4}, HCN and CH{sub 3}CN. An estimation of density functional theory (DFT) and Hartree-Fock complete basis-set limit (CBS) parameters from a 2 (3) point exact fit vs. least-squares fit was obtained with the cc-pVxZ and aug-cc-pVxZ basis sets (x=D, T, Q, 5, 6). Both Hartree-Fock- and DFT-predicted CBS shielding anisotropies and shielding tensor components of the model molecules were in reasonable agreement with available experimental data. The utility of using a limited CBS approach for calculating accurate anisotropic shielding parameters of larger molecules as complementary methods to solid-state NMR is proposed.
Cui, Yao; Bulik, Ireneusz W; Jiménez-Hoyos, Carlos A; Henderson, Thomas M; Scuseria, Gustavo E
2013-10-21
We study the spectra of the molecular orbital Hessian (stability matrix) and random-phase approximation (RPA) Hamiltonian of broken-symmetry Hartree-Fock solutions, focusing on zero eigenvalue modes. After all negative eigenvalues are removed from the Hessian by following their eigenvectors downhill, one is left with only positive and zero eigenvalues. Zero modes correspond to orbital rotations with no restoring force. These rotations determine states in the Goldstone manifold, which originates from a spontaneously broken continuous symmetry in the wave function. Zero modes can be classified as improper or proper according to their different mathematical and physical properties. Improper modes arise from symmetry breaking and their restoration always lowers the energy. Proper modes, on the other hand, correspond to degeneracies of the wave function, and their symmetry restoration does not necessarily lower the energy. We discuss how the RPA Hamiltonian distinguishes between proper and improper modes by doubling the number of zero eigenvalues associated with the latter. Proper modes in the Hessian always appear in pairs which do not double in RPA. We present several pedagogical cases exemplifying the above statements. The relevance of these results for projected Hartree-Fock methods is also addressed.
Weimer, Martin; Hieringer, Wolfgang; Sala, Fabio Della; Goerling, Andreas
2005-02-21
The electronic and optical properties of extended functionalized carbyne chains, polyynes and cumulenes, are investigated with the localized Hartree-Fock method, with conventional Kohn-Sham methods, and with the Hartree-Fock method. It is found that even for very long polyynes the carbon-carbon bond lengths within a polyyne alternate while for long cumulenes no carbon-carbon bond length alternation occurs. Polyynes exhibit a finite HOMO-LUMO gap even if they become very long while cumulenes are found to become metallic in the limit of long chain lengths. The geometry and the electro-optical properties of polyynes cannot be influenced significantly by simple sp-{sigma}-bonded end groups. The optically active {sup 1}{sigma}{sub u}{sup +} <- X{sup 1}{sigma}{sub g}{sup +} electronic transition in polyynes is investigated by time-dependent density-functional theory (TDDFT). The known systematic underestimation of excitation energies in large chain-like systems by TDDFT methods is also found for the systems considered here. Deficiencies in the commonly used exchange-correlation kernels are identified as the main source of this shortcoming of TDDFT methods. Unphysical Coulomb self-interactions present in conventional Kohn-Sham potentials seem to not contribute significantly to the problem.
Bernardos, P. [Universidad de Cantabria, Departamento de Matematica Aplicada y Ciencias de la Computacion, 39005, Santander (Spain); Fomenko, V.N. [St Petersburg University for Railway Engineering, Department of Mathematics, 190031, St Petersburg (Russian Federation); Marcos, S.; Niembro, R. [Universidad de Cantabria, Departamento de Fisica Moderna, 39005, Santander (Spain); Lopez-Quelle, M. [Universidad de Cantabria, Departamento de Fisica Aplicada, 39005, Santander (Spain); Savushkin, L.N. [St Petersburg University for Telecommunications, Department of Physics, 191186, St Petersburg (Russian Federation)
2001-02-01
An effective nuclear model describing {omega}-, {rho}- and axial-mesons as gauge fields is applied to nuclear matter in the relativistic Hartree-Fock approximation. The isoscalar two-pion exchange is simulated by a scalar field s similar to that used in the conventional relativistic mean-field approach. Two more scalar fields are essential ingredients of the present treatment: the {sigma}-field, the chiral partner of the pion, and the {sigma}-field, the Higgs field for the {omega}-meson. Two versions of the model are used depending on whether the {sigma}-field is considered as a dynamical variable or 'frozen', by taking its mass as infinite. The model contains four free parameters in the first case and three in the second one which are fitted to the nuclear matter saturation conditions. The nucleon and meson effective masses, compressibility modulus and symmetry energy are calculated. The results prove the reliability of the Dirac-Hartree-Fock approach within the linear realization of the chiral symmetry. (author)
Small, David W.; Sundstrom, Eric J.; Head-Gordon, Martin [Department of Chemistry, University of California, Berkeley, California 94720, USA and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)
2015-01-14
Restricted Hartree Fock using complex-valued orbitals (cRHF) is studied. We introduce an orbital pairing theorem, with which we obtain a concise connection between cRHF and real-valued RHF, and use it to uncover the close relationship between cRHF, unrestricted Hartree Fock, and generalized valence bond perfect pairing. This enables an intuition for cRHF, contrasting with the generally unintuitive nature of complex orbitals. We also describe an efficient computer implementation of cRHF and its corresponding stability analysis. By applying cRHF to the Be + H{sub 2} insertion reaction, a Woodward-Hoffmann violating reaction, and a symmetry-driven conical intersection, we demonstrate in genuine molecular systems that cRHF is capable of removing certain potential energy surface singularities that plague real-valued RHF and related methods. This complements earlier work that showed this capability in a model system. We also describe how cRHF is the preferred RHF method for certain radicaloid systems like singlet oxygen and antiaromatic molecules. For singlet O{sub 2}, we show that standard methods fail even at the equilibrium geometry. An implication of this work is that, regardless of their individual efficacies, cRHF solutions to the HF equations are fairly commonplace.
Kalinowski, Jaroslaw; Wennmohs, Frank; Neese, Frank
2017-07-11
A resolution of identity based implementation of the Hartree-Fock method on graphical processing units (GPUs) is presented that is capable of handling basis functions with arbitrary angular momentum. For practical reasons, only functions up to (ff|f) angular momentum are presently calculated on the GPU, thus leaving the calculation of higher angular momenta integrals on the CPU of the hybrid CPU-GPU environment. Speedups of up to a factor of 30 are demonstrated relative to state-of-the-art serial and parallel CPU implementations. Benchmark calculations with over 3500 contracted basis functions (def2-SVP or def2-TZVP basis sets) are reported. The presented implementation supports all devices with OpenCL support and is capable of utilizing multiple GPU cards over either MPI or OpenCL itself.
Kambe, Takahide; Saito, Koichi
2016-01-01
As the interior density of a neutron star can become very high, it has been expected and discussed that quark matter may exist inside it. To describe the transition from hadron to quark phases (and vice versa), there are mainly two methods; one is the first-order phase transition, and the other is the crossover phenomenon. In the present study, using the flavor-SU (3) NJL model with the vector coupling interaction, we have calculated the equation of state for the quark phase at high density. Furthermore, for the hadron phase at low density, we have used two kinds of the equations of state; one is a relatively soft one by the QHD model, and the other is a stiff one calculated with relativistic Brueckner-Hartree-Fock approximation. Using those equations of state for the two phases, we have investigated the influence of various choices of parameters concerning the crossover region on the mass and radius of a neutron star.
Thiele, Robert; Son, Sang-Kil [Center for Free-Electron Laser Science, DESY, 22607 Hamburg (Germany); Ziaja, Beata [Center for Free-Electron Laser Science, DESY, 22607 Hamburg (Germany); Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, 31-342 Krakow (Poland); Santra, Robin [Center for Free-Electron Laser Science, DESY, 22607 Hamburg (Germany); Department of Physics, University of Hamburg, 20355 Hamburg (Germany)
2013-07-01
X-ray free-electron lasers (XFELs) are a promising tool for the structural determination of macro- and biomolecules, using coherent diffractive imaging. During imaging, the intense XFEL pulses also efficiently ionize the molecules, so it is important to estimate how the charged environment within the molecule modifies atomic properties, in comparison to the case of an isolated atom. Here, we apply the XATOM toolkit to obtain predictions on the modified ionization thresholds and rates of some photoinduced processes in carbon. The Hartree-Fock-Slater model is extended to include the electron screening and ion correlation effects, induced by external charges. With this extended model, we obtain predictions on modifications of orbital energies, photoabsorption cross sections, Auger decay rates, fluorescence emission rates, and atomic scattering factors as a function of the density and temperature of the surrounding charges. Our results have implications for the studies of dynamics within XFEL irradiated samples, in particular for those dedicated to coherent diffraction imaging.
Application of a solvable model to test the accuracy of the time-dependent Hartree-Fock method
Bouayad, N. [Blida Univ. (Algeria). Inst. de Phys.; Zettili, N. [Blida Univ. (Algeria). Inst. de Phys.]|[Department of Physics, King Fahd University of Petroleum and Minerals, Dhahran 31261 (Saudi Arabia)
1996-11-11
This work deals with the application of a solvable model to study the accuracy of a nuclear many-body approximation method. Using a new exactly solvable model, we carry out here a quantitative test of the accuracy of the time-dependent Hartree-Fock (TDHF) method. The application of the TDHF method to the model reveals that the model is suitable for describing various forms of collective motion: harmonic and anharmonic oscillations as well as rotations. We then show that, by properly quantizing the TDHF results, the TDHF approximation method yields energy spectra that are in very good agreement with their exact counterparts. This work shows that the model offers a rich and comprehensive framework for studying the various aspects of the TDHF method and also for assessing quantitatively its accuracy. (orig.).
Application of a solvable model to test the accuracy of the time-dependent Hartree-Fock method
Bouayad, Nouredine; Zettili, Nouredine
1996-02-01
This work deals with the application of a solvable model to study the accuracy of a nuclear many-body approximation method. Using a new exactly solvable model, we carry out here a quantitative test of the accuracy of the time-dependent Hartree-Fock (TDHF) method. The application of the TDHF method to the model reveals that the model is suitable for describing various forms of collective motion: harmonic and anharmonic oscillations as well as rotations. We then show that, by properly quantizing the TDHF results, the TDHF approximation method yields energy spectra that are in very good agreement with their exact counterparts. This work shows that the model offers a rich and comprehensive framework for studying the various aspects of the TDHF method and also for assessing quantitatively its accuracy.
Greenman, Loren; Haxton, Daniel J; McCurdy, C William
2016-01-01
We have verified a mechanism for Raman excitation of atoms through continuum levels previously obtained by quantum optimal control using the multi-configurational time-dependent Hartree-Fock (MCTDHF) method. This mechanism, which was obtained at the time-dependent configuration interaction singles (TDCIS) level of theory, involves sequentially exciting an atom from the ground state to an intermediate core-hole state using a long pump pulse, and then transferring this population to the target Raman state with a shorter Stokes pulse. This process represents the first step in a multidimensional x-ray spectroscopy scheme that will provide a local probe of valence electronic correlations. Although at the optimal pulse intensities at the TDCIS level of theory the MCTDHF method predicts multiple ionization of the atom, at slightly lower intensities (reduced by a factor of about 4) the TDCIS mechanism is shown to hold qualitatively. Quantitatively, the MCTDHF populations are reduced from the TDCIS calculations by a f...
Lata, K. Ramani [State University of New York at Albany, Department of Physics (United States); Sahoo, N. [University of Texas M.D. Anderson Cancer Center, Department of Radiation Physics (United States); Dubey, Archana [University of Central Florida, Department of Physics (United States); Scheicher, R. H. [Uppsala University, Condensed Matter Theory Group, Department of Physics and Materials Science (Sweden); Badu, S. R.; Pink, R. H.; Mahato, Dip N. [State University of New York at Albany, Department of Physics (United States); Schulte, A. F.; Saha, H. P. [University of Central Florida, Department of Physics (United States); Maharjan, N. B. [State University of New York at Albany, Department of Physics (United States); Chow, Lee [University of Central Florida, Department of Physics (United States); Das, T. P., E-mail: tpd56@albany.edu [State University of New York at Albany, Department of Physics (United States)
2008-01-15
The electronic structure of the heme unit of deoxyhemoglobin including the proximal imidazole has been studied using the first-principles Hartree-Fock procedure. Our results for the {sup 57m}Fe isomer shift and asymmetry parameter are in very good agreement with the values obtained from Moessbauer spectroscopy measurements. The {sup 57m}Fe nuclear quadrupole coupling constant is smaller than the experimental result and possible ways to improve the agreement in the future are discussed. Improved analysis of the Moessbauer data, removing some approximations made for deriving the magnetic hyperfine tensor for the {sup 57m}Fe nucleus, is suggested to allow quantitative comparison with our results in the future.
Bierón, Jacek; Indelicato, Paul; Jönsson, Per; Pyykkö, Pekka
2009-01-01
The multiconfiguration Dirac-Hartree-Fock (MCDHF) model has been employed to calculate the expectation values for the hyperfine splittings of the 5d96s2 2D3/2 and 5d96s2 2D5/2 levels of atomic gold. One-, two-, and three-body electron correlation effects involving all 79 electrons have been included in a systematic manner. The approximation employed in this study is equivalent to a Complete Active Space (CAS) approach. Calculated electric field gradients, together with experimental values of the electric quadrupole hyperfine structure constants, allow us to extract a nuclear electric quadrupole moment Q(197Au)=521.5(5.0) mb.
Jansík, Branislav; Høst, Stinne; Johansson, Mikael P; Olsen, Jeppe; Jørgensen, Poul; Helgaker, Trygve
2009-07-21
A hierarchical optimisation strategy has been introduced for minimising the Hartree-Fock/Kohn-Sham energy, consisting of three levels (3L): an atom-in-a-molecule optimisation, a valence-basis molecular optimisation, and a full-basis molecular optimisation. The density matrix formed at one level is used as a starting density matrix at the next level with no loss of information. To ensure a fast and reliable convergence to a minimum, the augmented Roothaan-Hall (ARH) algorithm is used in both the valence-basis and full-basis molecular optimisations. The performance of the ARH-3L method is compared with standard optimisation algorithms. Both for efficiency and reliability, we recommend to use the ARH-3L algorithm.
Kuwahara, Riichi; Tadokoro, Yoichi; Ohno, Kaoru
2014-08-28
In this paper, we calculate kinetic and potential energy contributions to the electronic ground-state total energy of several isolated atoms (He, Be, Ne, Mg, Ar, and Ca) by using the local density approximation (LDA) in density functional theory, the Hartree-Fock approximation (HFA), and the self-consistent GW approximation (GWA). To this end, we have implemented self-consistent HFA and GWA routines in our all-electron mixed basis code, TOMBO. We confirm that virial theorem is fairly well satisfied in all of these approximations, although the resulting eigenvalue of the highest occupied molecular orbital level, i.e., the negative of the ionization potential, is in excellent agreement only in the case of the GWA. We find that the wave function of the lowest unoccupied molecular orbital level of noble gas atoms is a resonating virtual bound state, and that of the GWA spreads wider than that of the LDA and thinner than that of the HFA.
Smeyers, Y.G.; Delgado-Barrio, G.
1976-05-01
The half-projected Hartree--Fock function for singlet states (HPHF) is analyzed in terms of natural electronic configurations. For this purpose the HPHF spinless density matrix and its natural orbitals are first deduced. It is found that the HPHF function does not contain any contribution from odd-times excited configurations. It is seen in addition, in the case of the singlet ground states, this function is approximately equivalent to two closed-shell configurations, although the nature of the excited one depends on the nuclear geometry. An example is given in the case of the LiH ground state. Finally, the application of this model for studying systems of more than two atoms is criticized.
Sil, T; Reinhard, P G; Shlomo, S; Sil, Tapas
2006-01-01
We provide accurate assessments of the consequences of violations of self-consistency in Hartree-Fock (HF) based random phase approximation (RPA) calculations of the centroid energy $E_{cen}$ of isoscalar and isovector giant resonances of multi-polarities $L=0-3$ in a wide range of nuclei. This is done by carrying out highly accurate HF-RPA calculations neglecting the particle-hole (ph) spin-orbit or Coulomb interaction in the RPA and comparing with the fully self-consistent HF-RPA results. We find that the shifts in the value of $E_{cen}$ due to self-consistency violation associated with the spin-orbit and Coulomb interactions are comparable or larger than the current experimental errors in $E_{cen}$.
Dziedzic, J; Hill, Q; Skylaris, C-K
2013-12-07
We present a method for the calculation of four-centre two-electron repulsion integrals in terms of localised non-orthogonal generalised Wannier functions (NGWFs). Our method has been implemented in the ONETEP program and is used to compute the Hartree-Fock exchange energy component of Hartree-Fock and Density Functional Theory (DFT) calculations with hybrid exchange-correlation functionals. As the NGWFs are optimised in situ in terms of a systematically improvable basis set which is equivalent to plane waves, it is possible to achieve large basis set accuracy in routine calculations. The spatial localisation of the NGWFs allows us to exploit the exponential decay of the density matrix in systems with a band gap in order to compute the exchange energy with a computational effort that increases linearly with the number of atoms. We describe the implementation of this approach in the ONETEP program for linear-scaling first principles quantum mechanical calculations. We present extensive numerical validation of all the steps in our method. Furthermore, we find excellent agreement in energies and structures for a wide variety of molecules when comparing with other codes. We use our method to perform calculations with the B3LYP exchange-correlation functional for models of myoglobin systems bound with O2 and CO ligands and confirm that the same qualitative behaviour is obtained as when the same myoglobin models are studied with the DFT+U approach which is also available in ONETEP. Finally, we confirm the linear-scaling capability of our method by performing calculations on polyethylene and polyacetylene chains of increasing length.
Dupuis, M. (ed.)
1981-02-01
Twenty-seven papers are included in four sessions titled: generalized Fock operator methods, annihilation of single excitations methods, second-order MCSCF methods, and applications of MCHF methods. Separate abstracts were prepared for eight papers; one of the remaining had been previously abstracted. (DLC)
Karasiev, V.; López-Boada, R.
1998-09-01
The line-integral method developed by van Leeuwen and Baerends [Phys. Rev. A 51, 170 (1995)] is applied to the calculation of the differences of correlation energy functional values ΔEDFTc=EDFTc[ρHF]- EDFTc[ρexact], where ρHF is the Hartree-Fock density and ρexact is the near-exact one (DFT is density-functional theory). From the Kohn-Sham wave functions yielding Hartree-Fock and the near-exact densities, the corresponding noninteracting kinetic energies and the exchange energies are calculated. An approximate relation between EDFTc[ρHF] and the conventional quantum chemistry correlation energy is presented, accurate to <=4μ hartree for the isoelectronic series of He, and Li, and for the Be atom.
Nishiyama, Seiya
2014-01-01
In this paper we present the induced representation of SO(2N) canonical transformation group and introduce SO(2N)/U(N) coset variables. We give a derivation of the time dependent Hartree-Bogoliubov (TDHB) equation on the Kaehler coset space G/H=SO(2N)/U(N) from the Euler-Lagrange equation of motion for the coset variables. The TDHB wave function represents the TD behavior of Bose condensate of fermion pairs. It is a good approximation for the ground state of the fermion system with a pairing interaction, producing the spontaneous Bose condensation. To describe the classical motion on the coset manifold, we start from the local equation of motion. This equation becomes a Riccati-type equation. After giving a simple two-level model and a solution for a coset variable, we can get successfully a general solution of TDRHB equation for the coset variables. We obtain the Harish-Chandra decomposition for the SO(2N) matrix based on the nonlinear Moebius transformation together with the geodesic flow on the manifold.
Dyall, Kenneth G.
1992-01-01
The effect of omission of two-electron integrals involving basis functions for the small component of the wavefunction on the eigenvalue spectrum in the Dirac-Hartree-Fock problem is studied. From an analysis of the Fock matrix it is shown that omission of these integrals moves the negative-energy states down, not up. Their complete omission does not give rise to intruder states. The appearance of intruder states occurs when only some of the core integrals are omitted, due to the nature of particular contraction schemes used for the core basis functions. Use of radially localized functions rather than atomic functions alleviates the intruder state problem.
Buica, Gabriela; 10.1016/j.jqsrt.2007.05.004
2013-01-01
We theoretically study multiphoton ionization of Mg in the circularly as well as the linearly polarized laser fields. Specifically two-, three-, and four-photon ionization cross sections from the ground and first excited states are calculated as a function of photon energy. Calculations are performed using the frozen-core Hartree-Fock and also the model potential approaches and the results are compared. We find that the model potential approach provide results as good as or even slightly better than those by the frozen-core Hartree-Fock approach. We also report the relative ratios of the ionization cross sections by the circularly and linearly polarized laser fields as a function of photon energy, which exhibit clear effects of electron correlations.
Pototzky, K J; Reinhard, P -G; Nesterenko, V O
2010-01-01
We present a systematic analysis of the description of odd nuclei by the Skyrme-Hartree-Fock approach augmented with pairing in BCS approximation and blocking of the odd nucleon. Current and spin densities in the Skyrme functional produce time-odd mean fields (TOMF) for odd nuclei. Their effect on basic properties (binding energies, odd-even staggering, separation energies and spectra) is investigated for the three Skyrme parameterizations SkI3, SLy6, and SV-bas. About 1300 spherical and axially-deformed odd nuclei with 16 < Z < 92 are considered. The calculations demonstrate that the TOMF effect is generally small, although not fully negligible. The influence of the Skyrme parameterization and the consistency of the calculations are much more important. With a proper choice of the parameterization, a good description of binding energies and their differences is obtained, comparable to that for even nuclei. The description of low-energy excitation spectra of odd nuclei is of varying quality depending on...
Kato, Tsuyoshi; Ide, Yoshihiro; Yamanouchi, Kaoru [Department of Chemistry, School of Science, The University of Tokyo, 7-3-1, Hongo Bunkyo-ku, Tokyo, 113-0033 (Japan)
2015-12-31
We first calculate the ground-state molecular wave function of 1D model H{sub 2} molecule by solving the coupled equations of motion formulated in the extended multi-configuration time-dependent Hartree-Fock (MCTDHF) method by the imaginary time propagation. From the comparisons with the results obtained by the Born-Huang (BH) expansion method as well as with the exact wave function, we observe that the memory size required in the extended MCTDHF method is about two orders of magnitude smaller than in the BH expansion method to achieve the same accuracy for the total energy. Second, in order to provide a theoretical means to understand dynamical behavior of the wave function, we propose to define effective adiabatic potential functions and compare them with the conventional adiabatic electronic potentials, although the notion of the adiabatic potentials is not used in the extended MCTDHF approach. From the comparison, we conclude that by calculating the effective potentials we may be able to predict the energy differences among electronic states even for a time-dependent system, e.g., time-dependent excitation energies, which would be difficult to be estimated within the BH expansion approach.
Wang, Hao
2014-07-01
The metal-insulator transition of VO2 so far has evaded an accurate description by density functional theory. The screened hybrid functional of Heyd, Scuseria and Ernzerhof leads to reasonable solutions for both the low-temperature monoclinic and high-temperature rutile phases only if spin polarization is excluded from the calculations. We explore whether a satisfactory agreement with experiment can be achieved by tuning the fraction of Hartree Fock exchange (α) in the density functional. It is found that two branches of locally stable solutions exist for the rutile phase for 12.5%≤α≤20%. One is metallic and has the correct stability as compared to the monoclinic phase, the other is insulating with lower energy than the metallic branch. We discuss these observations based on the V 3d orbital occupations and conclude that α=10% is the best possible choice for spin-polarized VO2 calculations. © 2014 Elsevier B.V. All rights reserved.
Lewis, Cannada A; Valeev, Edward F
2015-01-01
Clustered Low Rank (CLR) framework for block-sparse and block-low-rank tensor representation and computation is described. The CLR framework depends on 2 parameters that control precision: one controlling the CLR block rank truncation and another that controls screening of small contributions in arithmetic operations on CLR tensors. As these parameters approach zero CLR representation and arithmetic become exact. There are no other ad-hoc heuristics, such as domains. Use of the CLR format for the order-2 and order-3 tensors that appear in the context of density fitting (DF) evaluation of the Hartree-Fock (exact) exchange significantly reduced the storage and computational complexities below their standard $\\mathcal{O}(N^3)$ and $\\mathcal{O}(N^4)$ figures. Even for relatively small systems and realistic basis sets CLR-based DF HF becomes more efficient than the standard DF approach, and significantly more efficient than the conventional non-DF HF, while negligibly affecting molecular energies and properties.
$\\it{Ab}$ $\\it{initio}$ nuclear many-body perturbation calculations in the Hartree-Fock basis
Hu, Baishan; Sun, Zhonghao; Vary, James P; Li, Tong
2016-01-01
Starting from realistic nuclear forces, the chiral N$^3$LO and JISP16, we have applied many-body perturbation theory (MBPT) to the structure of closed-shell nuclei, $^4$He and $^{16}$O. The two-body N$^3$LO interaction is softened by a similarity renormalization group transformation while JISP16 is adopted without renormalization. The MBPT calculations are performed within the Hartree-Fock (HF) bases. The angular momentum coupled scheme is used, which can reduce the computational task. Corrections up to the third order in energy and up to the second order in radius are evaluated. Higher-order corrections in the HF basis are small relative to the leading-order perturbative result. Using the anti-symmetrized Goldstone diagram expansions of the wave function, we directly correct the one-body density for the calculation of the radius, rather than calculate corrections to the occupation propabilities of single-particle orbits as found in other treatments. We compare our results with other methods where available a...
Brorsen, Kurt R.; Sirjoosingh, Andrew; Pak, Michael V.; Hammes-Schiffer, Sharon
2015-06-01
The nuclear electronic orbital (NEO) reduced explicitly correlated Hartree-Fock (RXCHF) approach couples select electronic orbitals to the nuclear orbital via Gaussian-type geminal functions. This approach is extended to enable the use of a restricted basis set for the explicitly correlated electronic orbitals and an open-shell treatment for the other electronic orbitals. The working equations are derived and the implementation is discussed for both extensions. The RXCHF method with a restricted basis set is applied to HCN and FHF- and is shown to agree quantitatively with results from RXCHF calculations with a full basis set. The number of many-particle integrals that must be calculated for these two molecules is reduced by over an order of magnitude with essentially no loss in accuracy, and the reduction factor will increase substantially for larger systems. Typically, the computational cost of RXCHF calculations with restricted basis sets will scale in terms of the number of basis functions centered on the quantum nucleus and the covalently bonded neighbor(s). In addition, the RXCHF method with an odd number of electrons that are not explicitly correlated to the nuclear orbital is implemented using a restricted open-shell formalism for these electrons. This method is applied to HCN+, and the nuclear densities are in qualitative agreement with grid-based calculations. Future work will focus on the significance of nonadiabatic effects in molecular systems and the further enhancement of the NEO-RXCHF approach to accurately describe such effects.
Dubey, Archana; Badu, S. R.; Scheicher, R. H.; Sahoo, N.; Pink, R. H.; Schulte, A.; Saha, H. P.; Chow, Lee; Nagamine, K.; Das, T. P.
2008-03-01
The observation of paramagnetic susceptibility [1] in Oxy-Hb from measurements over a broad temperature range has stimulated interest in the occurrence of a low-lying excited triplet state close to the ground singlet state of Oxy-Hb. An earlier theoretical investigation [2] has shown the existence of such a triplet state providing support to the interpretation of the susceptibility data [1]. Support for the low-lying excited triplet state has been augmented recently [3] from microscopic relaxation rate measurements for muon attached to the heme group of Oxy-Hb. We are studying by first principles Hartree-Fock procedure the energies and the electronic wave functions of the ground and triplet states and the quantitative theoretical prediction of muon magnetic hyperfine interaction in room temperature μSR measurements on Oxy-Hb. Results will be presented for hyperfine interactions of muon and other nuclei in Oxy-Hb [1] M.Cerdonio etal. Proc. Nat. Acad. Sci USA 75, 4916(1978). [2] Zalek S. Herman and Gilda H Loew JACS 102, 1815(1980).[ 3] K. Nagamine etal Proc. Jpn. Acad.Ser.B 83,120(2007).
Xu Sun; You-song Gu; Xue-qiang Wang; Yue Zhang
2012-01-01
The electronic properties and stability of Li-doped ZnO with various defects have been studied by calculating the electronic structures and defect formation energies via first-principles calculations using hybrid Hartree-Fock and density functional methods.The results from formation energy calculations show that Li pair complexes have the lowest formation energy in most circumstances and they consume most of the Li content in Li doped ZnO,which make the p-type conductance hard to obtain.The formation of Li pair complexes is the main obstacle to realize p-type conductance in Li doped ZnO.However,the formation energy of Lizn decreases as environment changes from Zn-rich to O-rich and becomes more stable than that of Li-pair complexes at highly O-rich environment.Therefore,p-type conductance can be obtained by Li doped ZnO grown or post annealed in oxygen rich atmosphere.
Saravanan, S. P.; Sankar, A.; Parimala, K.
2017-01-01
The complete structural and vibrational analysis of the 2,5-Difluoronitrobenzene (DNB) was carried out by Hartree-Fock (HF) and density functional theory (DFT) method (B3LYP) with 6-311++G (d,p) basis set. The fundamental vibrations are assigned on the basis of the potential energy distribution (PED) of the vibrational modes calculated with scaled quantum mechanics (SQM) method. Using the time-dependent density functional theory (TD-DFT) method, electronic absorption spectra of the title compound have been predicted and a good agreement with the experimental ones is determined. 13C and 1H NMR spectra were recorded and chemical shifts of the molecule were calculated using the gauge independent atomic orbital (GIAO) method. The hyperconjugative interaction energy (E(2)) and electron densities of donor (i) and acceptor (j) bonds were calculated using natural bond orbital (NBO) analysis. In addition, molecular electrostatic potential (MEP) and atomic charges were calculated using B3LYP/6-311++G (d,p) level of theory. Moreover, thermodynamic properties (heat capacities, entropy, enthalpy and Gibb's free energy) of the title compound at different temperatures were calculated.
Augspurger, Joseph D.; Dykstra, Clifford E.
1993-08-01
Molecular Sternheimer shielding constants, γ, the proportionality constants relating the electric field gradient at a quadrupolar nucleus to an external electric field gradient are usually introduced phenomenologically. In this report, we take a comprehensive view of the sensitivity of the electric field gradient at a nucleus to arbitrary external electrical potentials and we show how the response can be obtained from analytically determined properties via derivative Hartree-Fock theory. From application of this ab initio technique, values have been obtained for the first and second order changes in nuclear quadrupole coupling with respect to external fields and field gradients, as well as nearby ideal multipole moments, for HCN and HCl. These values have been used to evaluate the change in the nuclear quadrupole coupling for several weakly bound complexes and to provide a nonempirical approach to relative effects on Sternheimer shielding. In weak molecular complexes, the effect of uniform fields can be as sizable as the effect of external field gradients in the overall change in nuclear quadrupole coupling, and so the underlying issue of convergence of multipolar expansions is considered over a range of geometries. This is important for structural interpretations of both nuclear magnetic resonance (NMR) and microwave data, and a simple formula, representing a practical point of truncation, is presented for quadrupole coupling analysis.
Neese, Frank
2007-10-28
The zero-field splitting (ZFS) (expressed in terms of the D tensor) is the leading spin-Hamiltonian parameter for systems with a ground state spin S>12. To first order in perturbation theory, the ZFS arises from the direct spin-spin dipole-dipole interaction. To second order, contributions arise from spin-orbit coupling (SOC). The latter contributions are difficult to treat since the SOC mixes states of different multiplicities. This is an aspect of dominant importance for the correct prediction of the D tensor. In this work, the theory of the D tensor is discussed from the point of view of analytic derivative theory. Starting from a general earlier perturbation treatment [F. Neese and E. I. Soloman, Inorg. Chem. 37, 6568 (1998)], straightforward response equations are derived that are readily transferred to the self-consistent field (SCF) Hartree-Fock (HF) or density functional theory (DFT) framework. The main additional effort in such calculations arises from the solution of nine sets of nonstandard coupled-perturbed SCF equations. These equations have been implemented together with the spin-orbit mean-field representation of the SOC operator and a mean-field treatment of the direct spin-spin interaction into the ORCA electronic structure program. A series of test calculations on diatomic molecules with accurately known zero-field splittings shows that the new approach corrects most of the shortcomings of previous DFT based methods and, on average, leads to predictions within 10% of the experimental values. The slope of the correlation line is essentially unity for the B3LYP and BLYP functionals compared to approximately 0.5 in previous treatments.
Potential energy curves for Mo2: multi-component symmetry-projected Hartree-Fock and beyond
Bytautas, Laimutis; Jiménez-Hoyos, Carlos A.; Rodríguez-Guzmán, R.; Scuseria, Gustavo E.
2014-07-01
The molybdenum dimer is an example of a transition metal system with a formal sextuple bond that constitutes a challenging case for ab initio quantum chemistry methods. In particular, the complex binding pattern in the Mo2 molecule requires a high-quality description of non-dynamic and dynamic electron correlation in order to yield the correct shape of the potential energy curve. The present study examines the performance of a recently implemented multi-component symmetry projected Hartree-Fock (HF) approach. In this work, the spin and spatial symmetries of a trial wavefunction written in terms of non-orthogonal Slater determinants are deliberately broken and then restored in a variation-after-projection framework. The resulting symmetry-projected HF wavefunctions, which possess well-defined quantum numbers, can account for static and some dynamic correlations. A single symmetry-projected configuration in a D∞hS-UHF or a D∞hKS-UHF framework offers a reasonable description of the potential energy curve of Mo2, though the binding energy is too small for the former. Our multi-component strategy offers a way to improve on the single configuration result in a systematic way towards the exact wavefunction: in the def2-TZVP basis set considered in this study, a 7-determinant multi-component D∞hS-UHF approach yields a bond length of 2.01 Å, in good agreement with experimental results, while the predicted binding energy is 39.2 mhartree. The results of this exploratory study suggest that a multi-component symmetry-projected HF stategy is a promising alternative in a high-accuracy description of the electronic structure of challenging systems. We also present and discuss some benchmark calculations based on the CEEIS-FCI (correlation energy extrapolation by intrinsic scaling - full configuration interaction) method for selected geometries.
Forte, G; March, N H; Pucci, R
2014-01-01
The Hartree-Fock (HF) method, supplemented by low-order Moller-Plesset (MP2) perturbation theory, has been utilized to predict the nuclear geometry, assuming planarity, of a low-lying isomer of the free space cluster BOSi$_2$. The planar structure found at equilibrium geometry is shown to be stable against small amplitude molecular vibrations. Finally, some brief comments are made on the possible relevance of the above free-space cluster geometry to the known B-O defects which limit the improvement of minority carrier lifetime in a form of p-type silicon.
Forte, G.; Angilella, G. G. N.; March, N. H.; Pucci, R.
2014-07-01
The Hartree-Fock (HF) method, supplemented by low-order Møller-Plesset (MP2) perturbation theory, has been utilized to predict the nuclear geometry, assuming planarity, of a low-lying isomer of the free space cluster BOSi2. The planar structure found at equilibrium geometry is shown to be stable against small amplitude molecular vibrations. Finally, some brief comments are made on the possible relevance of the above free-space cluster geometry to the known B-O defects which limit the improvement of minority carrier lifetime in a form of p-type silicon.
Maschio, Lorenzo; Kirtman, Bernard; Rérat, Michel; Orlando, Roberto; Dovesi, Roberto
2013-10-28
We present a fully analytical formulation for calculating Raman intensities of crystalline periodic systems using a local basis set. Numerical differentiation with respect to atomic coordinates and with respect to wavevectors is entirely avoided as is the determination of crystal orbital coefficient derivatives with respect to nuclear displacements. Instead, our method utilizes the orbital energy-weighted density matrix and is based on the self-consistent solution of first- and second-order Coupled Perturbed Hartree-Fock/Kohn-Sham equations for the electronic response to external electric fields at the equilibrium geometry. This method has also been implemented in the Crystal program, which uses a Gaussian type basis set.
Y. Sajeev
2015-08-01
Full Text Available The equation-of-motion coupled cluster (EOMCC method based on the excited state Hartree-Fock (ESHF solutions is shown to be appropriate for computing the entire ground state potential energy curves of strongly correlated higher-order bonds. The new approach is best illustrated for the homolytic dissociation of higher-order bonds in molecules. The required multireference character of the true ground state wavefunction is introduced through the linear excitation operator of the EOMCC method. Even at the singles and doubles level of cluster excitation truncation, the nonparallelity error of the ground state potential energy curve from the ESHF based EOMCC method is small.
Zhou, Fuyang; Li, Jiguang; Wang, Jianguo
2015-01-01
The multi-configuration Dirac-Hartree-Fock method was employed to calculate the total and excitation energies, oscillator strengths and hyperfine structure constants for low-lying levels of Sm I. In the first-order perturbation approximation, we systematically analyzed correlation effects from each electrons and electron pairs. It was found that the core correlations are of importance for physical quantities concerned. Based on the analysis, the important configuration state wave functions were selected to constitute atomic state wave functions. By using this computational model, our excitation energies, oscillator strengths, and hyperfine structure constants are in better agreement with experimental values than earlier theoretical works.
Symbolic computation of the Hartree-Fock energy from a chiral EFT three-nucleon interaction at N 2LO
Gebremariam, B.; Bogner, S. K.; Duguet, T.
2010-06-01
We present the first of a two-part Mathematica notebook collection that implements a symbolic approach for the application of the density matrix expansion (DME) to the Hartree-Fock (HF) energy from a chiral effective field theory (EFT) three-nucleon interaction at N 2LO. The final output from the notebooks is a Skyrme-like energy density functional that provides a quasi-local approximation to the non-local HF energy. In this paper, we discuss the derivation of the HF energy and its simplification in terms of the scalar/vector-isoscalar/isovector parts of the one-body density matrix. Furthermore, a set of steps is described and illustrated on how to extend the approach to other three-nucleon interactions. Program summaryProgram title: SymbHFNNN Catalogue identifier: AEGC_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGC_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 96 666 No. of bytes in distributed program, including test data, etc.: 378 083 Distribution format: tar.gz Programming language: Mathematica 7.1 Computer: Any computer running Mathematica 6.0 and later versions Operating system: Windows Xp, Linux/Unix RAM: 256 Mb Classification: 5, 17.16, 17.22 Nature of problem: The calculation of the HF energy from the chiral EFT three-nucleon interaction at N 2LO involves tremendous spin-isospin algebra. The problem is compounded by the need to eventually obtain a quasi-local approximation to the HF energy, which requires the HF energy to be expressed in terms of scalar/vector-isoscalar/isovector parts of the one-body density matrix. The Mathematica notebooks discussed in this paper solve the latter issue. Solution method: The HF energy from the chiral EFT three-nucleon interaction at N 2LO is cast into a form suitable for an automatic simplification of
He, Liming; Zhu, Yunxia; Zhang, Meng; Tu, Yaoquan
2011-11-01
We present a new second-order representation of the relativistic Hartree-Fock equation, which can be solved by the standard Hartree-Fock technique. An alternative reduction for the magnetic part of the Breit interaction is presented in an explicit expression. A corresponding program has been developed, which improves significantly the scaled linear mesh introduced by Herman and Skillman. The structures for a number of atoms and ions are calculated and the agreement of our results with those published is excellent. We evaluate the fine-structure intervals of nd(n = 3-40) Rydberg series for sodium. The inverted fine-structure splitting values are obtained directly as the differences of eigenvalues obtained from a self-consistent field procedure. Taking into account the Gaunt effect enables the accuracy of the calculation to be substantially improved. The complete treatments reproduce very well the inverted fine structures along the Rydberg series and the relative difference between the present results and the experiments does not exceed 4.4%.
Marcos, S [Departamento de FIsica Moderna, Universidad de Cantabria, E-39005 Santander (Spain); Savushkin, L N [Department of Physics, St Petersburg University for Telecommunications, 191065 St Petersburg (Russian Federation); Fomenko, V N [Department of Mathematics, St Petersburg University for Railway Engineering, 190031 St Petersburg (Russian Federation); Lopez-Quelle, M [Departamento de FIsica Aplicada, Universidad de Cantabria, E-39005 Santander (Spain); Niembro, R [Departamento de FIsica Moderna, Universidad de Cantabria, E-39005 Santander (Spain)
2004-06-01
An exact method is suggested to treat the nonlinear self-interactions (NLSI) in the relativistic Hartree-Fock (RHF) approach for nuclear systems. We consider here the NLSI constructed from the relativistic scalar nucleon densities including products of six and eight fermion fields. This type of NLSI corresponds to the zero-range limit of the standard cubic and quartic self-interactions of the scalar field. The method to treat the NLSI uses the Fierz transformation, which enables one to express the exchange (Fock) components in terms of the direct (Hartree) ones. The method is applied to nuclear matter and finite nuclei. It is shown that, in the RHF formalism, the NLSI, which are explicitly isovector-independent, generate scalar, vector and tensor nucleon self-energies with a strong isovector dependence. This strong isovector structure of the self-energies is due to the exchange terms of the RHF method. Calculations are carried out with a parametrization containing five free parameters. The model allows a description of both types of systems compatible with experimental data.
Martínez, E; Rincon, L
2002-01-01
Theoretical results of photoemission energy spectral of the atomic sulfur and of the SO sub 2 molecule, adsorbed over surfaces of Ni(110) and Ni(l l l) clusters, are reported in this work. Clusters with 11, 13, 15 and 17 atoms of Ni were used for the model. The calculations were done by Hartree-Fock method, and basis sets of type STO-NG and p-q1G (p3,6; q= 2,3; N= 3,6) were used. The ionization potentials (IP) were interpreted within the Koopmans Theorem. The results obtained for the IP of 1s, 2s and 2p orbitals are 2472.03 eV, 238.14 eV and 173.55 eV, respectively; while for the same orbitals of the sulfur in SO sub 2 these values are 2481.30 eV, 246.61 eV and 182.17 eV. The theoretical results were compared with experimental results reported in the references, and the error ranges are between 5 eV and 30 eV, in agreement with the standard for the Hartree-Fock method. (Author)
Bučinský, Lukáš
2015-05-11
"Kramers pairs symmetry breaking" is evaluated at the 2-component (2c) Kramers unrestricted and/or general complex Hartree-Fock (GCHF) level of theory, and its analogy with "spin contamination" at the 1-component (1c) unrestricted Hartree-Fock (UHF) level of theory is emphasized. The GCHF "Kramers pairs symmetry breaking" evaluation is using the square of overlaps between the set of occupied spinorbitals with the projected set of Kramers pairs. In the same fashion, overlaps between α and β orbitals are used in the evaluation of "spin contamination" at the UHF level of theory. In this manner, UHF Š2 expectation value is made formally extended to the GCHF case. The directly evaluated GCHF expectation value of the Š2 operator is considered for completeness. It is found that the 2c GCHF Kramers pairs symmetry breaking has a very similar extent in comparison to the 1c UHF spin contamination. Thus higher excited states contributions to the 1c and 2c unrestricted wave functions of open shell systems have almost the same extent and physical consequences. Moreover, it is formally shown that a single determinant wave function in the restricted open shell Kramers case has the expectation value of K2 operator equal to the negative number of open shell electrons, while the eigenvalue of K2 for the series of simple systems (H, He, He*-triplet, Li and Li*-quartet) are found to be equal to minus the square of the number of open shell electrons. The concept of unpaired electron density is extended to the GCHF regime and compared to UHF and restricted open shell Hartree-Fock spin density. The "collinear" and "noncollinear" analogs of spin density at the GCHF level of theory are considered as well. Spin contamination and/or Kramers pairs symmetry breaking, spin populations and spin densities are considered for H2O+, Cl, HCl+, phenoxyl radical (C6H5O) as well as for Cu, Cu2+, Fe and the [OsCl5(1H-pyrazole)]- anion. The 1c and 2c unpaired electron density representation is found
Kjærgaard, Thomas; Jørgensen, Poul; Thorvaldsen, Andreas;
2009-01-01
-orbital density-matrix based formulation of response theory and use London atomic orbitals to parametrize the magnetic field dependence. It yields a computational procedure which is both gauge-origin independent and suitable for linear-scaling at the level of time-dependent Hartree-Fock and density functional......A Lagrangian approach has been used to derive gauge-origin independent expressions for two properties that rationalize magneto-optical activity, namely the Verdet constant V(ω) of the Faraday effect and the B term of magnetic circular dichroism. The approach is expressed in terms of an atomic...... theory. The formulation includes a modified preconditioned conjugated gradient algorithm, which projects out the excited state component from the solution to the linear response equation. This is required when solving one of the response equations for the determination of the B term and divergence...
Ucun, Fatih; Sağlam, Adnan; Güçlü, Vesile
2007-06-01
The molecular structures, vibrational frequencies and corresponding vibrational assignments of xanthine and its methyl derivatives (caffeine and theobromine) have been calculated using ab initio Hartree-Fock (HF) and density functional theory (B3LYP) methods with 6-31G(d, p) basis set level. The calculations were utilized to the CS symmetries of the molecules. The obtained vibrational frequencies and optimised geometric parameters (bond lengths and bond angles) were seen to be well agreement with the experimental data. The used scale factors which have been obtained the ratio of the frequency values of the strongest peaks in the calculated and experimental spectra seem to cause the gained vibrations well corresponding to the experimental ones. Theoretical infrared intensities and Raman activities are also reported.
Akamatsu, Hirofumi; Kumagai, Yu; Oba, Fumiyasu; Fujita, Koji; Murakami, Hideo; Tanaka, Katsuhisa; Tanaka, Isao
2011-06-01
A superexchange mechanism between Eu2+ 4f spins via the 3d states of nonmagnetic Ti4+ ions is proposed through first-principles calculations based on a hybrid Hartree-Fock density functional approach to explain G-type antiferromagnetism in EuTiO3. This mechanism is supported by systematic calculations for related Eu2+-based perovskite oxides. In EuTiO3, the competition between the antiferromagnetic superexchange and an indirect ferromagnetic exchange via the Eu 5d states leads to a delicate balance between antiferromagnetic and ferromagnetic phases. The superexchange mechanism involving the Ti 3d states hints at the microscopic origin of the strong spin-lattice coupling in EuTiO3.
Gundra, Kondayya
2011-01-01
Pariser-Parr-Pople (P-P-P) model Hamiltonian is employed frequently to study the electronic structure and optical properties of $\\pi$-conjugated systems. In this paper we describe a Fortran 90 computer program which uses the P-P-P model Hamiltonian to solve the Hartree-Fock (HF) equation for infinitely long, one-dimensional, periodic, $\\pi$-electron systems. The code is capable of computing the band structure, as also the linear optical absorption spectrum, by using the tight-binding (TB) and the HF methods. Furthermore, using our program the user can solve the HF equation in the presence of a finite external electric field, thereby, allowing the simulation of gated systems. We apply our code to compute various properties of polymers such as $trans$-polyacetylene ($t$-PA), poly-\\emph{para}-phenylene (PPP), and armchair and zigzag graphene nanoribbons, in the infinite length limit.
Inakura, T.; Mizutori, S.; Yamagami, M.; Matsuyanagi, K. E-mail: ken@ruby.scphys.kyoto-u.ac.jp
2002-11-18
With the use of the symmetry-unrestricted cranked Skyrme-Hartree-Fock method in the three-dimensional coordinate-mesh representation, we have carried out a systematic theoretical search for the superdeformed and hyperdeformed rotational bands in the mass A=30-50 region. Along the N=Z line, we have found superdeformed solutions in {sup 32}S, {sup 36}Ar, {sup 40}Ca, {sup 44}Ti, and hyperdeformed solutions in {sup 36}Ar, {sup 40}Ca, {sup 44}Ti, {sup 48}Cr. The superdeformed band in {sup 40}Ca is found to be extremely soft against both the axially symmetric (Y{sub 30}) and asymmetric (Y{sub 31}) octupole deformations. An interesting role of symmetry breaking in the mean field is pointed out.
Inakura, T.; Yamagami, M.; Matsuyanagi, K. [Kyoto Univ., Dept. of Physics, Kyoto (Japan); Mizutori, S. [Kansai Women' s College, Dept. of Human Science, Kashiwara, Osaka (Japan)
2003-02-01
With the use of the symmetry-unrestricted cranked Skyrme-Hartree-Fock method in the three-dimensional coordinate-mesh representation, we have carried out a systematic theoretical search for the superdeformed and hyperdeformed rotational bands in the mass A=30-50 region. Along the N=Z line, we have found superdeformed solutions in {sup 32}S, {sup 36}Ar, {sup 40}Ca, {sup 44}Ti, and hyperdeformed solutions in {sup 36}Ar, {sup 40}Ca, {sup 44}Ti, {sup 48}Cr. The superdeformed band in {sup 40}Ca is found to be extremely soft against both the axially symmetric (Y{sub 30}) and asymmetric (Y{sub 31}) octupole deformations. An interesting role of symmetry breaking in the mean field is pointed out. (author)
Inakura, T.; Mizutori, S.; Yamagami, M.; Matsuyanagi, K.
2002-11-01
With the use of the symmetry-unrestricted cranked Skyrme-Hartree-Fock method in the three-dimensional coordinate-mesh representation, we have carried out a systematic theoretical search for the superdeformed and hyperdeformed rotational bands in the mass A=30-50 region. Along the N= Z line, we have found superdeformed solutions in 32S, 36Ar, 40Ca, 44Ti, and hyperdeformed solutions in 36Ar, 40Ca, 44Ti, 48Cr. The superdeformed band in 40Ca is found to be extremely soft against both the axially symmetric ( Y30) and asymmetric ( Y31) octupole deformations. An interesting role of symmetry breaking in the mean field is pointed out.
Joshi, Bhawani Datt; Srivastava, Anubha; Tandon, Poonam; Jain, Sudha
2011-11-01
Yohimbine hydrochloride (YHCl) is an aphrodisiac and promoted for erectile dysfunction, weight loss and depression. The optimized geometry, total energy, potential energy surface and vibrational wavenumbers of yohimbine hydrochloride have been determined using ab initio, Hartree-Fock (HF) and density functional theory (DFT/B3LYP) method with 6-311++G(d,p) basis set. A complete vibrational assignment is provided for the observed Raman and IR spectra of YHCl. The UV absorption spectrum was examined in ethanol solvent and compared with the calculated one in gas phase as well as in solvent environment (polarizable continuum model, PCM) using TD-DFT/6-31G basis set. These methods are proposed as a tool to be applied in the structural characterization of YHCl. The calculated highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) with frontier orbital gap are presented.
Yoshida, Tatsusada; Hayashi, Takahisa; Mashima, Akira; Chuman, Hiroshi
2015-10-01
One of the most challenging problems in computer-aided drug discovery is the accurate prediction of the binding energy between a ligand and a protein. For accurate estimation of net binding energy ΔEbind in the framework of the Hartree-Fock (HF) theory, it is necessary to estimate two additional energy terms; the dispersion interaction energy (Edisp) and the basis set superposition error (BSSE). We previously reported a simple and efficient dispersion correction, Edisp, to the Hartree-Fock theory (HF-Dtq). In the present study, an approximation procedure for estimating BSSE proposed by Kruse and Grimme, a geometrical counterpoise correction (gCP), was incorporated into HF-Dtq (HF-Dtq-gCP). The relative weights of the Edisp (Dtq) and BSSE (gCP) terms were determined to reproduce ΔEbind calculated with CCSD(T)/CBS or /aug-cc-pVTZ (HF-Dtq-gCP (scaled)). The performance of HF-Dtq-gCP (scaled) was compared with that of B3LYP-D3(BJ)-bCP (dispersion corrected B3LYP with the Boys and Bernadi counterpoise correction (bCP)), by taking ΔEbind (CCSD(T)-bCP) of small non-covalent complexes as 'a golden standard'. As a critical test, HF-Dtq-gCP (scaled)/6-31G(d) and B3LYP-D3(BJ)-bCP/6-31G(d) were applied to the complex model for HIV-1 protease and its potent inhibitor, KNI-10033. The present results demonstrate that HF-Dtq-gCP (scaled) is a useful and powerful remedy for accurately and promptly predicting ΔEbind between a ligand and a protein, albeit it is a simple correction procedure.
Kondayya, Gundra; Shukla, Alok
2012-03-01
Pariser-Parr-Pople (P-P-P) model Hamiltonian is employed frequently to study the electronic structure and optical properties of π-conjugated systems. In this paper we describe a Fortran 90 computer program which uses the P-P-P model Hamiltonian to solve the Hartree-Fock (HF) equation for infinitely long, one-dimensional, periodic, π-electron systems. The code is capable of computing the band structure, as also the linear optical absorption spectrum, by using the tight-binding and the HF methods. Furthermore, using our program the user can solve the HF equation in the presence of a finite external electric field, thereby, allowing the simulation of gated systems. We apply our code to compute various properties of polymers such as trans-polyacetylene, poly- para-phenylene, and armchair and zigzag graphene nanoribbons, in the infinite length limit. Program summaryProgram title: ppp_bulk.x Catalogue identifier: AEKW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 87 464 No. of bytes in distributed program, including test data, etc.: 2 046 933 Distribution format: tar.gz Programming language: Fortran 90 Computer: PCs and workstations Operating system: Linux, Code was developed and tested on various recent versions of 64-bit Fedora including Fedora 14 (kernel version 2.6.35.12-90). Classification: 7.3 External routines: This program needs to link with LAPACK/BLAS libraries compiled with the same compiler as the program. For the Intel Fortran Compiler we used the ACML library version 4.4.0, while for the gfortran compiler we used the libraries supplied with the Fedora distribution. Nature of problem: The electronic structure of one-dimensional periodic π-conjugated systems is an intense area of research at
Schimeczek, C.; Engel, D.; Wunner, G.
2014-05-01
Our previously published code for calculating energies and bound-bound transitions of medium-Z elements at neutron star magnetic field strengths [D. Engel, M. Klews, G. Wunner, Comp. Phys. Comm. 180, 3-2-311 (2009)] was based on the adiabatic approximation. It assumes a complete decoupling of the (fast) gyration of the electrons under the action of the magnetic field and the (slow) bound motion along the field under the action of the Coulomb forces. For the single-particle orbitals this implied that each is a product of a Landau state and an (unknown) longitudinal wave function whose B-spline coefficients were determined self-consistently by solving the Hartree-Fock equations for the many-electron problem on a finite-element grid. In the present code we go beyond the adiabatic approximation, by allowing the transverse part of each orbital to be a superposition of Landau states, while assuming that the longitudinal part can be approximated by the same wave function in each Landau level. Inserting this ansatz into the energy variational principle leads to a system of coupled equations in which the B-spline coefficients depend on the weights of the individual Landau states, and vice versa, and which therefore has to be solved in a doubly self-consistent manner. The extended ansatz takes into account the back-reaction of the Coulomb motion of the electrons along the field direction on their motion in the plane perpendicular to the field, an effect which cannot be captured by the adiabatic approximation. The new code allows for the inclusion of up to 8 Landau levels. This reduces the relative error of energy values as compared to the adiabatic approximation results by typically a factor of three (1/3 of the original error) and yields accurate results also in regions of lower neutron star magnetic field strengths where the adiabatic approximation fails. Further improvements in the code are a more sophisticated choice of the initial wave functions, which takes into
Goerigk, Lars; Collyer, Charles A; Reimers, Jeffrey R
2014-12-18
We demonstrate the importance of properly accounting for London dispersion and basis-set-superposition error (BSSE) in quantum-chemical optimizations of protein structures, factors that are often still neglected in contemporary applications. We optimize a portion of an ensemble of conformationally flexible lysozyme structures obtained from highly accurate X-ray crystallography data that serve as a reliable benchmark. We not only analyze root-mean-square deviations from the experimental Cartesian coordinates, but also, for the first time, demonstrate how London dispersion and BSSE influence crystallographic R factors. Our conclusions parallel recent recommendations for the optimization of small gas-phase peptide structures made by some of the present authors: Hartree-Fock theory extended with Grimme's recent dispersion and BSSE corrections (HF-D3-gCP) is superior to popular density functional theory (DFT) approaches. Not only are statistical errors on average lower with HF-D3-gCP, but also the convergence behavior is much better. In particular, we show that the BP86/6-31G* approach should not be relied upon as a black-box method, despite its widespread use, as its success is based on an unpredictable cancellation of errors. Using HF-D3-gCP is technically straightforward, and we therefore encourage users of quantum-chemical methods to adopt this approach in future applications.
G(U)M(U)(S), Sedat; (O)ZDO(G)AN, Telhat
2004-01-01
Hartree-Fock-Roothaan (HFR) calculations for ground states of some atoms, i.e. He, Be, Ne, Ar, and Kr have been performed using minimal basis sets of Slater type orbitals (STOs) with integer and noninteger principal quantum numbers (integer n-STOs and noninteger n-STOs). The obtained total energies for these atoms using minimal basis sets of integer n-STOs are in good agreement with those in the previous literature. On the other hand, for the case of minimal basis sets of noninteger n-STOs, although the calculated total energies of these atoms agree well with the results in literature, some striking results have been obtained for atoms Ar and Kr. Our computational results for the energies of atoms Ar and Kr are slightly better than those in literature, by amount of 0.00222 and 0.000054 a.u., respectively. The improvement in the energies of atoms Ar and Kr may result from the efficient calculations of one-center two-electron integrals over noninteger n-STOs. For some atomic ions in their ground state,HFR calculations have been carried out using minimal basis sets of noninteger n-STOs. The obtained total energies for these atomic ions are substantially lower than those available in literature.
Rodriguez-Bautista, Mariano; Díaz-García, Cecilia; Navarrete-López, Alejandra M.; Vargas, Rubicelia; Garza, Jorge, E-mail: jgo@xanum.uam.mx [Departamento de Química, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Col. Vicentina, Iztapalapa C. P. 09340, México D. F., México (Mexico)
2015-07-21
In this report, we use a new basis set for Hartree-Fock calculations related to many-electron atoms confined by soft walls. One- and two-electron integrals were programmed in a code based in parallel programming techniques. The results obtained with this proposal for hydrogen and helium atoms were contrasted with other proposals to study just one and two electron confined atoms, where we have reproduced or improved the results previously reported. Usually, an atom enclosed by hard walls has been used as a model to study confinement effects on orbital energies, the main conclusion reached by this model is that orbital energies always go up when the confinement radius is reduced. However, such an observation is not necessarily valid for atoms confined by penetrable walls. The main reason behind this result is that for atoms with large polarizability, like beryllium or potassium, external orbitals are delocalized when the confinement is imposed and consequently, the internal orbitals behave as if they were in an ionized atom. Naturally, the shell structure of these atoms is modified drastically when they are confined. The delocalization was an argument proposed for atoms confined by hard walls, but it was never verified. In this work, the confinement imposed by soft walls allows to analyze the delocalization concept in many-electron atoms.
Pernpointner, M.
2004-11-01
In this paper we present the third-order extension of the four-component one-particle propagator method in the non-Dyson version of the algebraic diagrammatic construction (ADC) for the calculation of valence ionization energies. Relativistic and electron correlation effects are incorporated consistently by starting from the Dirac-Hamiltonian. The ADC equations derived from the Feynman diagrams can hereby be used in their spin-orbital form and need not be transformed to the spin-free version as required for a nonrelativistic treatment. For the calculation of the constant self-energy contribution the Dyson expansion method was implemented being superior to a perturbational treatment of Σ(∞). The Dirac-Hartree-Fock- (DHF-) ADC(3) was applied to the calculation of valence photoionization spectra of the noble gas atoms, carbon monoxide and ICN now also reproducing spin-orbit features in the spectrum. Comparison with DHF-ADC(2), nonrelativistic ADC(3), and experimental data was made in order to demonstrate the characteristics and performance of the method.
de Lara-Castells, María Pilar; Mitrushchenkov, Alexander O.; Stoll, Hermann
2015-09-01
A combined density functional (DFT) and incremental post-Hartree-Fock (post-HF) approach, proven earlier to calculate He-surface potential energy surfaces [de Lara-Castells et al., J. Chem. Phys. 141, 151102 (2014)], is applied to describe the van der Waals dominated Ag2/graphene interaction. It extends the dispersionless density functional theory developed by Pernal et al. [Phys. Rev. Lett. 103, 263201 (2009)] by including periodic boundary conditions while the dispersion is parametrized via the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)]. Starting with the elementary cluster unit of the target surface (benzene), continuing through the realistic cluster model (coronene), and ending with the periodic model of the extended system, modern ab initio methodologies for intermolecular interactions as well as state-of-the-art van der Waals-corrected density functional-based approaches are put together both to assess the accuracy of the composite scheme and to better characterize the Ag2/graphene interaction. The present work illustrates how the combination of DFT and post-HF perspectives may be efficient to design simple and reliable ab initio-based schemes in extended systems for surface science applications.
Seel, M.; Ladik, J.
1985-10-01
Hartree-Fock Green's-function studies of end effects on the core-level structure of metallic and insulating quasi-one-dimensional model polymers reveal additional core peaks outside the bulk bands. In the metallic case, shifts to both lower (~-150 meV) and higher (~+50 meV) binding energies are observed, whereas in the insulating case, split-off peaks occur only at the lower-binding-energy side (~-150 meV). It is shown that a positive or negative net valence population alone does not determine the direction of the shift. The binding-energy changes are determined by a detailed balance between the energy loss due to a decrease in the electron-nuclear attraction and the energy gain due to a decrease in the electron-electron repulsion experienced by the core electrons of the end atoms. This can probably also explain why for some metal surfaces, shifts towards lower, and for others, shifts towards higher, binding energies are found. In the valence region of the investigated lithium chains, the ends do not produce localized end states.
Nemykin, Victor N; Hadt, Ryan G
2006-10-01
Influence of molecular geometry, type of exchange-correlation functional, and contraction scheme of basis set applied at the iron nuclei have been tested in the calculation of 57Fe Mössbauer isomer shifts and quadrupole splittings for a wide range of ligand types, as well as oxidation and spin states, in inorganic and organometallic systems. It has been found that uncontraction of the s-part of Wachter's full-electron basis set at the iron nuclei does not appreciably improve the calculated isomer shifts. The observed correlations for all tested sets of geometries are close to each other and predominantly depend on the employed exchange-correlation functional with B3LYP functional being slightly better as compared to BPW91. Both hybrid (B3LYP) and pure (BPW91) exchange-correlation functionals are suitable for the calculation of isomer shifts in organometallic compounds. Surprisingly, it has been found that the hybrid B3LYP exchange-correlation functional completely fails in accurate prediction of quadrupole splittings in ferrocenes, while performance of the pure BPW91 functional for the same systems was excellent. This observation has been explained on the basis of relationship between the amount of Hartree-Fock exchange involved in the applied exchange-correlation functional and the calculated HOMO-LUMO energy gap in ferrocenes. On the basis of this explanation, use of only pure exchange-correlation functionals has been suggested for accurate prediction of Mössbauer spectra parameters in ferrocenes.
H. Mariji
2016-01-01
Full Text Available The nucleon single-particle energies (SPEs of the selected nuclei, that is, O16, Ca40, and Ni56, are obtained by using the diagonal matrix elements of two-body effective interaction, which generated through the lowest-order constrained variational (LOCV calculations for the symmetric nuclear matter with the Aυ18 phenomenological nucleon-nucleon potential. The SPEs at the major levels of nuclei are calculated by employing a Hartree-Fock inspired scheme in the spherical harmonic oscillator basis. In the scheme, the correlation influences are taken into account by imposing the nucleon effective mass factor on the radial wave functions of the major levels. Replacing the density-dependent one-body momentum distribution functions of nucleons, n(k,ρ, with the Heaviside functions, the role of n(k,ρ in the nucleon SPEs at the major levels of the selected closed shell nuclei is investigated. The best fit of spin-orbit splitting is taken into account when correcting the major levels of the nuclei by using the parameterized Wood-Saxon potential and the Aυ18 density-dependent mean field potential which is constructed by the LOCV method. Considering the point-like protons in the spherical Coulomb potential well, the single-proton energies are corrected. The results show the importance of including n(k,ρ, instead of the Heaviside functions, in the calculation of nucleon SPEs at the different levels, particularly the valence levels, of the closed shell nuclei.
Simenel, Cédric; Kedziora, David J
2011-01-01
Collisions of actinide nuclei form, during very short times of few zs ($10^{-21}$ s), the heaviest ensembles of interacting nucleons available on Earth. Such collisions are used to produce super-strong electric fields by the huge number of interacting protons to test spontaneous positron-electron pair emission (vacuum decay) predicted by the quantum electrodynamics (QED) theory. Multi-nucleon transfer in actinide collisions could also be used as an alternative way to fusion in order to produce neutron-rich heavy and superheavy elements thanks to inverse quasifission mechanisms. Actinide collisions are studied in a dynamical quantum microscopic approach. The three-dimensional time-dependent Hartree-Fock (TDHF) code {\\textsc{tdhf3d}} is used with a full Skyrme energy density functional to investigate the time evolution of expectation values of one-body operators, such as fragment position and particle number. This code is also used to compute the dispersion of the particle numbers (e.g., widths of fragment mass...
Rodriguez-Bautista, Mariano; Díaz-García, Cecilia; Navarrete-López, Alejandra M; Vargas, Rubicelia; Garza, Jorge
2015-07-21
In this report, we use a new basis set for Hartree-Fock calculations related to many-electron atoms confined by soft walls. One- and two-electron integrals were programmed in a code based in parallel programming techniques. The results obtained with this proposal for hydrogen and helium atoms were contrasted with other proposals to study just one and two electron confined atoms, where we have reproduced or improved the results previously reported. Usually, an atom enclosed by hard walls has been used as a model to study confinement effects on orbital energies, the main conclusion reached by this model is that orbital energies always go up when the confinement radius is reduced. However, such an observation is not necessarily valid for atoms confined by penetrable walls. The main reason behind this result is that for atoms with large polarizability, like beryllium or potassium, external orbitals are delocalized when the confinement is imposed and consequently, the internal orbitals behave as if they were in an ionized atom. Naturally, the shell structure of these atoms is modified drastically when they are confined. The delocalization was an argument proposed for atoms confined by hard walls, but it was never verified. In this work, the confinement imposed by soft walls allows to analyze the delocalization concept in many-electron atoms.
Bouazza, Safa; Palmeri, Patrick; Quinet, Pascal
2017-09-01
We present a semi-empirical determination of Mo II radiative parameters in a wide wavelength range 1716-8789 Å. Our fitting procedure to experimental oscillator strengths available in the literature permits us to provide reliable values for a large number of Mo II lines, predicting previously unmeasured oscillator strengths of lines involving 4d45p and 4d35s5p odd-parity configurations. The extracted transition radial integral values are compared with ab-initio calculations: on average they are 0.88 times the values obtained with the basic pseudo-relativistic Hartree Fock method and they agree well when core polarization effects are included. When making a survey of our present and previous studies and including also those given in the literature we observe as general trends a decreasing of transition radial integral values with filling nd shells of the same principal quantum numbers for ndk(n + 1)s → ndk(n + 1)p transitions.
Rodriguez-Bautista, Mariano; Díaz-García, Cecilia; Navarrete-López, Alejandra M.; Vargas, Rubicelia; Garza, Jorge
2015-07-01
In this report, we use a new basis set for Hartree-Fock calculations related to many-electron atoms confined by soft walls. One- and two-electron integrals were programmed in a code based in parallel programming techniques. The results obtained with this proposal for hydrogen and helium atoms were contrasted with other proposals to study just one and two electron confined atoms, where we have reproduced or improved the results previously reported. Usually, an atom enclosed by hard walls has been used as a model to study confinement effects on orbital energies, the main conclusion reached by this model is that orbital energies always go up when the confinement radius is reduced. However, such an observation is not necessarily valid for atoms confined by penetrable walls. The main reason behind this result is that for atoms with large polarizability, like beryllium or potassium, external orbitals are delocalized when the confinement is imposed and consequently, the internal orbitals behave as if they were in an ionized atom. Naturally, the shell structure of these atoms is modified drastically when they are confined. The delocalization was an argument proposed for atoms confined by hard walls, but it was never verified. In this work, the confinement imposed by soft walls allows to analyze the delocalization concept in many-electron atoms.
Mariji, Hodjat
2016-01-01
The nucleon single-particle energies (SPEs) of the selected closed shell nuclei; that is, 16O, 40Ca, and 56Ni, are obtained by using the diagonal matrix elements of two-body effective interaction, which generated through the lowest order constrained variational (LOCV) calculations for the symmetric nuclear matter with the AV18 phenomenological nucleon-nucleon potential. The SPEs at the major levels of nuclei are calculated by employing a Hartree-Fock inspired-scheme in the spherical harmonic oscillator basis. In the scheme, the correlation influences are taken into account by imposing the nucleon effective mass factor on the radial wave functions of the major levels. Replacing the density-dependent one-body momentum distribution functions of nucleons, n(k,rho), with the Heaviside functions, the role of n(k,rho) on the nucleon SPEs at the major levels of the selected closed shell nuclei, is investigated. The best fit of spin-orbit splitting is taken into account when correcting the major levels of the nuclei b...
Lara-Castells, María Pilar de, E-mail: Pilar.deLara.Castells@csic.es [Instituto de Física Fundamental (C.S.I.C.), Serrano 123, E-28006 Madrid (Spain); Mitrushchenkov, Alexander O. [Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallée (France); Stoll, Hermann [Institut für Theoretische Chemie, Universität Stuttgart, D-70550 Stuttgart (Germany)
2015-09-14
A combined density functional (DFT) and incremental post-Hartree-Fock (post-HF) approach, proven earlier to calculate He-surface potential energy surfaces [de Lara-Castells et al., J. Chem. Phys. 141, 151102 (2014)], is applied to describe the van der Waals dominated Ag{sub 2}/graphene interaction. It extends the dispersionless density functional theory developed by Pernal et al. [Phys. Rev. Lett. 103, 263201 (2009)] by including periodic boundary conditions while the dispersion is parametrized via the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)]. Starting with the elementary cluster unit of the target surface (benzene), continuing through the realistic cluster model (coronene), and ending with the periodic model of the extended system, modern ab initio methodologies for intermolecular interactions as well as state-of-the-art van der Waals-corrected density functional-based approaches are put together both to assess the accuracy of the composite scheme and to better characterize the Ag{sub 2}/graphene interaction. The present work illustrates how the combination of DFT and post-HF perspectives may be efficient to design simple and reliable ab initio-based schemes in extended systems for surface science applications.
Agrawal, B K
2004-01-01
We provide for the first time accurate assessments of the consequences of violations of self-consistency in the Hartree-Fock based random phase approximation (RPA) as commonly used to calculate the energy $E_c$ of the nuclear breathing mode. Using several Skyrme interactions we find that the self-consistency violated by ignoring the spin-orbit interaction in the RPA calculation causes a spurious enhancement of the breathing mode energy for spin unsaturated systems. Contrarily, neglecting the Coulomb interaction in the RPA or performing the RPA calculations in the TJ scheme underestimates the breathing mode energy. Surprisingly, our results for the $^{90}$Zr and $^{208}$Pb nuclei for several Skyrme type effective nucleon-nucleon interactions having a wide range of nuclear matter incompressibility ($K_{nm} \\sim 215 - 275$ MeV) and symmetry energy ($J \\sim 27 - 37$ MeV) indicate that the net uncertainty ($\\delta E_c \\sim 0.3$ MeV) is comparable to the experimental one.
Cheng, Lan, E-mail: chenglanster@gmail.com [Institute for Theoretical Chemistry, Department of Chemistry and Biochemistry, The University of Texas at Austin, Austin, Texas 78712 (United States); Stopkowicz, Stella, E-mail: stella.stopkowicz@kjemi.uio.no [Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, N-0315 Oslo (Norway); Gauss, Jürgen, E-mail: gauss@uni-mainz.de [Institut für Physikalische Chemie, Universität Mainz, D-55099 Mainz (Germany)
2013-12-07
A perturbative approach to compute second-order spin-orbit (SO) corrections to a spin-free Dirac-Coulomb Hartree-Fock (SFDC-HF) calculation is suggested. The proposed scheme treats the difference between the DC and SFDC Hamiltonian as perturbation and exploits analytic second-derivative techniques. In addition, a cost-effective scheme for incorporating relativistic effects in high-accuracy calculations is suggested consisting of a SFDC coupled-cluster treatment augmented by perturbative SO corrections obtained at the HF level. Benchmark calculations for the hydrogen halides HX, X = F-At as well as the coinage-metal fluorides CuF, AgF, and AuF demonstrate the accuracy of the proposed perturbative treatment of SO effects on energies and electrical properties in comparison with the more rigorous full DC treatment. Furthermore, we present, as an application of our scheme, results for the electrical properties of AuF and XeAuF.
Caffarel, Michel; Scemama, Anthony; Ramírez-Solís, Alejandro
2014-01-01
We present a comparative study of the spatial distribution of the spin density (SD) of the ground state of CuCl2 using Density Functional Theory (DFT), quantum Monte Carlo (QMC), and post-Hartree-Fock wavefunction theory (WFT). A number of studies have shown that an accurate description of the electronic structure of the lowest-lying states of this molecule is particularly challenging due to the interplay between the strong dynamical correlation effects in the 3d shell of the copper atom and the delocalization of the 3d hole over the chlorine atoms. It is shown here that qualitatively different results for SD are obtained from these various quantum-chemical approaches. At the DFT level, the spin density distribution is directly related to the amount of Hartree-Fock exchange introduced in hybrid functionals. At the QMC level, Fixed-node Diffusion Monte Carlo (FN-DMC) results for SD are strongly dependent on the nodal structure of the trial wavefunction employed (here, Hartree-Fock or Kohn-Sham with a particula...
Dobaczewski, J.; Olbratowski, P.
2005-05-01
We describe the new version (v2.08k) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. Similarly as in the previous version (v2.08i), all symmetries can be broken, which allows for calculations with angular frequency and angular momentum tilted with respect to the mass distribution. In the new version, three minor errors have been corrected. New Version Program SummaryTitle of program: HFODD; version: 2.08k Catalogue number: ADVA Catalogue number of previous version: ADTO (Comput. Phys. Comm. 158 (2004) 158) Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVA Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Does the new version supersede the previous one: yes Computers on which this or another recent version has been tested: SG Power Challenge L, Pentium-II, Pentium-III, AMD-Athlon Operating systems under which the program has been tested: UNIX, LINUX, Windows-2000 Programming language used: Fortran Memory required to execute with typical data: 10M words No. of bits in a word: 64 No. of lines in distributed program, including test data, etc.: 52 631 No. of bytes in distributed program, including test data, etc.: 266 885 Distribution format:tar.gz Nature of physical problem: The nuclear mean-field and an analysis of its symmetries in realistic cases are the main ingredients of a description of nuclear states. Within the Local Density Approximation, or for a zero-range velocity-dependent Skyrme interaction, the nuclear mean-field is local and velocity dependent. The locality allows for an effective and fast solution of the self-consistent Hartree-Fock equations, even for heavy nuclei, and for various nucleonic ( n-particle n-hole) configurations, deformations, excitation energies, or angular momenta. Similar Local Density Approximation in the particle-particle channel, which is equivalent to using a zero
Salah, Wa'el; Hassouneh, Ola
2017-04-01
We computed the energy levels, oscillator strengths f_{ij}, the radiative transition rates A_{ij}, the Landé g -factor, the magnetic dipole moment and the electric quadrupole hyperfine constants of the intermediate Rydberg series ns [k]J ( 4 ≤ n ≤ 6), nd [k]J (3 ≤ n ≤ 4), np [k]J (4 ≤ n ≤ 5) relative to the ground state 3p6 1S0 for neutral argon atom spectra. The values are obtained in the framework of the multiconfiguration Dirac-Hartree-Fock (MCDHF) approach. In this approach, Breit interaction, leading quantum electrodynamics (QED) effects and self-energy correction are taken into account. Moreover, these spectroscopic parameters have been calculated for many levels belonging to the configuration 3p54s, 3p55s, 3p56s, 3p53d, 3p54d, 3p54p, 3p55p as well as for transitions between levels 3p54s-3p54p, 3p54p-3p53d, 3p54p-3p55s, 3p55s-3p55p and 3p55p-3p56s. The large majority of the lines from the 4p-5s and 4p-3d, 5s-5p and 5p-6s transition arrays have been observed and the calculations are consistent with the J -file-sum rule. The obtained theoretical values are compared with previous experimental and theoretical data available in the literature. An overall satisfactory agreement is noticed allowing assessing the reliability of our data.
Sundholm, Dage; Olsen, Jeppe
1993-04-01
The atomic quadrupole moments Qzz of Be(2s2p;3P2), Al(3p;2P3/2), In(5p;2P3/2), Ne(2p53s3P2), Ar(3p54s;3P2), Kr(4p55s;3P2), and Xe(5p56s;3P2) have been calculated using a finite-element multiconfiguration Hartree-Fock method. The obtained Qzz(Be) of 2.265 a.u. agrees with previously calculated values. The calculated Qzz(Al) and Qzz(In) of 2.579 and 3.165 a.u. are in good agreement with the experimental values of 2.53(15) a.u. and 2.94(10) a.u. A large s-d polarization contribution to the Qzz of the rare gases is found in the present calculations. The correlation contributions from double (D), triple (T), and quadruple (Q) excitations to the Qzz of the rare gases alternate; the total DTQ correlation contribution is negligibly small for Ne, Ar, and Kr, while the DTQ correlation contribution to the Qzz(Xe) is 25% of the final Qzz. The final values are Qzz(Ne)=-0.0506 a.u., Qzz(Ar)=-0.0553 a.u., Qzz(Kr)=+0.0601 a.u., and Qzz(Xe)=+0.4505 a.u., as compared to the experimental values of -0.048(5) a.u., -0.042(4) a.u., +0.046(5) a.u., and +0.30(3) a.u. for Ne, Ar, Kr, and Xe, respectively.
Yoshida, Tatsusada; Hayashi, Takahisa; Mashima, Akira; Sasahara, Katsunori; Chuman, Hiroshi
2016-01-15
Accurate prediction of the intermolecular interaction energy (ΔEbind) has been a challenging and serious problem. Current in silico drug screening demands efficient and accurate evaluation of ΔEbind for ligands and their target proteins. It is desirable that ΔEbind including the dispersion interaction energy (Edisp) is calculated using a post-Hartree-Fock (HF) theory, such as the high-order coupled-cluster one, with a larger basis set. However, it remains computationally too expensive to apply such a one to large molecular systems. As another problem, it is necessary to consider the contribution of the basis set superposition error (BSSE) in calculation of ΔEbind. In Bioorg. Med. Chem. Lett. 2014 and 2015, we proposed simple and efficient corrections of dispersion and BSSE for the HF theory, which is not able to express the dispersion interaction energy correctly. The current Letter, as the final one in the series, aims to verify the HF theory enhanced by the dispersion correction (HF-Dtq) in the light of reproducibility of 'accurate' intermolecular ligand-protein interaction energy values, with comprehensive comparison with the MP2 and recently proposed various DFT-D theories. Taking ΔEbind calculated with the coupled-cluster theory coupled with a complete basis set as a reference, ΔEbind of over a hundred small sized noncovalent complexes as well as real ligand-protein complexes models was systematically examined in terms of accuracy and computational cost. The comprehensive comparison in the current work showed that HF-Dtq is a practical and reliable approach for in silico drug screening and quantitative structure-activity relationships.
Phillips, Jordan J; Peralta, Juan E
2011-01-21
We assess the dependence of magnetic exchange couplings on the variation of Hartree-Fock exchange (HFX) admixture in global hybrid functionals and the range-separation parameter ω in range-separated hybrid functionals in a set of 12 spin-1/2 binuclear transition metal complexes. The global hybrid PBEh (hybrid Perdew-Burke-Ernzerhof) and range-separated hybrids HSE (Heyd-Scuseria-Ernzerhof) and LC-ωPBE (long-range corrected hybrid PBE) are employed for this assessment, and exchange couplings are calculated from energy differences within the framework of the spin-projected approach. It is found that these functionals perform optimally for magnetic exchange couplings with 35% HFX admixture for PBEh, ω = 0.50 a.u.(-1) for LC-ωPBE, and ω at or near 0.0 a.u.(-1) for HSE (which corresponds to PBEh). We find that in their standard respective forms, LC-ωPBE slightly outperforms PBEh, while PBEh with 35% HFX yields exchange couplings closer to experiment than those of LC-ωPBE with ω = 0.50 a.u.(-1). Additionally, we show that the profile of exchange couplings with respect to ω in HSE is appreciably flat from 0 to 0.2 a.u.(-1). This combined with the fact that HSE is computationally more tractable than global hybrids makes HSE an attractive alternative for the evaluation of exchange couplings in extended systems. These results are rationalized with respect to how varying the parameters within these functionals affects the delocalization of the magnetic orbitals, and conclusions are made regarding the relative importance of range separation versus global mixing of HFX for the calculation of exchange couplings.
Gontchar, I. I.; Bhattacharya, R.; Chushnyakova, M. V.
2014-03-01
We calculate the capture (fusion) cross sections for nine reactions involving spherical nuclei: O16 + O16, Si28, Zr92, Sm144, Pb208; Si28 + Si28, Zr92, Pb208; S32 + Pb208. For six of them precision data are available in the literature. Analysis of these precision data within the framework of the single-barrier penetration model based on the Woods-Saxon profile for the strong nucleus-nucleus interaction potential (SnnP) gave rise to the problem of the apparently large diffuseness of the SnnP [Newton et al., Phys. Rev. C 70, 024605 (2004), 10.1103/PhysRevC.70.024605]. Our fluctuation-dissipation trajectory model is based on the double-folding approach with the density-dependent M3Y NN forces including the finite-range exchange part. For the nuclear matter density the Skyrme-Hartree-Fock approach including the tensor interaction is applied. The resulting nucleus-nucleus potential possesses rather small (normal) diffuseness. The strength of the radial friction KR is used as the free parameter of the model. It turns out that for four of the five reactions induced by O16 (except O16 + Pb208) the calculated cross sections cannot be brought into agreement with the data within the experimental errors. This suggests that the calculated nuclear density is incorrect for O16. For the reactions not involving O16 and, surprisingly, for the O16 + Pb208 reaction the agreement with the data within 2-5% is achieved at KR=1.2×10-2 to 3.0×10-2MeV-1zs which is in accord with the previous works.
Umar, A. S.; Oberacker, V. E.; Simenel, C.
2016-08-01
Background: Synthesis of superheavy elements (SHEs) with fusion-evaporation reactions is strongly hindered by the quasifission (QF) mechanism which prevents the formation of an equilibrated compound nucleus and which depends on the structure of the reactants. New SHEs have been recently produced with doubly-magic 48Ca beams. However, SHE synthesis experiments with single-magic 50Ti beams have so far been unsuccessful. Purpose: In connection with experimental searches for Z =117 ,119 superheavy elements, we perform a theoretical study of fusion and quasifission mechanisms in 48Ca,50Ti+249Bk reactions in order to investigate possible differences in reaction mechanisms induced by these two projectiles. Methods: The collision dynamics and the outcome of the reactions are studied using unrestricted time-dependent Hartree-Fock (TDHF) calculations as well as the density-constrained TDHF method to extract the nucleus-nucleus potentials and the excitation energy in each fragment. Results: Nucleus-nucleus potentials, nuclear contact times, masses and charges of the fragments, as well as their kinetic and excitation energies strongly depend on the orientation of the prolate 249Bk nucleus. Long contact times associated with fusion are observed in collisions of both projectiles with the side of the 249Bk nucleus, but not on collisions with its tip. The energy and impact parameter dependencies of the fragment properties, as well as their mass-angle and mass-total kinetic energy correlations are investigated. Conclusions: Entrance channel reaction dynamics are similar with both 48Ca and 50Ti projectiles. Both are expected to lead to the formation of a compound nucleus by fusion if they have enough energy to get in contact with the side of the 249Bk target.
Boblest, S.; Meyer, D.; Wunner, G.
2014-11-01
We present a quantum Monte Carlo application for the computation of energy eigenvalues for atoms and ions in strong magnetic fields. The required guiding wave functions are obtained with the Hartree-Fock-Roothaan code described in the accompanying publication (Schimeczek and Wunner, 2014). Our method yields highly accurate results for the binding energies of symmetry subspace ground states and at the same time provides a means for quantifying the quality of the results obtained with the above-mentioned Hartree-Fock-Roothaan method. Catalogue identifier: AETV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AETV_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 72 284 No. of bytes in distributed program, including test data, etc.: 604 948 Distribution format: tar.gz Programming language: C++. Computer: Cluster of 1-˜500 HP Compaq dc5750. Operating system: Linux. Has the code been vectorized or parallelized?: Yes. Code includes MPI directives. RAM: 500 MB per node Classification: 2.1. External routines: Boost::Serialization, Boost::MPI, LAPACK BLAS Nature of problem: Quantitative modelings of features observed in the X-ray spectra of isolated neutron stars are hampered by the lack of sufficiently large and accurate databases for atoms and ions up to the last fusion product iron, at high magnetic field strengths. The predominant amount of line data in the literature has been calculated with Hartree-Fock methods, which are intrinsically restricted in precision. Our code is intended to provide a powerful tool for calculating very accurate energy values from, and thereby improving the quality of, existing Hartree-Fock results. Solution method: The Fixed-phase quantum Monte Carlo method is used in combination with guiding functions obtained in Hartree-Fock
Hamel, Sébastien; Casida, Mark E.; Salahub, Dennis R.
2001-05-01
The Roothaan-Hartree-Fock (HF) method has been implemented in deMon-DynaRho within the resolution-of-the-identity (RI) auxiliary-function approximation. While previous studies have focused primarily upon the effect of the RI approximation on total energies, very little information has been available regarding the effect of the RI approximation on orbital energies, even though orbital energies play a central role in many theories of ionization and excitation. We fill this gap by testing the accuracy of the RI approximation against non-RI-HF calculations using the same basis sets, for the occupied orbital energies and an equal number of unoccupied orbital energies of five small molecules, namely CO, N2, CH2O, C2H4, and pyridine (in total 102 orbitals). These molecules have well-characterized excited states and so are commonly used to test and validate molecular excitation spectra computations. Of the deMon auxiliary basis sets tested, the best results are obtained with the (44) auxiliary basis sets, yielding orbital energies to within 0.05 eV, which is adequate for analyzing typical low resolution polyatomic molecule ionization and excitation spectra. Interestingly, we find that the error in orbital energies due to the RI approximation does not seem to increase with the number of electrons. The absolute RI error in the orbital energies is also roughly related to their absolute magnitude, being larger for the core orbitals where the magnitude of orbital energy is large and smallest where the molecular orbital energy is smallest. Two further approximations were also considered, namely uniterated ("zero-order") and single-iteration ("first-order") calculations of orbital energies beginning with a local density approximation initial guess. We find that zero- and first-order orbital energies are very similar for occupied but not for unoccupied orbitals, and that the first-order orbital energies are fairly close to the corresponding fully converged values. Typical root
Matta, Chérif F
2010-04-30
This article compares molecular properties and atomic properties defined by the quantum theory of atoms in molecules (QTAIM) obtained from three underlying levels of theory: MP2(full), density functional theory (DFT) (B3LYP), and Hartree-Fock (H-F). The same basis set (6-311++G(d,p)) has been used throughout the study. The calculations and comparisons were applied to a set of 30 small molecules representing common fragments of biological molecules. The molecular properties investigated are the energies and the electrostatic moments (up to and including the quadrupoles), and the atomic properties include electron populations (and atomic charge), atomic dipolar and quadrupolar polarizations, atomic volumes, and corrected and raw atomic energies. The Cartesian distance between dipole vectors and the Frobenius distance between the quadrupole tensors calculated at the three levels of theory provide a measure of their correlation (or lack thereof). With the exception of energies (atomic and molecular), it is found that both DFT and H-F are in excellent agreement with MP2, especially with regards to the electrostatic mutipoles up to the quadrupoles, but DFT and MP2 agree better in almost all studied properties (with the exception of molecular geometries). QTAIM properties whether obtained from H-F, DFT(B3LYP), or MP2 calculations when used in the construction of empirical correlations with experiment such as quantitative structure-activity-(or property)-relationships (QSAR/QSPR) are equivalent (because the properties calculated at the three levels are very highly correlated among themselves with r(2) typically >0.95, and therefore preserving trends). These results suggest that the massive volume of results that were published in the older literature at the H-F level is valid especially when used to study trends or in QSAR or QSPR studies, and, as long as our test set of molecules is representative, there is no pressing need to re-evaluate them at other levels of theory
Simenel, Cédric; Golabek, Cédric; Kedziora, David J.
2011-10-01
Collisions of actinide nuclei form, during very short times of few zs (10-21 s), the heaviest ensembles of interacting nucleons available on Earth. Such collisions are used to produce super-strong electric fields by the huge number of interacting protons to test spontaneous positron-electron pair emission (vacuum decay) predicted by the quantum electrodynamics (QED) theory. Multi-nucleon transfer in actinide collisions could also be used as an alternative way to fusion in order to produce neutron-rich heavy and superheavy elements thanks to inverse quasifission mechanisms. Actinide collisions are studied in a dynamical quantum microscopic approach. The three-dimensional time-dependent Hartree-Fock (TDHF) code tdhf3d is used with a full Skyrme energy density functional to investigate the time evolution of expectation values of one-body operators, such as fragment position and particle number. This code is also used to compute the dispersion of the particle numbers (e.g., widths of fragment mass and charge distributions) from TDHF transfer probabilities, on the one hand, and using the BalianVeneroni variational principle, on the other hand. A first application to test QED is discussed. Collision times in 238U+238U are computed to determine the optimum energy for the observation of the vacuum decay. It is shown that the initial orientation strongly affects the collision times and reaction mechanism. The highest collision times predicted by TDHF in this reaction are of the order of ~ 4 zs at a center of mass energy of 1200 MeV. According to modern calculations based on the Dirac equation, the collision times at Ecm > 1 GeV are sufficient to allow spontaneous electron-positron pair emission from QED vacuum decay, in case of bare uranium ion collision. A second application of actinide collisions to produce neutron-rich transfermiums is discussed. A new inverse quasifission mechanism associated to a specific orientation of the nuclei is proposed to produce transfermium
Chushnyakova, M. V.; Bhattacharya, R.; Gontchar, I. I.
2014-07-01
Background: In our previous paper [Gontchar et al., Phys. Rev. C 89, 034601 (2014), 10.1103/PhysRevC.89.034601] we have calculated the capture (fusion) excitation functions for several reactions with O16,Si28, and S32 nuclei as the projectiles and Zr92,Sm144, and Pb208 nuclei as the targets. These calculations were performed by using our fluctuation-dissipation trajectory model based on the double-folding approach with the density-dependent M3Y NN forces that include the finite range exchange part. For the nuclear matter density the Hartree-Fock approach with the SKP coefficient set that includes the tensor interaction was applied. It was found that for most of the reactions induced by O16 the calculated cross sections cannot be brought into agreement with the data. This suggested that the deviation in the calculated nuclear density for O16 from the experimental one was crucial. Method: The SKX parameter set is used to obtain the nuclear densities. Reactions with C12 and S36 as the projectiles and Pb204 as the target are included in the analysis in addition to those of the previous paper. Only data that correspond to the collision energy Ec.m.>1.1UB0 (UB0 is the s-wave fusion barrier height) are included in the analysis. The radial friction strength KR is used as the individual adjustable parameter for each reaction. Results: For all 13 reactions (91 points) it is possible to reach an agreement with the experimental fusion cross sections within 10%. Only at ten points does the deviation exceed 5%. The value of KR, which provides the best agreement with the data in general, decreases as the system gets heavier in accord with the previous paper [Gontchar et al., Phys. Rev. C 89, 034601 (2014), 10.1103/PhysRevC.89.034601]. A universal analytical approximation for the dependence of KR upon the Coulomb barrier height is found. Conclusions: The developed model is able to reproduce the above-barrier portion of the fusion excitation function within 5% with a probability of
Lara-Castells, María Pilar de, E-mail: Pilar.deLara.Castells@csic.es; Bartolomei, Massimiliano [Instituto de Física Fundamental (C.S.I.C.), Serrano 123, E-28006 Madrid (Spain); Mitrushchenkov, Alexander O. [Laboratoire Modélisation et Simulation Multi Echelle, Université Paris-Est, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallée (France); Stoll, Hermann [Institut für Theoretische Chemie, Universität Stuttgart, D-70550 Stuttgart (Germany)
2015-11-21
The accuracy and transferability of the electronic structure approach combining dispersionless density functional theory (DFT) [K. Pernal et al., Phys. Rev. Lett. 103, 263201 (2009)] with the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)], are validated for the interaction between the noble-gas Ne, Ar, Kr, and Xe atoms and coronene/graphene/graphite surfaces. This approach uses the method of increments for surface cluster models to extract intermonomer dispersion-like (2- and 3-body) correlation terms at coupled cluster singles and doubles and perturbative triples level, while periodic dispersionless density functionals calculations are performed to estimate the sum of Hartree-Fock and intramonomer correlation contributions. Dispersion energy contributions are also obtained using DFT-based symmetry-adapted perturbation theory [SAPT(DFT)]. An analysis of the structure of the X/surface (X = Ne, Ar, Kr, and Xe) interaction energies shows the excellent transferability properties of the leading intermonomer correlation contributions across the sequence of noble-gas atoms, which are also discussed using the Drude oscillator model. We further compare these results with van der Waals-(vdW)-corrected DFT-based approaches. As a test of accuracy, the energies of the low-lying nuclear bound states supported by the laterally averaged X/graphite potentials (X = {sup 3}He, {sup 4}He, Ne, Ar, Kr, and Xe) are calculated and compared with the best estimations from experimental measurements and an atom-bond potential model using the ab initio-assisted fine-tuning of semiempirical parameters. The bound-state energies determined differ by less than 6–7 meV (6%) from the atom-bond potential model. The crucial importance of including incremental 3-body dispersion-type terms is clearly demonstrated, showing that the SAPT(DFT) approach effectively account for these terms. With the deviations from the best experimental-based estimations smaller than 2.3 meV (1.9%), the
Schimeczek, C.; Engel, D.; Wunner, G.
2012-07-01
Our previously published code for calculating energies and bound-bound transitions of medium-Z elements at neutron star magnetic field strengths [D. Engel, M. Klews, G. Wunner, Comput. Phys. Comm. 180 (2009) 302-311] was based on the adiabatic approximation. It assumes a complete decoupling of the (fast) gyration of the electrons under the action of the magnetic field and the (slow) bound motion along the field under the action of the Coulomb forces. For the single-particle orbitals this implied that each is a product of a Landau state and an (unknown) longitudinal wave function whose B-spline coefficients were determined self-consistently by solving the Hartree-Fock equations for the many-electron problem on a finite-element grid. In the present code we go beyond the adiabatic approximation, by allowing the transverse part of each orbital to be a superposition of Landau states, while assuming that the longitudinal part can be approximated by the same wave function in each Landau level. Inserting this ansatz into the energy variational principle leads to a system of coupled equations in which the B-spline coefficients depend on the weights of the individual Landau states, and vice versa, and which therefore has to be solved in a doubly self-consistent manner. The extended ansatz takes into account the back-reaction of the Coulomb motion of the electrons along the field direction on their motion in the plane perpendicular to the field, an effect which cannot be captured by the adiabatic approximation. The new code allows for the inclusion of up to 8 Landau levels. This reduces the relative error of energy values as compared to the adiabatic approximation results by typically a factor of three (1/3 of the original error), and yields accurate results also in regions of lower neutron star magnetic field strengths where the adiabatic approximation fails. Further improvements in the code are a more sophisticated choice of the initial wave functions, which takes into
Schunck, N; McDonnell, J; Satula, W; Sheikh, J A; Staszczak, A; Stoitsov, M; Toivanen, P
2011-01-01
We describe the new version (v2.49s) of the code HFODD which solves the nuclear Skyrme Hartree-Fock (HF) or Skyrme Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite temperature formalism for the HFB and HF+BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead...
El Aouad, N.; Dobaczewski, J.; Dudek, J.; Li, X.; Luo, W.D.; Molique, H.; Bouguettoucha, A.; Byrski, Th.; Beck, F.A.; Curien, D.; Duchene, G.; Finck, Ch.; Kharraja, B
2000-08-28
Structure of eight experimentally known superdeformed bands in the nucleus {sup 151}Tb is analyzed using the results of the Hartree-Fock and Woods-Saxon cranking approaches. It is demonstrated that far going detailed similarities between the two approaches exist and predictions related to the structure of rotational bands calculated within the two models are nearly parallel. An interpretation scenario for the structure of the superdeformed bands is presented and predictions related to the exit spins are made. Small but systematic discrepancies between experiment and theory, analyzed in terms of the dynamical moments, J{sup (2)}, are shown to exist. These discrepancies can be parametrized in terms of a scaling factor f, such that modifications J{sup (1),(2)}{yields}fJ{sup (1),(2)} together with the implied scaling of the frequencies {omega}{yields}f{sup -1}{omega}, correspond systematically better with the experimental data (f{approx_equal}0.9) for both the Woods-Saxon and Hartree-Fock with Skyrme SkM* interactions. The pairing correlations taken into account by using the particle-number-projection technique are shown to increase the disagreement. Sources of these systematic discrepancies are discussed -- they are most likely related to the not yet optimal parametrization of the nuclear interactions used.
Kedziora David J.
2011-10-01
Full Text Available Collisions of actinide nuclei form, during very short times of few zs (10−21 s, the heaviest ensembles of interacting nucleons available on Earth. Such collisions are used to produce super-strong electric ﬁelds by the huge number of interacting protons to test spontaneous positron-electron pair emission (vacuum decay predicted by the quantum electrodynamics (QED theory. Multi-nucleon transfer in actinide collisions could also be used as an alternative way to fusion in order to produce neutron-rich heavy and superheavy elements thanks to inverse quasiﬁssion mechanisms. Actinide collisions are studied in a dynamical quantum microscopic approach. The three-dimensional time-dependent Hartree-Fock (TDHF code tdhf3d is used with a full Skyrme energy density functional to investigate the time evolution of expectation values of one-body operators, such as fragment position and particle number. This code is also used to compute the dispersion of the particle numbers (e.g., widths of fragment mass and charge distributions from TDHF transfer probabilities, on the one hand, and using the BalianVeneroni variational principle, on the other hand. A ﬁrst application to test QED is discussed. Collision times in 238U+238U are computed to determine the optimum energy for the observation of the vacuum decay. It is shown that the initial orientation strongly affects the collision times and reaction mechanism. The highest collision times predicted by TDHF in this reaction are of the order of ~ 4 zs at a center of mass energy of 1200 MeV. According to modern calculations based on the Dirac equation, the collision times at Ecm > 1 GeV are suﬃcient to allow spontaneous electron-positron pair emission from QED vacuum decay, in case of bare uranium ion collision. A second application of actinide collisions to produce neutron-rich transfermiums is discussed. A new inverse quasiﬁssion mechanism associated to a speciﬁc orientation of the nuclei is proposed to
Mackrodt, W. C.
1999-02-01
First principles periodic Hartree-Fock calculations are reported for the P4 2/ mnm(rutile), I4 1/ amd(anatase), Pbca(brookite), Pnma(ramsdellite), Pcbn(colombite), Fdoverline3m(spinel), and Imma(orthorhombic) polymorphs of TiO 2, from which the predicted order of stability is The calculated difference in energy between the rutile and anatase structures is 0.02-0.06 eV, in good agreement with a recent local density approximation (LDA) estimate of 0.033 eV and an experiment enthalpy difference of 0.05 eV. The corresponding Hartree-Fock and LDA differences for the brookite structure are 0.06 and 0.058 eV, respectively. The calculated volumes, which are based on isotropic volume-optimized Hartree-Fock energies, are also in good agreement with recent LDA calculations and with experiment. Spin-unrestricted calculations are reported for the Fmoverline3m, Imma, Pnma, and P4 2/ mmmof LiTiO 2, where the stability is in the order The only reported phase for LiTiO 2is Fmoverline3m, for which the calculated volume is in good agreement with experiment. From the relative stabilities of TiO 2and LiTiO 2, the relative lithium insertion potentials corresponding to TiO 2 → LiTiO 2are deduced, with a maximum variation of 1.6 eV for the different polymorphic routes. The maximum voltage predicted is that for the Immaroute which is ˜1 eV larger than that for Pnma. Direct comparisons with the calculated energy for C2/ mLi 0.5MnO 2 → LiMnO 2lead to an estimate of the voltage for ImmaTiO 2 → LiTiO 2of ˜1.3 eV, which is ˜2.5 eV anodicto the Mn system. The corresponding values for the Pnmapolymorphic route are ˜3 and ˜3.5 eV, respectively. Mulliken population analyses indicate that lithium is completely ionized in LiTiO 2and that the charge transfer is predominantly to the oxygen sublattice. There is a rehybridization of the titanium valence orbitals leading to a slight increase in the 3 dpopulation and strong localization of spin density at the titanium sites with local moments of
Inakura, T; Yamagami, M; Matsuyanagi, K
2002-01-01
With the use of the symmetry-unrestricted cranked Skyrme-Hartree-Fock method in the three-dimensional coordinate-mesh representation, we have carried out a systematic theoretical search for the superdeformed and hyperdeformed rotational bands in the mass A=30-50 region. Along the N=Z line, we have found superdeformed solutions in sup 3 sup 2 S, sup 3 sup 6 Ar, sup 4 sup 0 Ca, sup 4 sup 4 Ti, and hyperdeformed solutions in sup 3 sup 6 Ar, sup 4 sup 0 Ca, sup 4 sup 4 Ti, sup 4 sup 8 Cr. The superdeformed band in sup 4 sup 0 Ca is found to be extremely soft against both the axially symmetric (Y sub 3 sub 0) and asymmetric (Y sub 3 sub 1) octupole deformations. An interesting role of symmetry breaking in the mean field is pointed out.
Nakajima, Yuya; Seino, Junji; Nakai, Hiromi
2016-05-10
An analytical energy gradient for the spin-dependent general Hartree-Fock method based on the infinite-order Douglas-Kroll-Hess (IODKH) method was developed. To treat realistic systems, the local unitary transformation (LUT) scheme was employed both in energy and energy gradient calculations. The present energy gradient method was numerically assessed to investigate the accuracy in several diatomic molecules containing fifth- and sixth-period elements and to examine the efficiency in one-, two-, and three-dimensional silver clusters. To arrive at a practical calculation, we also determined the geometrical parameters of fac-tris(2-phenylpyridine)iridium and investigated the efficiency. The numerical results confirmed that the present method describes a highly accurate relativistic effect with high efficiency. The present method can be a powerful scheme for determining geometries of large molecules, including heavy-element atoms.
Lacivita, Valentina; Rérat, Michel; Kirtman, Bernard; Ferrero, Mauro; Orlando, Roberto; Dovesi, Roberto
2009-11-01
The high-frequency dielectric ɛ and the first nonlinear electric susceptibility χ(2) tensors of crystalline potassium dihydrogen phosphate (KH2PO4) are calculated by using the coupled perturbed Hartree-Fock and Kohn-Sham methods as implemented in the CRYSTAL code. The effect of basis sets of increasing size on ɛ and χ(2) is explored. Five different levels of theory, namely, local-density approximation, generalized gradient approximation (PBE), hybrids (B3LYP and PBE0), and HF are compared using the experimental and theoretical structures corresponding not only to the tetragonal geometry I4d2 at room temperature but also to the orthorhombic phase Fdd2 at low temperature. Comparison between the two phases and their optical behavior is made. The calculated results for the tetragonal phase are in good agreement with the experimental data.
Langhoff, S. R.; Scott, W. R.; Suzuki, N.; Chong, D. P.
1979-01-01
Ordinary Rayleigh-Schroudinger perturbation theory with Moller-Plesset (RSMP) partitioning is used to calculate second- and third-order correlation corrections to the CHF polarizability and dipole moment of the water molecule by a finite-field procedure. Pade approximants are found to be useful in accelerating the convergence of the property perturbation expansions. Field-induced polarization functions suitable for polarizability calculations are determined. The average polarizability calculated, neglecting vibrational averaging, with Dunning's (9s5p/4s-4s2p/2s) contracted GTO basis set augmented by field-induced lslp2d/lp polarization functions is within 3 per cent of the experimental result. Correlation corrections to the dipole moment and polarizability of the water molecule calculated by the finite-field RSMP and single + double excitation CI(SDCI) methods for the same basis set are found to be in close agreement. The RSMP approach has the advantages of being size-consistent and of being capable of greater efficiency than the SCDI method. Comparative calculations carried out using Epstein-Nesbet partitioning show that through third order RSEN correlation perturbation expansions for the dipole moment and polarizability are less rapidly convergent than RSMP expansions. However, reasonable accord with RSMP results can be achieved by using Pade approximants to accelerate the convergence of RSEN energy perturbation expansions. The convergence of RSMP property correlation expansions based on the zeroth-order uncoupled-Hartree-Fock (UCHF) and coupled-Hartree-Fock (CHF) approximations are compared through third order. Whereas the CHF + RSMP expansions are for practical purposes fully converged, the UCHF + RSMP expansions are not adequately converged.
Linker, Gerrit-Jan; Loosdrecht , van Paul H.M.; van Duijnen, Piet Th.; Broer, Ria
2015-01-01
The insulating and conducting phases of (EDO-TTF)(2)PF6 were studied by all electron, periodic Hartre-Fock and hybrid density functional calculations. Electronic properties, such as the electronic band structure, the density of states and the Fermi surface are discussed in relation to the metal-insu
Kussmann, Jörg; Ochsenfeld, Christian
2007-11-28
A density matrix-based time-dependent self-consistent field (D-TDSCF) method for the calculation of dynamic polarizabilities and first hyperpolarizabilities using the Hartree-Fock and Kohn-Sham density functional theory approaches is presented. The D-TDSCF method allows us to reduce the asymptotic scaling behavior of the computational effort from cubic to linear for systems with a nonvanishing band gap. The linear scaling is achieved by combining a density matrix-based reformulation of the TDSCF equations with linear-scaling schemes for the formation of Fock- or Kohn-Sham-type matrices. In our reformulation only potentially linear-scaling matrices enter the formulation and efficient sparse algebra routines can be employed. Furthermore, the corresponding formulas for the first hyperpolarizabilities are given in terms of zeroth- and first-order one-particle reduced density matrices according to Wigner's (2n+1) rule. The scaling behavior of our method is illustrated for first exemplary calculations with systems of up to 1011 atoms and 8899 basis functions.
Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
Nam, Phan Thanh; Napiorkowski, Marcin; Solovej, Jan Philip
2016-01-01
We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our...
Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
Nam, Phan Thanh; Napiorkowski, Marcin; Solovej, Jan Philip
2016-01-01
We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our...
Rabilloud, Franck
2014-10-14
Absorption spectra of Ag20 and Ag55(q) (q = +1, -3) nanoclusters are investigated in the framework of the time-dependent density functional theory in order to analyse the role of the d electrons in plasmon-like band of silver clusters. The description of the plasmon-like band from calculations using density functionals containing an amount of Hartree-Fock exchange at long range, namely, hybrid and range-separated hybrid (RSH) density functionals, is in good agreement with the classical interpretation of the plasmon-like structure as a collective excitation of valence s-electrons. In contrast, using local or semi-local exchange functionals (generalized gradient approximations (GGAs) or meta-GGAs) leads to a strong overestimation of the role of d electrons in the plasmon-like band. The semi-local asymptotically corrected model potentials also describe the plasmon as mainly associated to d electrons, though calculated spectra are in fairly good agreement with those calculated using the RSH scheme. Our analysis shows that a portion of non-local exchange modifies the description of the plasmon-like band.
Andrea Alparone
2014-05-01
Structural, energetic, spectroscopic, linear and nonlinear optical (NLO) properties of the environmental mutagens 1- and 3-nitro-6-azabenzo[]pyrene -oxides were characterized by means of Hartree-Fock as well as B3LYP and CAM-B3LYP density functional theory computations. The NLO investigations were performed for the second harmonic generation (SHG) and electro-optical Pockels effect (EOPE) at the incident wavelength of 1064 nm. The results show that, the predicted structures, vibrational spectra, nucleus independent chemical shifts, ionization energy, electron affinity as well as electronic polarizabilities are little influenced by the position of the nitro substituent. Differently, the dipole moment () and the first-order hyperpolarizabilities () are significantly dependent on the isomerization. The rather different mutagenic activity of the investigated isomers could be related to their diverse polarity. At the CAM-B3LYP level, when passing from the 1- to the 3-nitro-6-azabenzo[a]pyrene -oxide isomer, the datum increases by about 5 D (a factor of three), whereas the static and dynamic values decrease by ca. 50%. Dipole moment measurement and SHG and EOPE NLO techniques are potentially useful to distinguish these important environmental mutagens.
Mamedov, B. A.; Çopuroğlu, E.
2016-06-01
In this work, we study the effects of self-friction field on the states of a single configuration of closed and open shells by using the Combined Hartree-Fock-Roothaan equations for atomic-molecular and nuclear systems. Here, we present a program that implements the evaluation of the various properties of atoms and molecular systems with respect to the various values of self-friction quantum numbers. An especially fast and accurate algorithm for the calculation of the self-friction multicenter molecular integrals is obtained by using one-range addition theorems. To demonstrate the action of self-friction field on the atomic and molecular systems we have performed the calculations of H2O, CH3, CH2 and NH3 molecules. For the derivations of the orbital, kinetic and total energies and linear combination coefficients, the results are given for various values of self-friction quantum numbers. For various values of self-friction quantum numbers the obtained results of the orbital, kinetic and total energies and linear combination coefficients have been analyzed.
He, Xiao; Ryu, Shinsei; Hirata, So
2014-01-14
Finite-temperature extensions of ab initio Gaussian-basis-set spin-restricted Hartree-Fock (HF) and second-order many-body perturbation (MP2) theories are implemented for infinitely extended, periodic, one-dimensional solids and applied to the Peierls and charge-density-wave (CDW) transitions in polyyne and all-trans polyacetylene. The HF theory predicts insulating CDW ground states for both systems in their equidistant structures at low temperatures. In the same structures, they turn metallic at high temperatures. Starting from the "dimerized" low-temperature equilibrium structures, the systems need even higher temperatures to undergo a Peierls transition, which is accompanied by geometric as well as electronic distortions from dimerized to non-dimerized forms. The conventional finite-temperature MP2 theory shows a sign of divergence in any phase at any nonzero temperature and is useless. The renormalized finite-temperature MP2 (MP2R) theory is divergent only near metallic electronic structures, but is well behaved elsewhere. MP2R also predicts CDW and Peierls transitions occurring at two different temperatures. The effect of electron correlation is primarily to lower the Peierls transition temperature.
Caffarel, Michel; Giner, Emmanuel; Scemama, Anthony; Ramírez-Solís, Alejandro
2014-12-09
We present a comparative study of the spatial distribution of the spin density of the ground state of CuCl2 using Density Functional Theory (DFT), quantum Monte Carlo (QMC), and post-Hartree-Fock wave function theory (WFT). A number of studies have shown that an accurate description of the electronic structure of the lowest-lying states of this molecule is particularly challenging due to the interplay between the strong dynamical correlation effects in the 3d shell and the delocalization of the 3d hole over the chlorine atoms. More generally, this problem is representative of the difficulties encountered when studying open-shell metal-containing molecular systems. Here, it is shown that qualitatively different results for the spin density distribution are obtained from the various quantum-mechanical approaches. At the DFT level, the spin density distribution is found to be very dependent on the functional employed. At the QMC level, Fixed-Node Diffusion Monte Carlo (FN-DMC) results are strongly dependent on the nodal structure of the trial wave function. Regarding wave function methods, most approaches not including a very high amount of dynamic correlation effects lead to a much too high localization of the spin density on the copper atom, in sharp contrast with DFT. To shed some light on these conflicting results Full CI-type (FCI) calculations using the 6-31G basis set and based on a selection process of the most important determinants, the so-called CIPSI approach (Configuration Interaction with Perturbative Selection done Iteratively) are performed. Quite remarkably, it is found that for this 63-electron molecule and a full CI space including about 10(18) determinants, the FCI limit can almost be reached. Putting all results together, a natural and coherent picture for the spin distribution is proposed.
Schunck, N.; Dobaczewski, J.; McDonnell, J.; Satuła, W.; Sheikh, J. A.; Staszczak, A.; Stoitsov, M.; Toivanen, P.
2012-01-01
We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite-temperature formalism for the HFB and HF + BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex-breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected. New version program summaryProgram title:HFODD (v2.49t) Catalogue identifier: ADFL_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFL_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence v3 No. of lines in distributed program, including test data, etc.: 190 614 No. of bytes in distributed program, including test data, etc.: 985 898 Distribution
Entanglement in fermionic Fock space
Sárosi, Gábor
2013-01-01
We propose a generalization of the usual SLOCC and LU classification of entangled pure state fermionic systems based on the Spin group. Our generalization uses the fact that there is a representation of this group acting on the fermionic Fock space which when restricted to fixed particle number subspaces recovers naturally the usual SLOCC transformations. The new ingredient is the occurrence of Bogoliubov transformations of the whole Fock space changing the particle number. The classification scheme built on the Spin group prohibits naturally entanglement between states containing even and odd number of fermions. In our scheme the problem of classification of entanglement types boils down to the classification of spinors where totally separable states are represented by so called pure spinors. We construct the basic invariants of the Spin group and show how some of the known SLOCC invariants are just their special cases. As an example we present the classification of fermionic systems with a Fock space based ...
Integrable Bogoliubov Transform and Integrable Model
王宁
2003-01-01
By defining Bogoliubov transform as a function of parameters, the integrability of the Bogoliubov transform in parameter space is investigated. It is shown that integrable Bogoliubov transform is closely related to the known integrable model. The relation between the integrable Bogoliubov transform and geometric phase of vacuum induced by the Bogoliubov transform is also discussed.
Entanglement in the Bogoliubov vacuum
Poulsen, Uffe Vestergaard; Meyer, T.; Lewenstein, M.
2005-01-01
We analyze the entanglement properties of the Bogoliubov vacuum, which is obtained as a second-order approximation to the ground state of an interacting Bose-Einstein condensate. We work in one- and two-dimensional lattices and study the entanglement between two groups of sites as a function...
Ab initio Bogoliubov coupled cluster theory for open-shell nuclei
Signoracci, A.; Duguet, T.; Hagen, G.; Jansen, G. R.
2015-06-01
constant for all five nuclei, in both the Hartree-Fock-Bogoliubov and BCCD approximations. Conclusions: The newly developed many-body formalism increases the potential span of ab initio calculations based on single-reference coupled cluster techniques tremendously, i.e., potentially to reach several hundred additional midmass nuclei. The new formalism offers a wealth of potential applications and further extensions dedicated to the description of ground and excited states of open-shell nuclei. Short-term goals include the implementation of three-nucleon forces at the normal-ordered two-body level. Midterm extensions include the approximate treatment of triples corrections and the development of the equation-of-motion methodology to treat both excited states and odd nuclei. Long-term extensions include exact restoration of U(1) and SU(2) symmetries.
Huynh, Tri H V; Shim, Irene; Bohr, Henrik; Abrahamsen, Bjarke; Nielsen, Birgitte; Jensen, Anders A; Bunch, Lennart
2012-06-14
The excitatory amino acid transporters (EAATs) play essential roles in regulating the synaptic concentration of the neurotransmitter glutamate in the mammalian central nervous system. To date, five subtypes have been identified, named EAAT1-5 in humans, and GLAST, GLT-1, EAAC1, EAAT4, and EAAT5 in rodents, respectively. In this paper, we present the design, synthesis, and pharmacological evaluation of seven 7-N-substituted analogues of UCPH-101/102. Analogue 9 inhibited EAAT1 in the micromolar range (IC(50) value 20 μM), whereas analogues 8 and 10 were inactive (IC(50) values >100 μM). The diastereomeric pairs 11a/11b and 12a/12b were separated by HPLC and the absolute configuration assigned by VCD technique in combination with ab initio Hartree-Fock calculations. Analogues 11a (RS-isomer) and 12b (RR-isomer) inhibited EAAT1 (IC(50) values 5.5 and 3.8 μM, respectively), whereas analogues 11b (SS-isomer) and 12a (SR-isomer) failed to inhibit EAAT1 uptake (IC(50) values >300 μM).
Iso-spin Dependent Microscopic Optical Model Potential Based on Dirac Bruckner Haretree Fock Method
无
2011-01-01
The microscopic optical model is investigated in the Dirac-Brueckner-Hartree-Fock (DBHF) framework with Bonn B meson exchange potential. Both real and imaginary parts of isospin-dependent self-energies are derived from a strict projection
Bozkaya, Uğur
2014-09-28
General analytic gradient expressions (with the frozen-core approximation) are presented for density-fitted post-HF methods. An efficient implementation of frozen-core analytic gradients for the second-order Møller-Plesset perturbation theory (MP2) with the density-fitting (DF) approximation (applying to both reference and correlation energies), which is denoted as DF-MP2, is reported. The DF-MP2 method is applied to a set of alkanes, conjugated dienes, and noncovalent interaction complexes to compare the computational cost of single point analytic gradients with MP2 with the resolution of the identity approach (RI-MP2) [F. Weigend and M. Häser, Theor. Chem. Acc. 97, 331 (1997); R. A. Distasio, R. P. Steele, Y. M. Rhee, Y. Shao, and M. Head-Gordon, J. Comput. Chem. 28, 839 (2007)]. In the RI-MP2 method, the DF approach is used only for the correlation energy. Our results demonstrate that the DF-MP2 method substantially accelerate the RI-MP2 method for analytic gradient computations due to the reduced input/output (I/O) time. Because in the DF-MP2 method the DF approach is used for both reference and correlation energies, the storage of 4-index electron repulsion integrals (ERIs) are avoided, 3-index ERI tensors are employed instead. Further, as in case of integrals, our gradient equation is completely avoid construction or storage of the 4-index two-particle density matrix (TPDM), instead we use 2- and 3-index TPDMs. Hence, the I/O bottleneck of a gradient computation is significantly overcome. Therefore, the cost of the generalized-Fock matrix (GFM), TPDM, solution of Z-vector equations, the back transformation of TPDM, and integral derivatives are substantially reduced when the DF approach is used for the entire energy expression. Further application results show that the DF approach introduce negligible errors for closed-shell reaction energies and equilibrium bond lengths.
Bozkaya, Uğur, E-mail: ugur.bozkaya@atauni.edu.tr [Department of Chemistry, Atatürk University, Erzurum 25240, Turkey and Department of Chemistry, Middle East Technical University, Ankara 06800 (Turkey)
2014-09-28
General analytic gradient expressions (with the frozen-core approximation) are presented for density-fitted post-HF methods. An efficient implementation of frozen-core analytic gradients for the second-order Møller–Plesset perturbation theory (MP2) with the density-fitting (DF) approximation (applying to both reference and correlation energies), which is denoted as DF-MP2, is reported. The DF-MP2 method is applied to a set of alkanes, conjugated dienes, and noncovalent interaction complexes to compare the computational cost of single point analytic gradients with MP2 with the resolution of the identity approach (RI-MP2) [F. Weigend and M. Häser, Theor. Chem. Acc. 97, 331 (1997); R. A. Distasio, R. P. Steele, Y. M. Rhee, Y. Shao, and M. Head-Gordon, J. Comput. Chem. 28, 839 (2007)]. In the RI-MP2 method, the DF approach is used only for the correlation energy. Our results demonstrate that the DF-MP2 method substantially accelerate the RI-MP2 method for analytic gradient computations due to the reduced input/output (I/O) time. Because in the DF-MP2 method the DF approach is used for both reference and correlation energies, the storage of 4-index electron repulsion integrals (ERIs) are avoided, 3-index ERI tensors are employed instead. Further, as in case of integrals, our gradient equation is completely avoid construction or storage of the 4-index two-particle density matrix (TPDM), instead we use 2- and 3-index TPDMs. Hence, the I/O bottleneck of a gradient computation is significantly overcome. Therefore, the cost of the generalized-Fock matrix (GFM), TPDM, solution of Z-vector equations, the back transformation of TPDM, and integral derivatives are substantially reduced when the DF approach is used for the entire energy expression. Further application results show that the DF approach introduce negligible errors for closed-shell reaction energies and equilibrium bond lengths.
Analysis of the Bogoliubov free energy functional
Reuvers, Robin
In this thesis, we analyse a variational reformulation of the Bogoliubov approximation that is used to describe weakly-interacting translationally-invariant Bose gases. For the resulting model, the `Bogoliubov free energy functional', we demonstrate existence of minimizers as well as the presence...
Shen, Xiaozhi; Liu, Juan; Zhou, Fuyang
2016-10-01
Wavefunctions were determined using the multi-configuration Dirac-Hartree-Fock method. The core-core, core-valence, valence correlation, Breit interaction and quantum electrodynamics effects, as well as some higher-order correlation effects, were considered to obtain accurate wavelengths (λ), oscillator strengths (gf) and transition rates (A) of 2s22p2 - 2s2p3, 2s2p3 - 2s22pnl (n ≥ 3) and 2s2p3 - 2s2p23s E1 transitions. The branching ratio of 2s2p3 5S^o_2 (namely Aλ2143.45/Aλ2139.68) based on the latest calculation of 2.462 ± 0.119 is recommended for the determination of a nebula's electron temperature and electron density. The largest calculated gf value of 2s2p3 - 2s22p4p is λ630.65, differing from that of λ1060.2 (i.e. 2s2p3 3P^o_2 - 2s22p4p 3S1) that was observed with the largest intensities in the Orion Nebula spectrum. In addition, the energy levels and the splittings of 2s2p3, the extremely difficult calculations of the rates of two-electron one-photon transitions as well as those of the very small intercombination A of 2s2p3 5S^o_2 were studied in detail. Because of the weak spin-orbit interaction, accurately calculating the levels 3P^o_{1,2,0} (or 3D^o_{3,2,1}) and their transition matrix elements is very sensitive to relativistic and electron correlation effects. A special case for this is when the transition operators synchronously applied to wavefunctions with regard to 2s2p3 3Po and 2s22pnl (n = 4) become extremely sensitive to some higher-order correlation effects.
Approaching the Hartree-Fock limit for organotransition metal complexes
Schaefer, III, Henry F. [Univ. of Texas, Austin, TX (United States). Dept. of Chemistry. Inst. for Theoretical Chemistry; Univ. of California, Berkeley, CA (United States). Dept. of Chemistry. Lawrence Berkeley Lab.
1981-04-01
In theoretical studies of the electronic structure of organometallic complexes, the choice of basis set is critical, much more so than for analogous studies of molecules containing only H, C, N, and O. In this paper, this problem is discussed in the light of structural predictions for the transition metal hydrides MH, MH_{2}, and MH_{4}, for the fluorides MF_{2} and MF_{3}, and for Ni(CO)_{4}, Ni(C_{2}H_{4})_{3}, (CO)_{3}NiCH_{2}, and Ni(C_{4}H_{4})_{2}.
Analysis of the Bogoliubov free energy functional
Reuvers, Robin
In this thesis, we analyse a variational reformulation of the Bogoliubov approximation that is used to describe weakly-interacting translationally-invariant Bose gases. For the resulting model, the `Bogoliubov free energy functional', we demonstrate existence of minimizers as well as the presence...... of a phase transition to Bose{Einstein condensation, and establish the phase diagram. We also give a calculation of the critical temperature assuming the gas is dilute, and nd that it agrees with earlier numerical studies. The thesis contains an introduction, a physical review paper outlining the main...
Bogoliubov Excited States and the Lyth Bound
Aravind, Aditya; Paban, Sonia
2014-01-01
We show that Bogoliubov excited scalar and tensor modes do not alleviate Planckian evolution during inflation if one assumes that $r$ and the Bogoliubov coefficients are approximately scale invariant. We constrain the excitation parameter for the scalar fluctuations, $\\beta$, and tensor perturbations, $\\tilde{\\beta}$, by requiring that there be at least three decades of scale invariance in the scalar and tensor power spectrum. For the scalar fluctuations this is motivated by the observed nearly scale invariant scalar power spectrum. For the tensor fluctuations this assumption may be shown to be valid or invalid by future experiments.
The $q$-deformed Bogoliubov transformations
Arraut, Ivan
2016-01-01
An algebraic generalization of the Bogoliubov transformation is introduced in the context of $q$-commutativity. The set of coefficients are promoted to operators where we work with a $q$-deformed action over the Bosonic algebra together with some generalized trigonometric hyperbolic identities. We make the analogous extension for the fermionic algebra.
Ab initio Bogoliubov coupled cluster theory
Signoracci, Angelo; Hagen, Gaute; Duguet, Thomas
2014-09-01
Coupled cluster (CC) theory has become a standard method in nuclear theory for realistic ab initio calculations of medium mass nuclei, but remains limited by its requirement of a Slater determinant reference state which reasonably approximates the nuclear system of interest. Extensions of the method, such as equation-of-motion CC, permit the calculation of nuclei with one or two nucleons added or removed from a doubly magic core, yet still only a few dozen nuclei are accessible with modern computational restrictions. In order to extend the applicability of ab initio methods to open-shell systems, the superfluid nature of nuclei must be taken into account. By utilizing Bogoliubov algebra and employing spontaneous symmetry breaking with respect to particle number conservation, superfluid systems can be treated by a single reference state. An ab initio theory to include correlations on top of a Bogoliubov reference state has been developed in the guise of standard CC theory. The formalism and first results of this Bogoliubov coupled cluster theory will be presented to demonstrate the applicability of the method.
Dirac-Fock atomic electronic structure calculations using different nuclear charge distributions
Visscher, L; Dyall, KG
1997-01-01
Numerical Hartree-Fock calculations based on the Dirac-Coulomb Hamiltonian for the first 109 elements of the periodic table are presented. The results give the total electronic energy, as a function of the nuclear model that is used, for four different models of the nuclear charge distribution. The
Dirac-Fock atomic electronic structure calculations using different nuclear charge distributions
Visscher, L; Dyall, KG
1997-01-01
Numerical Hartree-Fock calculations based on the Dirac-Coulomb Hamiltonian for the first 109 elements of the periodic table are presented. The results give the total electronic energy, as a function of the nuclear model that is used, for four different models of the nuclear charge distribution. The
A importância do método de Hartree no ensino de química quântica
Silmar A. do Monte
2011-01-01
Full Text Available Hartree's original ideas are described. Its connection with electrostatics can be explored in order to decrease the gap between teaching of Physics and Chemistry. As a consequence of its simplicity and connection with electrostatics, it is suggested that Hartree's method should be presented before the Hartree-Fock method. Besides, since the fundamental concepts of indistinguishibility of electrons along with the antissimetry of the wave function are missing in the Hartree's product, the method itself can be used to introduce these concepts. Despite the fact that these features are not included in the trial wavefunction, important qualitatively correct results can be obtained.
Accardi, Luigi
2009-01-01
We construct the quadratic analogue of the boson Fock functor. While in the first order case all contractions on the 1--particle space can be second quantized, the semigroup of contractions that admit a quadratic second quantization is much smaller due to the nonlinearity. Within this semigroup we characterize the unitary and the isometric elements.
Critical Analysis of the Bogoliubov Theory of Superfluidity
Adams, S
2003-01-01
The microscopic theory of superfluidity [1-3] was proposed by Bogoliubov in 1947 to explain the Landau-type excitation spectrum of helium 4. An analysis of the Bogoliubov theory has already been performed in the recent review [4]. Here we add some new critical analyses of this theory. This leads us to consider the superstable Bogoliubov model [5]. It gives rise to an improvement of the previous theory which will be explained with more details in a next paper [6]: coexistence in the superfluid liquid of particles inside and outside the Bose condensate (even at zero temperature), Bose/Bogoliubov statistics, ``Cooper pairs'' in the Bose condensate, Landau-type excitation spectrum...
Curiosities on free Fock spaces
Minic, D
1995-01-01
We consider some curious aspects of single-species free Fock spaces, such as novel bosonization and fermionization formulae and relations to various physical properties of bosonic particles. We comment on generalizations of these properties to physically more interesting many-species free Fock spaces.
Functional Representations for Fock Superalgebras
Kupsch, J; Kupsch, Joachim; Smolyanov, Oleg G.
1997-01-01
The Fock space of bosons and fermions and its underlying superalgebra are represented by algebras of functions on a superspace. We define Gaussian integration on infinite dimensional superspaces, and construct superanalogs of the classical function spaces with a reproducing kernel -- including the Bargmann-Fock representation -- and of the Wiener-Segal representation. The latter representation requires the investigation of Wick ordering on Z2-graded algebras. As application we derive a Mehler formula for the Ornstein-Uhlenbeck semigroup on the Fock space.
Generalized Bogoliubov Transformation for Confined Fields Applications in Casimir Effect
Silva, J C; Neto, A M; Santana, A E
2002-01-01
The Bogoliubov transformation in thermofield dynamics, an operator formalism for the finite-temperature quantum-field theory, is generalized to describe a field in arbitrary confined regions of space and time. Starting with the scalar field, the approach is extended to the electromagnetic field and the energy-momentum tensor is written via the Bogoliubov transformation. In this context, the Casimir effect is calculated for zero and non-zero temperature, and therefore it can be considered as a vacuum condensation effect of the electromagnetic field. This aspect opens an interesting perspective for using this procedure as an effective scheme for calculations in the studies of confined fields, including the interacting fields.
Localized form of Fock terms in nuclear covariant density functional theory
Liang, Haozhao; Ring, Peter; Roca-Maza, Xavier; Meng, Jie
2012-01-01
In most of the successful versions of covariant density functional theory in nuclei, the Fock terms are not included explicitly, which leads to local functionals and forms the basis of their widespread applicability at present. However, it has serious consequences for the description of Gamow-Teller resonances (GTR) and spin-dipole resonances (SDR) which can only be cured by adding further phenomenological parameters. Relativistic Hartree-Fock models do not suffer from these problems. They can successfully describe the GTR and SDR as well as the isovector part of the Dirac effective mass without any additional parameters. However, they are non-local and require considerable numerical efforts. By the zero-range reduction and the Fierz transformation, a new method is proposed to take into account the Fock terms in local functionals, which retains the simplicity of conventional models and provides proper descriptions of the spin-isospin channels and the Dirac masses.
Hartree potential dependent exchange functional
Constantin, L A; Della Sala, F
2016-01-01
We introduce a novel non-local ingredient for the construction of exchange density functionals: the reduced Hartree parameter, which is invariant under the uniform scaling of the density and represents the exact exchange enhancement factor for one- and two-electron systems. The reduced Hartree parameter is used together with the conventional meta-generalized gradient approximation (meta-GGA) semilocal ingredients (i.e. the electron density, its gradient and the kinetic energy density) to construct a new generation exchange functional, termed u-meta-GGA. This u-meta-GGA functional is exact for {the exchange of} any one- and two-electron systems, is size-consistent and non-empirical, satisfies the uniform density scaling relation, and recovers the modified gradient expansion derived from the semiclassical atom theory. For atoms, ions, jellium spheres, and molecules, it shows a good accuracy, being often better than meta-GGA exchange functionals. Our construction validates the use of the reduced Hartree ingredie...
Naturalness in see-saw mechanism and Bogoliubov transformation
Fujikawa, Kazuo; Tureanu, Anca
2017-04-01
We present an alternative perspective on the see-saw mechanism for the neutrino mass, according to which the small neutrino mass is given as a difference of two large masses. This view emerges when an analogue of the Bogoliubov transformation is used to describe Majorana neutrinos in the Lagrangian of the see-saw mechanism, which is analogous to the BCS theory. The Bogoliubov transformation clarifies the natural appearance of Majorana fermions when C is strongly violated by the right-handed neutrino mass term with good CP in the single flavor model. Analyzing typical models with mR =104 to 1015 GeV, it is shown that a hitherto unrecognized fine tuning of the order mν /mR =10-15 to 10-26 is required to make the commonly perceived see-saw mechanism work in a natural setting, namely, when none of the dimensionless coupling constants are very small.
Quadrature-dependent Bogoliubov transformations and multiphoton squeezed states
De Siena, S; Illuminati, F; Siena, Silvio De; Lisi, Antonio Di; Illuminati, Fabrizio
2001-01-01
We introduce a linear, canonical transformation of the fundamental single--mode field operators $a$ and $a^{\\dagger}$ that generalizes the linear Bogoliubov transformation familiar in the construction of the harmonic oscillator squeezed states. This generalization is obtained by adding to the linear transformation a nonlinear function of any of the fundamental quadrature operators $X_{1}$ and $X_{2}$, making the original Bogoliubov transformation quadrature--dependent. Remarkably, the conditions of canonicity do not impose any constraint on the form of the nonlinear function, and lead to a set of nontrivial algebraic relations between the $c$--number coefficients of the transformation. We examine in detail the structure and the properties of the new quantum states defined as eigenvectors of the transformed annihilation operator $b$. These eigenvectors define a class of multiphoton squeezed states. The structure of the uncertainty products and of the quasiprobability distributions in phase space shows that bes...
Generalized Bogoliubov Polariton Model: An Application to Stock Exchange Market
Thuy Anh, Chu; Anh, Truong Thi Ngoc; Lan, Nguyen Tri; Viet, Nguyen Ai
2016-06-01
A generalized Bogoliubov method for investigation non-simple and complex systems was developed. We take two branch polariton Hamiltonian model in second quantization representation and replace the energies of quasi-particles by two distribution functions of research objects. Application to stock exchange market was taken as an example, where the changing the form of return distribution functions from Boltzmann-like to Gaussian-like was studied.
The Brueckner-Hartree-Fock Equation of State for Nuclear Matter and Neutron Skin
Qing-Yang, Bu; Zeng-Hua, Li; Hans-Josef, Schulze
2016-03-01
Not Available Supported by the National Natural Science Foundation of China under Grant Nos 11075037 and 11475045, the Scientific Research Foundation for the Returned Overseas Chinese Scholars of the Ministry of Education of China, the Fundamental Research Funds for the Central Universities of China, the Shanghai Leading Academic Discipline Project under Grant No B107, and the ‘NewCompStar’, COST Action MP1304.
Predicting bond strength from a single Hartree-Fock ground state using the localized pair model.
Hennessey, Dylan C; Sheppard, Brendan J H; Mackenzie, Dalton E C K; Pearson, Jason K
2014-12-14
We present an application of the recently introduced Localized Pair Model (LPM) [Z. A. Zielinksi and J. K. Pearson, Comput. Theor. Chem., 2013, 1003, 7990] to characterize and quantify properties of the chemical bond in a series of substituted benzoic acid molecules. By computing interelectronic distribution functions for doubly-occupied Edmiston-Ruedenberg localized molecular orbitals (LMOs), we show that chemically intuitive electron pairs may be uniquely classified and bond strength may be predicted with remarkable accuracy. Specifically, the HF/u6-311G(d,p) level (where u denotes a complete uncontraction of the basis set) is used to generate the relevant LMOs and their respective interelectronic distribution functions can be linearly correlated to the well-known Hammett σp or σm parameters with near-unity correlation coefficients.
Hartree-Fock and density functional theory study of alpha-cyclodextrin conformers.
Jiménez, Verónica; Alderete, Joel B
2008-01-31
Herein, we report the geometry optimization of four conformers of alpha-cyclodextrin (alpha-CD) by means of PM3, HF/STO-3G, HF/3-21G, HF/6-31G(d), B3LYP/6-31G(d), and X3LYP/6-31G(d) calculations. The analysis of several geometrical parameters indicates that all conformers possess bond lengths, angles, and dihedrals that agree fairly well with the crystalline structure of alpha-CD. However, only three of them (1-3) resemble the polar character of CDs and show intramolecular hydrogen-bonding patterns that agree with experimental NMR data. Among them, conformer 3 appears to be the most stable species both in the gas phase and in solution; therefore, it is expected to be the most suitable representative structure for alpha-CD conformation. The purpose of selecting such a species is to identify an appropriate structure to be employed as a starting point for reliable computational studies on complexation phenomena. Our results indicate that the choice of a particular alpha-CD conformer should affect the results of ab initio computational studies on the inclusion complexation with this cyclodextrin since both the direction and the magnitude of the dipole moment depend strongly on the conformation of alpha-CD.
$L^2$ Analysis of the Multi-Configuration Time-Dependent Hartree-Fock Equations
Mauser, Norbert J
2010-01-01
The multiconfiguration methods are widely used by quantum physicists and chemists for numerical approximation of the many electron Schr\\"odinger equation. Recently, first mathematically rigorous results were obtained on the time-dependent models, e.g. short-in-time well-posedness in the Sobolev space $H^2$ for bounded interactions (C. Lubichand O. Koch} with initial data in $H^2$, in the energy space for Coulomb interactions with initial data in the same space (Trabelsi, Bardos et al.}, as well as global well-posedness under a sufficient condition on the energy of the initial data (Bardos et al.). The present contribution extends the analysis by setting an $L^2$ theory for the MCTDHF for general interactions including the Coulomb case. This kind of results is also the theoretical foundation of ad-hoc methods used in numerical calculation when modification ("regularization") of the density matrix destroys the conservation of energy property, but keeps invariant the mass.
Hyper Raman spectra calculated in a time-dependent Hartree-Fock method
Mohammed, Abdelsalam; Ågren, Hans; Ringholm, Magnus; Thorvaldsen, Andreas J.; Ruud, Kenneth
2012-10-01
Hyper Raman scattering (HRS) of the benzonitrile (BN) and 1,3,5-trinitro-1,3,5-triazacyclohexane (RDX) molecules is studied by means of ab initio calculations. The computational procedure employs a recently developed methodology for the analytic calculations of frequency-dependent polarizability gradients of arbitrary order, including perturbation dependent basis sets. The result are compared to normal Raman scattering (NRS) and coherent anti-Stokes Raman scattering (CARS) that previously have been studied using the same technology. It is found that some suppressed or silent modes in CARS and NRS spectra are clearly seen in HRS, and that although under general excitation conditions the HRS intensities are much lower than for CARS and NRS, HRS provides complementary information useful for target identification.
Theoretical Studies on Two Possible Conformers of TNDAIW at Hartree-Fock Level
WU Yu-kai; OU Yu-xiang; LIU Zhi-guo; MENG Zheng; ,LIU Jin-quan; CHEN Bo-ren
2005-01-01
Tetranitrodiazidoacetylhexaazaisowurtzitane (TNDAIW) is a novel polyazapolycyclic caged polyazidonitramine explosive first synthesized in our laboratory. Two possible conformers of TNDAIW with Cs symmetry were fully optimized using the HF/6-31G(d) level of theory. TNDAIW with the optimized geometries probably exists, and is predicted to be more stable than epsilon-hexanitrohexaazoisowurtzitane (epsilon-CL-20) based on the lengths of N-N, C-C and C-N bonds. The impact and shock sensitivities are lower for the possible conformers of TNDAIW than those for epsilon-CL-20. TNDAIW with the optimized possible conformers is estimated to be a promising novel high energy density explosive.
Relativity and the chemistry of UF6 : A molecular Dirac-Hartree-Fock-CI study
de Jong, W.A.; Nieuwpoort, W.C
1996-01-01
The electronic structure and bonding of UF6 and UF6- are studied within a relativistic framework using the MOLFDIR program package. A stronger bonding but more ionic molecule is found if one compares the relativistic with the nonrelativistic results. The first peak in the photoelectron spectrum of
Noncommutative spectral geometry, Bogoliubov transformations and neutrino oscillations
Vittoria Gargiulo, Maria; Sakellariadou, Mairi; Vitiello, Giuseppe
2015-07-01
In this report we show that neutrino mixing is intrinsically contained in Connes’ noncommutatives pectral geometry construction, thanks to the introduction of the doubling of algebra, which is connected to the Bogoliubov transformation. It is known indeed that these transformations are responsible for the mixing, turning the mass vacuum state into the flavor vacuum state, in such a way that mass and flavor vacuum states are not unitary equivalent. There is thus a red thread that binds the doubling of algebra of Connes’ model to the neutrino mixing.
Bose Fermi Supersymmetry with Bogoliubov transforms in Cosmology
Patwardhan, A
2006-01-01
Field theory including Supersymmetry and Bose Fermi Symmetry is an active subject of particle physics and cosmology. Recent and expected observational evidence gives indicators for the creation and destruction of normal and supersymmetric dark matter in the universe. This paper uses Bogoliubov transforms in supersymmetric and Bose Fermi form for obtaining the vaccuum expectation values at any two times in cosmological and black hole geometries. The isotropic Robertson Walker and slightly anisotropic Bianchi I geometry mode functions have a differential equation form analogous to the supersymmetric Hamiltonian. The condition for mixed and distinct representations for bosonic and fermionic fields of normal and supersymmetric partner particles are found.
Annihilation of colliding Bogoliubov quasiparticles reveals their Majorana nature.
Beenakker, C W J
2014-02-21
The single-particle excitations of a superconductor are coherent superpositions of electrons and holes near the Fermi level, called Bogoliubov quasiparticles. They are Majorana fermions, meaning that pairs of quasiparticles can annihilate. We calculate the annihilation probability at a beam splitter for chiral quantum Hall edge states, obtaining a 1±cosϕ dependence on the phase difference ϕ of the superconductors from which the excitations originated (with the ± sign distinguishing singlet and triplet pairing). This provides for a nonlocal measurement of the superconducting phase in the absence of any supercurrent.
Nonuniqueness of solution of Hartree equations
Amus' ya, M.Ya.; Kuchiev, M.Yu. (AN SSSR, Leningrad. Fiziko-Tekhnicheskij Inst.)
1981-12-01
The problem of uniqueness of Hartree equations solution is studied. Two simple models for multielectron ''atoms'' are considered. The possibility of existence in nature of states corresponding to such solutions is discussed. It is shown that besides normal solution in both models considered at a certain interpartial interaction special solutions appear. The emergence of special solutions is related to nonlinearity of Hartree equations.
Coherent states in the fermionic Fock space
Oeckl, Robert
2015-01-01
We construct the coherent states in the sense of Gilmore and Perelomov for the fermionic Fock space. Our treatment is from the outset adapted to the infinite-dimensional case. The fermionic Fock space becomes in this way a reproducing kernel Hilbert space of continuous holomorphic functions.
Bogoliubov-de Gennes method and its applications
Zhu, Jian-Xin
2016-01-01
The purpose of this book is to provide an elementary yet systematic description of the Bogoliubov-de Gennes (BdG) equations, their unique symmetry properties and their relation to Green’s function theory. Specifically, it introduces readers to the supercell technique for the solutions of the BdG equations, as well as other related techniques for more rapidly solving the equations in practical applications. The BdG equations are derived from a microscopic model Hamiltonian with an effective pairing interaction and fully capture the local electronic structure through self-consistent solutions via exact diagonalization. This approach has been successfully generalized to study many aspects of conventional and unconventional superconductors with inhomogeneities – including defects, disorder or the presence of a magnetic field – and becomes an even more attractive choice when the first-principles information of a typical superconductor is incorporated via the construction of a low-energy tight-binding model. ...
Naturalness in see-saw mechanism and Bogoliubov transformation
Fujikawa, Kazuo
2016-01-01
The see-saw mechanism is customarily regarded as the ratio of two masses leading to the tiny neutrino mass. We propose an alternative perspective on the see-saw, according to which the small neutrino mass is given as a difference of two large fermion masses of the order of the grand unification scale, and thus hitherto unrecognized fine tuning. This alternative view is motivated by the use of an analogue of Bogoliubov transformation to describe Majorana neutrinos in the Lagrangian defining the see-saw mechanism, which is analogous to the Lagrangian of the BCS theory. The naturalness issue of the neutrino mass thus becomes related to that of the Higgs mass in the Standard Model.
Weaving commutators: beyond Fock space
Arzano, Michele
2012-01-01
The symmetrization postulate and the associated Bose/Fermi (anti)-commutators for field mode operators are among the pillars on which local quantum field theory lays its foundations. They ultimately determine the structure of Fock space and are closely connected with the local properties of the fields and with the action of symmetry generators on observables and states. We here show that the quantum field theory describing relativistic particles coupled to three dimensional Einstein gravity as a topological defect must be constructed using a deformed algebra of creation and annihilation operators. This reflects a non-trivial group manifold structure of the classical momentum space and a modification of the Leibniz rule for the action of symmetry generators governed by Newton's constant. We outline various arguments suggesting that, at least at the qualitative level, these three-dimensional results could also apply to real four-dimensional world thus forcing us to re-think the ordinary multiparticle structure ...
Gharabaghi, Masumeh
2016-01-01
In this letter the conceptual and computational implications of the Hartree product type nuclear wavefunction introduced recently within context of the ab initio non-Born-Oppenheimer Nuclear-electronic orbital (NEO) methodology are considered. It is demonstrated that this wavefunction may imply a pseudo-adiabatic separation of the nuclei and electrons and each nucleus is conceived as a quantum oscillator while a non-Coulombic effective Hamiltonian is deduced for electrons. Using variational principle this Hamiltonian is used to derive a modified set of single-component Hartree-Fock equations which are equivalent to the multi-component version derived previously within context of the NEO and, easy to be implemented computationally.
Gharabaghi, Masumeh; Shahbazian, Shant
2016-12-01
In this letter the conceptual and computational implications of the Hartree product type nuclear wavefunction introduced recently within the context of the ab initio non-Born-Oppenheimer Nuclear-electronic orbital (NEO) methodology are considered. It is demonstrated that this wavefunction may imply a pseudo-adiabatic separation of the nuclei and electrons and each nucleus is conceived as a quantum oscillator while a non-Coulombic effective Hamiltonian is deduced for electrons. Using the variational principle this Hamiltonian is employed to derive a modified set of single-component Hartree-Fock equations which are equivalent to the multi-component version derived previously within the context of the NEO and, easy to be implemented computationally.
Sawada, Ryohto; Ishikawa, Kenichi L
2016-01-01
We report a three-dimensional numerical implementation of multiconfiguration time-dependent Hartree-Fock (MCTDHF) based on a multi-resolution Cartesian grid, with no need to assume any symmetry of molecular structure. We successfully compute high-harmonic generation (HHG) of H2 and H2O. The present implementation will open a way to the first-principle theoretical study of intense-field and attosecond-pulse induced ultrafast phenomena in general molecules.
The Extended Fock Basis of Clifford Algebra
Budinich, Marco
2010-01-01
We investigate the properties of the Extended Fock Basis (EFB) of Clifford algebras introduced in [1]. We show that a Clifford algebra can be seen as a direct sum of multiple spinor subspaces that are characterized as being left eigenvectors of $\\Gamma$. We also show that a simple spinor, expressed in Fock basis, can have a maximum number of non zero coordinates that equals the size of the maximal totally null plane (with the notable exception of vectorial spaces with 6 dimensions).
The Extended Fock Basis of Clifford Algebra
2010-01-01
We investigate the properties of the Extended Fock Basis (EFB) of Clifford algebras introduced in [1]. We show that a Clifford algebra can be seen as a direct sum of multiple spinor subspaces that are characterized as being left eigenvectors of \\Gamma. We also show that a simple spinor, expressed in Fock basis, can have a maximum number of non zero coordinates that equals the size of the maximal totally null plane (with the notable exception of vectorial spaces with 6 dimensions).
Bogoliubov-de Gennes soliton dynamics in unconventional Fermi superfluids
Takahashi, Daisuke A.
2016-01-01
Exact self-consistent soliton dynamics based on the Bogoliubov-de Gennes (BdG) formalism in unconventional Fermi superfluids/superconductors possessing an SU(d ) -symmetric two-body interaction is presented. The derivation is based on the ansatz having the similar form as the Gelfand-Levitan-Marchenko equation in the inverse scattering theory. Our solutions can be regarded as a multicomponent generalization of the solutions recently derived by Dunne and Thies [Phys. Rev. Lett. 111, 121602 (2013), 10.1103/PhysRevLett.111.121602]. We also propose superpositions of occupation states, which make it possible to realize various filling rates even in one-flavor systems, and include Dirac and Majorana fermions. The soliton solutions in the d =2 systems, which describe the mixture of singlet s -wave and triplet p -wave superfluids, exhibit a variety of phenomena such as rotating polar phases by soliton spins, SU(2)-DHN breathers, Majorana triplet states, s -p mixed dynamics, and so on. These solutions are illustrated by animations, where order parameters are visualized by spherical harmonic functions. The full formulation of the BdG theory is also supported, and the double-counting problem of BdG eigenstates and N -flavor generalization are discussed.
Comparison of Self-Consistent Skyrme and Gogny Calculations for Light Hg Isotopes
Warda, M; Próchniak, L
2009-01-01
The ground-state properties of neutron-deficient Hg isotopes have been investigated by the constrained self-consistent Hartree-Fock-Bogoliubov approach with the Skyrme and Gogny effective forces. In the case of the Skyrme interaction we h ave also applied the Hartree-Fock+BCS model with the state-dependent $\\delta$-pairing interaction. Potential energy surfaces and pairing properties have been compared for the both types of forces.
Staying Thermal with Hartree Ensemble Approximations
Salle, M; Vink, Jeroen C
2000-01-01
Using Hartree ensemble approximations to compute the real time dynamics of scalar fields in 1+1 dimension, we find that with suitable initial conditions, approximate thermalization is achieved much faster than found in our previous work. At large times, depending on the interaction strength and temperature, the particle distribution slowly changes: the Bose-Einstein distribution of the particle densities develops classical features. We also discuss variations of our method which are numerically more efficient.
Hankel transforms in generalized Fock spaces
John Schmeelk
1994-01-01
Full Text Available A classical Fock space consists of functions of the form,ϕ↔(ϕ0,ϕ1,…,ϕq,where ϕ0∈ℂ and ϕq∈Lp(ℝq, q≥1. We will replace the ϕq, q≥1 with test functions having Hankel transforms. This space is a natural generalization of a classical Fock space as seen by expanding functionals having abstract Taylor Series. The particular coefficients of such series are multilinear functionals having distributions as their domain. Convergence requirements set forth are somewhat in the spirit of ultra differentiable functions and ultra distribution theory. The Hankel transform oftentimes implemented in Cauchy problems will be introduced into this setting. A theorem will be proven relating the convergence of the transform to the inductive limit parameter, s, which sweeps out a scale of generalized Fock spaces.
Fourier transforms in generalized Fock spaces
John Schmeelk
1990-01-01
Full Text Available A classical Fock space consists of functions of the form,Φ↔(ϕ0,ϕ1,…,ϕq,…,where ϕ0∈C and ϕq∈L2(R3q, q≥1. We will replace the ϕq, q≥1 with q-symmetric rapid descent test functions within tempered distribution theory. This space is a natural generalization of a classical Fock space as seen by expanding functionals having generalized Taylor series. The particular coefficients of such series are multilinear functionals having tempered distributions as their domain. The Fourier transform will be introduced into this setting. A theorem will be proven relating the convergence of the transform to the parameter, s, which sweeps out a scale of generalized Fock spaces.
On the Fock Transformation in Nonlinear Relativity
Bouda, A
2012-01-01
In this paper, we propose a new deformed Poisson brackets which leads to the Fock coordinate transformation by using an analogous procedure as in Deformed Special Relativity. We therefore derive the corresponding momentum transformation which is revealed to be different from previous results. Contrary to the earlier version of Fock's nonlinear relativity for which plane waves cannot be described, our resulting algebra keeps invariant for any coordinate and momentum transformations the four dimensional contraction $p_{\\mu} x^{\\mu} $, allowing therefore to associate plane waves for free particles. As in Deformed Special Relativity, we also derive a canonical transformation with which the new coordinates and momentum satisfy the usual Poisson brackets and therefore transform like the usual Lorentz vectors. Finally, we establish the dispersion relation for Fock's nonlinear relativity.
Parallel scalability of Hartree–Fock calculations
Chow, Edmond, E-mail: echow@cc.gatech.edu; Liu, Xing [School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0765 (United States); Smelyanskiy, Mikhail; Hammond, Jeff R. [Parallel Computing Lab, Intel Corporation, Santa Clara, California 95054-1549 (United States)
2015-03-14
Quantum chemistry is increasingly performed using large cluster computers consisting of multiple interconnected nodes. For a fixed molecular problem, the efficiency of a calculation usually decreases as more nodes are used, due to the cost of communication between the nodes. This paper empirically investigates the parallel scalability of Hartree–Fock calculations. The construction of the Fock matrix and the density matrix calculation are analyzed separately. For the former, we use a parallelization of Fock matrix construction based on a static partitioning of work followed by a work stealing phase. For the latter, we use density matrix purification from the linear scaling methods literature, but without using sparsity. When using large numbers of nodes for moderately sized problems, density matrix computations are network-bandwidth bound, making purification methods potentially faster than eigendecomposition methods.
Atomic Fock State Preparation Using Rydberg Blockade
Ebert, Matthew; Gibbons, Michael; Zhang, Xianli; Saffman, Mark; Walker, Thad G
2013-01-01
We use coherent excitation of 3-16 atom ensembles to demonstrate collective Rabi flopping mediated by Rydberg blockade. Using calibrated atom number measurements, we quantitatively confirm the expected $\\sqrt{N}$ Rabi frequency enhancement to within 4%. The resulting atom number distributions are consistent with essentially perfect blockade. We then use collective Rabi $\\pi$ pulses to produce ${\\cal N}=1,2$ atom number Fock states with fidelities of 62% and 48% respectively. The ${\\cal N}=2$ Fock state shows the collective Rabi frequency enhancement without corruption from atom number fluctuations.
Linear and Nonlinear Bullets of the Bogoliubov-de Gennes Excitations
Kumar, S.; Perego, A. M.; Staliunas, K.
2017-01-01
We report on the focalization of Bogoliubov-de Gennes excitations of the nonlinear Schrödinger equation in the defocusing regime (Gross-Pitaevskii equation for repulsive Bose-Einstein condensates) with a spatially modulated periodic potential. Exploiting the modification of the dispersion relation induced by the modulation, we demonstrate the existence of localized structures of the Bogoliubov-de Gennes excitations, in both the linear and nonlinear regimes (linear and nonlinear "bullets"). These traveling Bogoliubov-de Gennes bullets, localized both spatially and temporally in the comoving reference frame, are robust and propagate remaining stable, without spreading or filamentation. The phenomena reported in this Letter could be observed in atomic Bose-Einstein condensates in the presence of a spatially periodic potential induced by an optical lattice.
Thermal effects in gravitational Hartree systems
Aki, Gonca L. [Weierstrass-Institut fuer Angewandte Analysis und Stochastik (WIAS) im Forschungsverbund Berlin e.V. (Germany); Dolbeault, Jean [Paris-Dauphine Univ. (FR). Ceremade (UMR CNRS 7534); Sparber, Christof [Illinois Univ., Chicago, IL (United States). Dept. of Mathematics, Statistics, and Computer Science
2010-07-01
We consider the non-relativistic Hartree model in the gravitational case, i.e. with attractive Coulomb-Newton interaction. For a given mass M>0, we construct stationary states with non-zero temperature T by minimizing the corresponding free energy functional. It is proved that minimizers exist if and only if the temperature of the system is below a certain threshold T*>0 (possibly infinite), which itself depends on the specific choice of the entropy functional. We also investigate whether the corresponding minimizers are mixed or pure quantum states and characterize a critical temperature T{sub c} element of (0,T*) above which mixed states appear. (orig.)
Thermal Effects in Gravitational Hartree Systems
Aki, Gonca L.
2011-04-06
We consider the non-relativistic Hartree model in the gravitational case, i. e. with attractive Coulomb-Newton interaction. For a given mass M > 0, we construct stationary states with non-zero temperature T by minimizing the corresponding free energy functional. It is proved that minimizers exist if and only if the temperature of the system is below a certain threshold T* > 0 (possibly infinite), which itself depends on the specific choice of the entropy functional. We also investigate whether the corresponding minimizers are mixed or pure quantum states and characterize a critical temperature Tc ∈ (0,T*) above which mixed states appear. © 2011 Springer Basel AG.
Classical limit for semirelativistic Hartree systems
Aki, Gonca L.
2008-01-01
We consider the three-dimensional semirelativistic Hartree model for fast quantum mechanical particles moving in a self-consistent field. Under appropriate assumptions on the initial density matrix as a (fully) mixed quantum state we prove by using Wigner transformation techniques that its classical limit yields the well known relativistic Vlasov-Poisson system. The result holds for the case of attractive and repulsive mean-field interactions, with an additional size constraint in the attractive case. © 2008 American Institute of Physics.
Many-body expansion of the Fock matrix in the fragment molecular orbital method
Fedorov, Dmitri G.; Kitaura, Kazuo
2017-09-01
A many-body expansion of the Fock matrix in the fragment molecular orbital method is derived up to three-body terms for restricted Hartree-Fock and density functional theory in the atomic orbital basis and compared to the expansion in the basis of fragment molecular orbitals (MOs). The physical nature of many-body corrections is revealed in terms of charge transfer terms. An improvement of the fragment MO expansion is proposed by adding exchange to the embedding. The accuracy of all developed methods is demonstrated in comparison to unfragmented results for polyalanines, a water cluster, Trp-cage (PDB: 1L2Y) and crambin (PDB: 1CRN) proteins, a zeolite cluster, a Si nano-wire, and a boron nitride ribbon. The physical nature of metallicity is discussed, and it is shown what kinds of metallic systems can be treated by fragment-based methods. The density of states is calculated for a fully closed and a partially open nano-ring of boron nitride with a diameter of 105 nm.
Bogoliubov q-transformation and Clebsch-Gordan coefficients for a q-oscillator
Zhedanov, A. S.
1992-05-01
The q-analog of the Bogoliubov transformation is found, yielding the third q-Bose operator from the two independent ones. In contrast to the ordinary case, this transformation is non-linear. Considered as a co-multiplication for the q-oscillator algebra, this transformation generates the Clebsch-Gordan series with coefficients expressed via the Kravchuk q-polynomials.
White noise calculus and Fock space
Obata, Nobuaki
1994-01-01
White Noise Calculus is a distribution theory on Gaussian space, proposed by T. Hida in 1975. This approach enables us to use pointwise defined creation and annihilation operators as well as the well-established theory of nuclear space.This self-contained monograph presents, for the first time, a systematic introduction to operator theory on fock space by means of white noise calculus. The goal is a comprehensive account of general expansion theory of Fock space operators and its applications. In particular,first order differential operators, Laplacians, rotation group, Fourier transform and their interrelations are discussed in detail w.r.t. harmonic analysis on Gaussian space. The mathematical formalism used here is based on distribution theory and functional analysis , prior knowledge of white noise calculus is not required.
Photons in Fock space and beyond
Honegger, Reinhard
2015-01-01
The three-volume major reference "Photons in Fock Space and Beyond" undertakes a new mathematical and conceptual foundation of the theory of light emphasizing mesoscopic radiation systems. The quantum optical notions are generalized beyond Fock representations where the richness of an infinite dimensional quantum field system, with its mathematical difficulties and theoretical possibilities, is fully taken into account. It aims at a microscopic formulation of a mesoscopic model class which covers in principle all stages of the generation and propagation of light within a unified and well-defined conceptual frame. The dynamics of the interacting systems is founded — according to original works of the authors — on convergent perturbation series and describes the developments of the quantized microscopic as well as the classical collective degrees of freedom at the same time. The achieved theoretical unification fits especially to laser and microwave applications inheriting objective information over quantu...
Fock expansion of multimode pure Gaussian states
Cariolaro, Gianfranco; Pierobon, Gianfranco, E-mail: gianfranco.pierobon@unipd.it [Università di Padova, Padova (Italy)
2015-12-15
The Fock expansion of multimode pure Gaussian states is derived starting from their representation as displaced and squeezed multimode vacuum states. The approach is new and appears to be simpler and more general than previous ones starting from the phase-space representation given by the characteristic or Wigner function. Fock expansion is performed in terms of easily evaluable two-variable Hermite–Kampé de Fériet polynomials. A relatively simple and compact expression for the joint statistical distribution of the photon numbers in the different modes is obtained. In particular, this result enables one to give a simple characterization of separable and entangled states, as shown for two-mode and three-mode Gaussian states.
Matrices related to some Fock space operators
Krzysztof Rudol
2011-01-01
Full Text Available Matrices of operators with respect to frames are sometimes more natural and easier to compute than the ones related to bases. The present work investigates such operators on the Segal-Bargmann space, known also as the Fock space. We consider in particular some properties of matrices related to Toeplitz and Hankel operators. The underlying frame is provided by normalised reproducing kernel functions at some lattice points.
Sekizawa, Kazuyuki
2016-01-01
Background: Multinucleon transfer (MNT) and quasifission (QF) processes are dominant processes in low-energy collisions of two heavy nuclei. They are expected to be useful to produce neutron-rich unstable nuclei. Nuclear dynamics leading to these processes depends sensitively on nuclear properties such as deformation and shell structure. Purpose: We elucidate reaction mechanisms of MNT and QF processes involving heavy deformed nuclei, making detailed comparisons between microscopic TDHF calculations and measurements for $^{64}$Ni+$^{238}$U reaction. Methods: Three-dimensional Skyrme-TDHF calculations are performed. Particle-number projection method is used to evaluate MNT cross sections from the TDHF wave function after collision. Results: Fragment masses, total kinetic energy (TKE), scattering angle, contact time, and MNT cross sections are investigated for $^{64}$Ni+$^{238}$U reaction. They show reasonable agreements with measurements. At small impact parameters, collision dynamics depends sensitively on th...
Adachi, H; Kawai, J
2006-01-01
Molecular-orbital calculations for materials design such as alloys, ceramics, and coordination compounds are now possible for experimentalists. Molecuar-orbital calculations for the interpretation of chemical effect of spectra are also possible for experimentalists. The most suitable molecular-orbital calculation method for these purpose is the DV-Xa method, which is robust in such a way that the calculation converges to a result even if the structure of the molecule or solid is impossible in the pressure and temperature ranges on earth. This book specially addresses the methods to design novel materials and to predict the spectralline shape of unknown materials using the DV-Xa molecular-orbital method, but is also useful for those who want to calculate electronic structures of materials using any kind of method.
de Lara-Castells, María Pilar; Fernández-Perea, Ricardo; Madzharova, Fani; Voloshina, Elena
2016-06-01
The adsorption of noble gases on metallic surfaces represents a paradigmatic case of van-der-Waals (vdW) interaction due to the role of screening effects on the corrugation of the interaction potential [J. L. F. Da Silva et al., Phys. Rev. Lett. 90, 066104 (2003)]. The extremely small adsorption energy of He atoms on the Mg(0001) surface (below 3 meV) and the delocalized nature and mobility of the surface electrons make the He/Mg(0001) system particularly challenging, even for state-of-the-art vdW-corrected density functional-based (vdW-DFT) approaches [M. P. de Lara-Castells et al., J. Chem. Phys. 143, 194701 (2015)]. In this work, we meet this challenge by applying two different procedures. First, the dispersion-corrected second-order Möller-Plesset perturbation theory (MP2C) approach is adopted, using bare metal clusters of increasing size. Second, the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)] is applied at coupled cluster singles and doubles and perturbative triples level, using embedded cluster models of the metal surface. Both approaches provide clear evidences of the anti-corrugation of the interaction potential: the He atom prefers on-top sites, instead of the expected hollow sites. This is interpreted as a signature of the screening of the He atom by the metal for the on-top configuration. The strong screening in the metal is clearly reflected in the relative contribution of successively deeper surface layers to the main dispersion contribution. Aimed to assist future dynamical simulations, a pairwise potential model for the He/surface interaction as a sum of effective He-Mg pair potentials is also presented, as an improvement of the approximation using isolated He-Mg pairs.
Papajak, Ewa; Truhlar, Donald G
2011-01-11
We present sets of convergent, partially augmented basis set levels corresponding to subsets of the augmented "aug-cc-pV(n+d)Z" basis sets of Dunning and co-workers. We show that for many molecular properties a basis set fully augmented with diffuse functions is computationally expensive and almost always unnecessary. On the other hand, unaugmented cc-pV(n+d)Z basis sets are insufficient for many properties that require diffuse functions. Therefore, we propose using intermediate basis sets. We developed an efficient strategy for partial augmentation, and in this article, we test it and validate it. Sequentially deleting diffuse basis functions from the "aug" basis sets yields the "jul", "jun", "may", "apr", etc. basis sets. Tests of these basis sets for Møller-Plesset second-order perturbation theory (MP2) show the advantages of using these partially augmented basis sets and allow us to recommend which basis sets offer the best accuracy for a given number of basis functions for calculations on large systems. Similar truncations in the diffuse space can be performed for the aug-cc-pVxZ, aug-cc-pCVxZ, etc. basis sets.
Staying thermal with Hartree ensemble approximations
Salle, Mischa E-mail: msalle@science.uva.nl; Smit, Jan E-mail: jsmit@science.uva.nl; Vink, Jeroen C. E-mail: jcvink@science.uva.nl
2002-03-25
We study thermal behavior of a recently introduced Hartree ensemble approximation, which allows for non-perturbative inhomogeneous field configurations as well as for approximate thermalization, in the phi (cursive,open) Greek{sup 4} model in 1+1 dimensions. Using ensembles with a free field thermal distribution as out-of-equilibrium initial conditions we determine thermalization time scales. The time scale for which the system stays in approximate quantum thermal equilibrium is an indication of the time scales for which the approximation method stays reasonable. This time scale turns out to be two orders of magnitude larger than the time scale for thermalization, in the range of couplings and temperatures studied. We also discuss simplifications of our method which are numerically more efficient and make a comparison with classical dynamics.
Lalitha Ravichandran; Debarati Bhattacharya; Nayana Vaval; Sourav Pal
2012-01-01
Dipole moment calculations of SF and ClO radicals have been carried out using the recently developed partial triples correction to Fock-space multi-reference coupled cluster method. Theoretical calculation of the doublet SF and ClO radicals is useful due to their importance in atmospheric chemistry. The dipole moments of these radicals are extremely sensitive to correlation effects. A brief insight to the way the triples correction has been implemented is presented. We compare the results obtained from our analytic response treatment with that of restricted open Hartree-Fock (ROHF) calculations. Results are presented for both relaxed and non-relaxed approach in the ROHF method. Results suggest the importance of triples corrections. The effects of orbital relaxation are also analysed from the results.
Shirkov, D V
2009-01-01
A retrospective historical overview of the phenomenon of spontaneous symmetry breaking (SSB) in quantum theory, the issue that has been implemented in particle physics in the form of the Higgs mechanism. The main items are: -- The Bogoliubov's microscopical theory of superfluidity (1946); -- The BCS-Bogoliubov theory of superconductivity (1957); -- Superconductivity as a superfluidity of Cooper pairs (Bogoliubov - 1958); -- Transfer of the SSB into the QFT models (early 60s); -- The Higgs model triumph in the electro-weak theory (early 80s). The role of the Higgs mechanism and its status in the current Standard Model is also touched upon.
Nonlinear Interferometry via Fock State Projection
Khoury, G; Eisenberg, H S; Fonseca, E J S
2006-01-01
We use a photon-number resolving detector to monitor the photon number distribution of the output of an interferometer, as a function of phase delay. As inputs we use coherent states with mean photon number up to seven. The postselection of a specific Fock (photon-number) state effectively induces high-order optical non-linearities. Following a scheme by Bentley and Boyd [S.J. Bentley and R.W. Boyd, Optics Express 12, 5735 (2004)] we explore this effect to demonstrate interference patterns a factor of five smaller than the Rayleigh limit.
Nonlinear Interferometry via Fock-State Projection
Khoury, G.; Eisenberg, H. S.; Fonseca, E. J. S.; Bouwmeester, D.
2006-05-01
We use a photon-number-resolving detector to monitor the photon-number distribution of the output of an interferometer, as a function of phase delay. As inputs we use coherent states with mean photon number up to seven. The postselection of a specific Fock (photon-number) state effectively induces high-order optical nonlinearities. Following a scheme by Bentley and Boyd [Opt. Express 12, 5735 (2004).OPEXFF1094-408710.1364/OPEX.12.005735], we explore this effect to demonstrate interference patterns a factor of 5 smaller than the Rayleigh limit.
On the rôle of rotations and Bogoliubov transformations in neutrino mixing
Blasone, M.; Gargiulo, M. V.; Vitiello, G.
2016-10-01
We show that mixing transformations for Dirac fields arise as a consequence of the non-trivial interplay between rotations and Bogoliubov transformations at level of ladder operators. Indeed the non-commutativity between the algebraic generators of such transformations turns out to be responsible of the unitary inequivalence of the flavor and mass representations and of the associated vacuum structure. A possible thermodynamic interpretation is also investigated.
Superintegrability of the Fock-Darwin system
Drigho-Filho, E.; Kuru, Ş.; Negro, J.; Nieto, L. M.
2017-08-01
The Fock-Darwin system is analyzed from the point of view of its symmetry properties in the quantum and classical frameworks. The quantum Fock-Darwin system is known to have two sets of ladder operators, a fact which guarantees its solvability. We show that for rational values of the quotient of two relevant frequencies, this system is superintegrable, the quantum symmetries being responsible for the degeneracy of the energy levels. These symmetries are of higher order and close a polynomial algebra. In the classical case, the ladder operators are replaced by ladder functions and the symmetries by constants of motion. We also prove that the rational classical system is superintegrable and its trajectories are closed. The constants of motion are also generators of symmetry transformations in the phase space that have been integrated for some special cases. These transformations connect different trajectories with the same energy. The coherent states of the quantum superintegrable system are found and they reproduce the closed trajectories of the classical one.
Modeling electron fractionalization with unconventional Fock spaces
Cobanera, Emilio
2017-08-01
It is shown that certain fractionally-charged quasiparticles can be modeled on D-dimensional lattices in terms of unconventional yet simple Fock algebras of creation and annihilation operators. These unconventional Fock algebras are derived from the usual fermionic algebra by taking roots (the square root, cubic root, etc) of the usual fermionic creation and annihilation operators. If the fermions carry non-Abelian charges, then this approach fractionalizes the Abelian charges only. In particular, the mth-root of a spinful fermion carries charge e/m and spin 1/2. Just like taking a root of a complex number, taking a root of a fermion yields a mildly non-unique result. As a consequence, there are several possible choices of quantum exchange statistics for fermion-root quasiparticles. These choices are tied to the dimensionality D=1,2,3,\\ldots of the lattice by basic physical considerations. One particular family of fermion-root quasiparticles is directly connected to the parafermion zero-energy modes expected to emerge in certain mesoscopic devices involving fractional quantum Hall states. Hence, as an application of potential mesoscopic interest, I investigate numerically the hybridization of Majorana and parafermion zero-energy edge modes caused by fractionalizing but charge-conserving tunneling.
Continuum Coupling and Pair Correlation in Weakly Bound Deformed Nuclei
Oba, Hiroshi
2009-01-01
We formulate a new Hartree-Fock-Bogoliubov method applicable to weakly bound deformed nuclei using the coordinate-space Green's function technique. An emphasis is put on treatment of quasiparticle states in the continuum, on which we impose the correct boundary condition of the asymptotic out-going wave. We illustrate this method with numerical examples.
Theoretical description of the octupole phase transition in Lanthanide nuclei at high spin
Garrote, E; Robledo, L M
1999-01-01
The phase transition to reflection asymmetric intrinsic nuclear shapes at high angular momentum is analyzed in the framework of the cranked Hartree-Fock-Bogoliubov approximation, with the Gogny interaction, using approximate parity projection before variation. The N=88 isotones are studied and good agreement is found for the energy splitting and dipole moments before and after the transition.
Dirac-Fock-Breit-Gaunt calculations for tungsten hexacarbonyl W(CO)6.
Malli, Gulzari L
2016-05-21
The first all-electron fully relativistic Dirac-Fock-Breit-Gaunt (DFBG), Dirac-Fock (DF), and nonrelativistic (NR) Hartree-Fock (HF) calculations are reported for octahedral (Oh) tungsten hexacarbonyl W(CO)6. Our DF and NR HF calculations predict atomization energy of 73.76 and 70.33 eV, respectively. The relativistic contribution of ∼3.4 eV to the atomization energy of W(CO)6 is fairly significant. The DF and NR energy for the reaction W + 6CO → W(CO)6 is calculated as -7.90 and -8.86 eV, respectively. The mean bond energy predicted by our NR and DF calculations is 142.5 kJ/mol and 177.5 kJ/mol, respectively, and our predicted DF mean bond energy is in excellent agreement with the experimental value of 179 kJ/mol quoted in the literature. The relativistic effects contribute ∼35 kJ/mol to the mean bond energy and the calculated BSSE is 1.6 kcal/mol, which indicates that the triple zeta basis set used here is fairly good. The mean bond energy and the atomization energy calculated in our DFBG SCF calculations, which include variationally both the relativistic and magnetic Breit effects, is 157.4 kJ/mol and 68.84 eV, respectively. The magnetic Breit effects lead to a decrease of ∼20 kJ/mol and ∼4.9 eV for the mean bond energy and atomization energy, respectively, for W(CO)6. Our calculated magnetic Breit interaction energy of -9.79 eV for the energy of reaction (ΔE) for W + 6CO → W(CO)6 is lower by ∼1.90 eV as compared to the corresponding DF value (ΔE) and contributes significantly to the ΔE. A detailed discussion is presented of electronic structure, bonding, and molecular energy levels at various levels of theory for W(CO)6.
Numerical Validation of the Delaunay Normalization and the Krylov-Bogoliubov-Mitropolsky Method
David Ortigosa
2014-01-01
Full Text Available A scalable second-order analytical orbit propagator programme based on modern and classical perturbation methods is being developed. As a first step in the validation and verification of part of our orbit propagator programme, we only consider the perturbation produced by zonal harmonic coefficients in the Earth’s gravity potential, so that it is possible to analyze the behaviour of the mathematical expressions involved in Delaunay normalization and the Krylov-Bogoliubov-Mitropolsky method in depth and determine their limits.
Exponential Renormalization II: Bogoliubov's R-operation and momentum subtraction schemes
Ebrahimi-Fard, Kurusch
2011-01-01
We develop further the recently introduced exponential method for renormalisation in perturbative quantum field theory. It turns out that exponential renormalisation provides a meaningful recursive method in the context of renormalisation using momentum subtraction schemes. We explore in detail its link to Bogoliubov's R-operation. Our results shed new light on classical ideas, such as the role of oversubtractions in the BPHZ method. They also suggest that the ambiguities of the renormalisation process carry, besides a physical structure (encoded, e.g. in the RG equations and the choice of subtraction points in momentum subtraction schemes), an interesting, though purely algebraic structure.
QMC approach based on the Bogoliubov independent quark model of the nucleon
Bohr, Henrik; Panda, Prafulla K; Providencia, Constanca; da Providencia, Joao
2015-01-01
The quark-meson coupling model due to Guichon is formulated on the basis of the independent quark model of the nucleon proposed by Bogoliubov and is applied to the phenomenological descriptions of symmetric and asymmetric nuclear matter. For symmetric matter, the model predicts, at saturation density, the incompressibility $K=335.17$ MeV, the quark effective mass $m_q^*=238.5$ MeV, and the effective nucleon mass $M^*= 0.76 M,$ where $M$ is the nucleon mass in vacuum. Neutron star massesabove two solar masses are obtained.
Incompatibility of Time-Dependent Bogoliubov-de-Gennes and Ginzburg-Landau Equations
Frank, Rupert L.; Hainzl, Christian; Schlein, Benjamin; Seiringer, Robert
2016-07-01
We study the time-dependent Bogoliubov-de-Gennes equations for generic translation-invariant fermionic many-body systems. For initial states that are close to thermal equilibrium states at temperatures near the critical temperature, we show that the magnitude of the order parameter stays approximately constant in time and, in particular, does not follow a time-dependent Ginzburg-Landau equation, which is often employed as a phenomenological description and predicts a decay of the order parameter in time. The full non-linear structure of the equations is necessary to understand this behavior.
Exponential renormalisation. II. Bogoliubov's R-operation and momentum subtraction schemes
Ebrahimi-Fard, Kurusch [Instituto de Ciencias Matematicas, C/ Nicolas Cabrera, no. 13-15, 28049 Madrid (Spain); Patras, Frederic [Laboratoire J.-A. Dieudonne UMR 6621, CNRS, Parc Valrose, 06108 Nice Cedex 02 (France)
2012-08-15
This article aims at advancing the recently introduced exponential method for renormalisation in perturbative quantum field theory. It is shown that this new procedure provides a meaningful recursive scheme in the context of the algebraic and group theoretical approach to renormalisation. In particular, we describe in detail a Hopf algebraic formulation of Bogoliubov's classical R-operation and counterterm recursion in the context of momentum subtraction schemes. This approach allows us to propose an algebraic classification of different subtraction schemes. Our results shed light on the peculiar algebraic role played by the degrees of Taylor jet expansions, especially the notion of minimal subtraction and oversubtractions.
On the Fock representation of the q-commutation relations
Dykema, K J; Dykema, Ken; Nica, Alexandru
1993-01-01
The q-commutation relations in the title are those that have recently received much attention, and that for -1Fock space of Bozejko-Speicher, and we find a canonical unitary U_q from the twisted Fock space to usual full Fock space, such that U_q R^q (U_q)^* contains the Cuntz algebra R^0, and such that we have equality for |q|<0.44.
Twisted Fock representations of noncommutative Kähler manifolds
Sako, Akifumi; Umetsu, Hiroshi
2016-09-01
We introduce twisted Fock representations of noncommutative Kähler manifolds and give their explicit expressions. The twisted Fock representation is a representation of the Heisenberg like algebra whose states are constructed by applying creation operators to a vacuum state. "Twisted" means that creation operators are not Hermitian conjugate of annihilation operators in this representation. In deformation quantization of Kähler manifolds with separation of variables formulated by Karabegov, local complex coordinates and partial derivatives of the Kähler potential with respect to coordinates satisfy the commutation relations between the creation and annihilation operators. Based on these relations, we construct the twisted Fock representation of noncommutative Kähler manifolds and give a dictionary to translate between the twisted Fock representations and functions on noncommutative Kähler manifolds concretely.
Twisted Fock Representations of Noncommutative K\\"ahler Manifolds
Sako, Akifumi
2016-01-01
We introduce twisted Fock representations of noncommutative K\\"ahler manifolds and give their explicit expressions. The twisted Fock representation is a representation of the Heisenberg like algebra whose states are constructed by acting creation operators on a vacuum state. "Twisted" means that creation operators are not hermitian conjugate of annihilation operators in this representation. In deformation quantization of K\\"ahler manifolds with separation of variables formulated by Karabegov, local complex coordinates and partial derivatives of the K\\"ahler potential with respect to coordinates satisfy the commutation relations between the creation and annihilation operators. Based on these relations, we construct the twisted Fock representation of noncommutative K\\"ahler manifolds and give a dictionary to translate between the twisted Fock representations and functions on noncommutative K\\"ahler manifolds concretely.
Ab initio Bogoliubov coupled cluster theory for open-shell nuclei
Signoracci, Angelo; Hagen, Gaute; Jansen, Gustav
2014-01-01
Ab initio many-body methods address closed-shell nuclei up to mass A ~ 130 on the basis of realistic two- and three-nucleon interactions. Several routes to address open-shell nuclei are currently under investigation, including ideas which exploit spontaneous symmetry breaking. Singly open-shell nuclei can be efficiently described via the sole breaking of $U(1)$ gauge symmetry associated with particle number conservation, to account for their superfluid character. The present work formulates and applies Bogoliubov coupled cluster (BCC) theory, which consists of representing the exact ground-state wavefunction of the system as the exponential of a quasiparticle excitation cluster operator acting on a Bogoliubov reference state. Equations for the ground-state energy and cluster amplitudes are derived at the singles and doubles level (BCCSD) both algebraically and diagrammatically. The formalism includes three-nucleon forces at the normal-ordered two-body level. The first BCC code is implemented in $m$-scheme, wh...
Quantum Computing in Fock Space Systems
Berezin, Alexander A.
1997-04-01
Fock space system (FSS) has unfixed number (N) of particles and/or degrees of freedom. In quantum computing (QC) main requirement is sustainability of coherent Q-superpositions. This normally favoured by low noise environment. High excitation/high temperature (T) limit is hence discarded as unfeasible for QC. Conversely, if N is itself a quantized variable, the dimensionality of Hilbert basis for qubits may increase faster (say, N-exponentially) than thermal noise (likely, in powers of N and T). Hence coherency may win over T-randomization. For this type of QC speed (S) of factorization of long integers (with D digits) may increase with D (for 'ordinary' QC speed polynomially decreases with D). This (apparent) paradox rests on non-monotonic bijectivity (cf. Georg Cantor's diagonal counting of rational numbers). This brings entire aleph-null structurality ("Babylonian Library" of infinite informational content of integer field) to superposition determining state of quantum analogue of Turing machine head. Structure of integer infinititude (e.g. distribution of primes) results in direct "Platonic pressure" resembling semi-virtual Casimir efect (presure of cut-off vibrational modes). This "effect", the embodiment of Pythagorean "Number is everything", renders Godelian barrier arbitrary thin and hence FSS-based QC can in principle be unlimitedly efficient (e.g. D/S may tend to zero when D tends to infinity).
Self-Adjointness Criterion for Operators in Fock Spaces
Falconi, Marco, E-mail: marco.falconi@univ-rennes1.fr [Université de Rennes I, IRMAR and Centre Henri Lebesgue (France)
2015-12-15
In this paper we provide a criterion of essential self-adjointness for operators in the tensor product of a separable Hilbert space and a Fock space. The class of operators we consider may contain a self-adjoint part, a part that preserves the number of Fock space particles and a non-diagonal part that is at most quadratic with respect to the creation and annihilation operators. The hypotheses of the criterion are satisfied in several interesting applications.
From the Hartree dynamics to the Vlasov equation
Benedikter, Niels Patriz; Porta, Marcello; Saffirio, Chiara;
2016-01-01
We consider the evolution of quasi-free states describing N fermions in the mean field limit, as governed by the nonlinear Hartree equation. In the limit of large N, we study the convergence towards the classical Vlasov equation. For a class of regular interaction potentials, we establish precise...... bounds on the 0rate of convergence....
Planck Scale Physics and Bogoliubov Spaces in a Bose--Einstein Condensate
Castellanos, E
2013-01-01
We analyze the consequences caused by a deformed relation, suggested in several quantum gravity models, upon a bosonic gas. Concerning the ground state of the Bogoliubov space of this system, we deduce the corrections in the pressure, the speed of sound, and the corresponding healing length. Indeed, we prove that the corrections in the relevant thermodynamic properties associated to the ground state, defines a non trivial function of the density of particles and the deformation parameters, allowing us to constrain, in principle, the form of the energy--momentum dispersion relation. In addition, we calculate the condensation temperature associated to the non-interacting system, and show that this fact could be used also, to infer representative bounds for the deformation parameters, under typical laboratory conditions.
Castellanos, Elías; Hernández-Hernández, Héctor H; Santos, Elí
2016-01-01
In the present report we analyze the eventual modifications caused by the polymer quantization upon the ground state of a homogeneous one-dimensional Bose-Einstein condensate. We obtain the ground state energy of the corresponding N-body system and, consequently, the corresponding speed of sound, allowing us to explore the sensitivity of the system to corrections caused by the polymer quantization. The corrections arising from the polymer quantization can be improved for dense systems together with small values of the corresponding one-dimensional scattering length. However, these corrections remain constrained due to finite size effects of the system. The contributions of the polymer length scale to the properties of the ground state energy of the system allow us to explore, as a first approximation and when the Bogoliubov's formalism is valid, the sensitivity of this many-body system to traces caused by the discreteness of space suggested by the polymer quantization.
A new class of quantum states generated by m-fold application of Bogoliubov's transformation
Wu Wei; Wu Ling-An; Xin Zong-Zheng
2004-01-01
By applying higher powers of the Bogoliubov transformation operator b = γ*a +μ* a to the two-photon coherent states (or minimum uncertainty squeezed states) we construct a new type of quantum state which we call the generalized excited two-photon coherent states. Analytic expressions for the quantum statistical properties are derived, and through numerical computation the phase space quasi-probability distributions are found. These states can exhibit highly nonclassical behaviour depending on the degree of excitation m and other parameters. For particular values of twc parameters λ and ρ, these generalized states reduce to other classes of coherent states formerly reported. Our theory thus presents a much broader approach to these types of quantum states.
Han, Qiang
2010-01-27
In this paper, we present a method to construct the eigenspace of the tight-binding electrons moving on a 2D square lattice with nearest-neighbor hopping in the presence of a perpendicular uniform magnetic field which imposes (quasi-)periodic boundary conditions for the wavefunctions in the magnetic unit cell. Exact unitary transformations are put forward to correlate the discrete eigenvectors of the 2D electrons with those of the Harper equation. The cyclic tridiagonal matrix associated with the Harper equation is then tridiagonalized by another unitary transformation. The obtained truncated eigenbasis is utilized to expand the Bogoliubov-de Gennes equations for the superconducting vortex lattice state, which shows the merit of our method in studying large-sized systems. To test our method, we have applied our results to study the vortex lattice state of an s-wave superconductor.
Quantum Harmonic Oscillator State Control in a Squeezed Fock Basis
Kienzler, D.; Lo, H.-Y.; Negnevitsky, V.; Flühmann, C.; Marinelli, M.; Home, J. P.
2017-07-01
We demonstrate control of a trapped-ion quantum harmonic oscillator in a squeezed Fock state basis, using engineered Hamiltonians analogous to the Jaynes-Cummings and anti-Jaynes-Cummings forms. We demonstrate that for squeezed Fock states with low n the engineered Hamiltonians reproduce the √{n } scaling of the matrix elements which is typical of Jaynes-Cummings physics, and also examine deviations due to the finite wavelength of our control fields. Starting from a squeezed vacuum state, we apply sequences of alternating transfer pulses which allow us to climb the squeezed Fock state ladder, creating states up to excitations of n =6 with up to 8.7 dB of squeezing, as well as demonstrating superpositions of these states. These techniques offer access to new sets of states of the harmonic oscillator which may be applicable for precision metrology or quantum information science.
Construction of the Fock-like Space for Quons
于挺; 吴兆颜
1994-01-01
The necessary and sufficient condition of the existence of the Fock-like space for quons with a fixed number q is proven, and the uniqueness theorem of the Fock-like space is given. The general-q operators, which satisfy the q-mutation relation a_ja_k - qa_ka_j =δ_jk, areconstructed by using the q = 0 operators as standard building blocks. The Fock-like spaces for quons with q∈(-1,1) prove to be the same as the one with q = 0, which manifestly is the direct sum of all the tensor product powers of the single particle state subspace, hence allow only the Boltzmann statistics .
Shirkov, Dmitrii V.
2009-06-01
This is a retrospective historical review of the ideas that led to the concept of the spontaneous symmetry breaking (SSB), the issue that has been implemented in quantum field theory in the form of the Higgs mechanism. The key stages covered include: the Bogoliubov microscopic theory of superfluidity (1946); the Bardeen-Cooper-Schrieffer-Bogoliubov microscopic theory of superconductivity (1957); superconductivity as superfluidity of Cooper pairs (Bogoliubov, 1958); the extension of the SSB concept to simple quantum field models (early 1960s); triumph of the Higgs model in electroweak theory (early 1980s). The role and status of the Higgs mechanism in the current Standard Model are discussed.
Quantum homodyne tomography of a two-photon Fock state
Ourjoumtsev, A; Grangier, P; Ourjoumtsev, Alexei; Tualle-Brouri, Rosa; Grangier, Philippe
2006-01-01
We present a continuous-variable experimental analysis of a two-photon Fock state of free-propagating light. This state is obtained from a pulsed non-degenerate parametric amplifier, which produces two intensity-correlated twin beams. Counting two photons in one beam projects the other beam in the desired two-photon Fock state, which is analyzed by using a pulsed homodyne detection. The Wigner function of the measured state is clearly negative. We developed a detailed analytic model which allows a fast and efficient analysis of the experimental results.
Quantum homodyne tomography of a two-photon Fock state.
Ourjoumtsev, Alexei; Tualle-Brouri, Rosa; Grangier, Philippe
2006-06-02
We present a continuous-variable experimental analysis of a two-photon Fock state of free-propagating light. This state is obtained from a pulsed nondegenerate parametric amplifier, which produces two intensity-correlated twin beams. Counting two photons in one beam projects the other beam in the desired two-photon Fock state, which is analyzed by using a pulsed homodyne detection. The Wigner function of the measured state is clearly negative. We developed a detailed analytic model which allows a fast and efficient analysis of the experimental results.
Representations Of The Super-virasoro Algebra fock Representations
Polychronidis, V J
1999-01-01
In this dissertation the complete classification of the Super- Virasoro modules M (h, c) of the Neveu-Schwarz and Ramond algebras is constructed. A family of representations F p, po of the Neveu- Schwarz and Ramond algebras, which generalize the Fock representations of the Virasoro algebra, is constructed. The Felder's construction of Fock space resolutions for the Virasoro minimal models is generalized in the Super-Virasoro minimal models case. In particular, a two-sided resolution of the irreducible Super-Verma module L( h, c) of the Neveu- Schwarz algebra is provided. --- 8 --- AN
Fasshauer, Elke
2015-01-01
We report on an implementation of the multiconfigurational time-dependent Hartree method (MCTDH) for spin-polarized fermions (MCTDHF). Our approach is based on a mapping for opera- tors in Fock space that allows a compact and efficient application of the Hamiltonian and solution of the MCTDHF equations of motion. Our implementation extends, builds on and exploits the recursive implementation of MCTDH for bosons (R-MCTDHB) package. Together with R-MCTDHB, the present implementation of MCTDHF forms the MCTDH-X package. We benchmark the accuracy of the algorithm with the harmonic interaction model and a time-dependent generalization thereof. These models consider parabolically trapped particles that interact through a harmonic interaction potential. We demonstrate, that MCTDHF is capable of solving the time-dependent many-fermion Schr\\"odinger equation to an in principle arbitrary degree of precision and can hence yield numerically exact results even in the case of Hamiltonians with time-dependent one-body and t...
Generation of Fock states in a superconducting quantum circuit.
Hofheinz, Max; Weig, E M; Ansmann, M; Bialczak, Radoslaw C; Lucero, Erik; Neeley, M; O'Connell, A D; Wang, H; Martinis, John M; Cleland, A N
2008-07-17
Spin systems and harmonic oscillators comprise two archetypes in quantum mechanics. The spin-1/2 system, with two quantum energy levels, is essentially the most nonlinear system found in nature, whereas the harmonic oscillator represents the most linear, with an infinite number of evenly spaced quantum levels. A significant difference between these systems is that a two-level spin can be prepared in an arbitrary quantum state using classical excitations, whereas classical excitations applied to an oscillator generate a coherent state, nearly indistinguishable from a classical state. Quantum behaviour in an oscillator is most obvious in Fock states, which are states with specific numbers of energy quanta, but such states are hard to create. Here we demonstrate the controlled generation of multi-photon Fock states in a solid-state system. We use a superconducting phase qubit, which is a close approximation to a two-level spin system, coupled to a microwave resonator, which acts as a harmonic oscillator, to prepare and analyse pure Fock states with up to six photons. We contrast the Fock states with coherent states generated using classical pulses applied directly to the resonator.
Asymptotic freedom of gluons in the Fock space
Głazek, Stanisław D
2015-01-01
Asymptotic freedom of gluons is described in terms of a family of scale-dependent renormalized Hamiltonian operators acting in the Fock space. The Hamiltonians are obtained by applying the renormalization group procedure for effective particles to quantum Yang-Mills theory.
Defacio, Brian; Kim, S.-H.; Vannevel, A.
1994-01-01
The squeezed states or Bogoliubov transformations and wavelets are applied to two problems in nonrelativistic statistical mechanics: the dielectric response of liquid water, epsilon(q-vector,w), and the bubble formation in water during insonnification. The wavelets are special phase-space windows which cover the domain and range of L(exp 1) intersection of L(exp 2) of classical causal, finite energy solutions. The multiresolution of discrete wavelets in phase space gives a decomposition into regions of time and scales of frequency thereby allowing the renormalization group to be applied to new systems in addition to the tired 'usual suspects' of the Ising models and lattice gasses. The Bogoliubov transformation: squeeze transformation is applied to the dipolaron collective mode in water and to the gas produced by the explosive cavitation process in bubble formation.
Presilla, M.; Panella, O.; Roy, P.
2017-02-01
It is shown that bound state solutions of the one dimensional Bogoliubov-de Gennes (BdG) equation may exist when the Fermi velocity becomes dependent on the space coordinate. The existence of bound states in continuum (BIC) like solutions has also been confirmed both in the normal phase as well as in the super-conducting phase. We also show that a combination of Fermi velocity and gap parameter step-like profiles provides scattering solutions with normal reflection and transmission.
M. Saifur Rahman
2012-12-01
Full Text Available Recently, a unified Krylov-Bogoliubov-Mitropolskii method has been presented (by Shamsul \\cite{1} for solving an $n$-th, $n=2$ or $n>2$, order nonlinear differential equation. Instead of amplitude(s and phase(s, a set of variables is used in \\cite{1} to obtain a general formula in which the nonlinear differential equations can be solved. By a simple variables transformation the usual form solutions (i.e., in terms of amplitude(s and phase(s have been found. In this paper a perturbation technique is developed to calculate the initial values of the variables used in \\cite{1}. By the noted transformation the initial amplitude(s and phase(s can be calculated quickly. Usually the conditional equations are nonlinear algebraic or transcendental equations; so that a numerical method is used to solve them. Rink \\cite{7} earlier employed an asymptotic method for solving the conditional equations of a second-order differential equation; but his derived results were not so good. The new results agree with their exact values (or numerical results nicely. The method can be applied whether the eigen-values of the unperturbed equation are purely imaginary, complex conjugate or real. Thus the derived solution is a general one and covers the three cases, i.e., un-damped, under-damped and over-damped.
Bogoliubov Fermi Surfaces in Superconductors with Broken Time-Reversal Symmetry
Agterberg, D. F.; Brydon, P. M. R.; Timm, C.
2017-03-01
It is commonly believed that, in the absence of disorder or an external magnetic field, there are three possible types of superconducting excitation gaps: The gap is nodeless, it has point nodes, or it has line nodes. Here, we show that, for an even-parity nodal superconducting state which spontaneously breaks time-reversal symmetry, the low-energy excitation spectrum generally does not belong to any of these categories; instead, it has extended Bogoliubov Fermi surfaces. These Fermi surfaces can be visualized as two-dimensional surfaces generated by "inflating" point or line nodes into spheroids or tori, respectively. These inflated nodes are topologically protected from being gapped by a Z2 invariant, which we give in terms of a Pfaffian. We also show that superconducting states possessing these Fermi surfaces can be energetically stable. A crucial ingredient in our theory is that more than one band is involved in the pairing; since all candidate materials for even-parity superconductivity with broken time-reversal symmetry are multiband systems, we expect these Z2-protected Fermi surfaces to be ubiquitous.
Bogoliubov coefficients for the twist operator in the D1D5 CFT
Carson, Zaq, E-mail: carson.231@osu.edu; Mathur, Samir D., E-mail: mathur.16@osu.edu; Turton, David, E-mail: turton.7@osu.edu
2014-12-15
The D1D5 CFT is a holographic dual of a near-extremal black hole in string theory. The interaction in this theory involves a twist operator which joins together different copies of a free CFT. Given a large number of D1 and D5 branes, the effective length of the circle on which the CFT lives is very large. We develop a technique to study the effect of the twist operator in the limit where the wavelengths of excitations are short compared to this effective length, which we call the ‘continuum limit’. The method uses Bogoliubov coefficients to compute the effect of the twist operator in this limit. For bosonic fields, we use the method to reproduce recent results describing the effect of the twist operator when it links together CFT copies with windings M and N, producing a copy of winding M+N. We also comment on possible generalizations of our results. The methods developed here may help in understanding the twist interaction at higher orders. This in turn should provide insight into the thermalization process in the D1D5 CFT, which gives a holographic description of black hole formation.
Bogoliubov coefficients for the twist operator in the D1D5 CFT
Carson, Zaq; Turton, David
2014-01-01
The D1D5 CFT is a holographic dual of a near-extremal black hole in string theory. The interaction in this theory involves a twist operator which joins together different copies of a free CFT. Given a large number of D1 and D5 branes, the effective length of the circle on which the CFT lives is very large. We develop a technique to study the effect of the twist operator in the limit where the wavelengths of excitations are short compared to this effective length, which we call the 'continuum limit'. The method uses Bogoliubov coefficients to compute the effect of the twist operator in this limit. For bosonic fields, we use the method to reproduce recent results describing the effect of the twist operator when it links together CFT copies with windings M and N, producing a copy of winding M+N. We also comment on possible generalizations of our results. The methods developed here may help in understanding the twist interaction at higher orders. This in turn should provide insight into the thermalization process...
Analytic Characterization for Hilbert-Schmidt Operators on Fock Space
Cai Shi WANG; Zhi Yuan HUANG; Xiang Jun WANG
2005-01-01
In this paper we first introduce and investigate some special classes of nonlinear maps and get several useful results. Then, by using these results, we obtain analytic criteria for checking whether or not an operator defined only on the exponential vectors of a symmetric Fock space becomes a Hilbert-Schmidt operator on the whole space. Additionally, as an application, we also get an analytic criterion for Hilbert-Schmidt operators on a Gaussian probability space through the Wiener-Ito-Segal isomorphism.
Baryons as Fock states of 3,5,... Quarks
Dmitri Diakonov; Victor Petrov
2004-09-01
We present a generating functional producing quark wave functions of all Fock states in the octet, decuplet and antidecuplet baryons in the mean field approximation, both in the rest and infinite momentum frames. In particular, for the usual octet and decuplet baryons we get the SU(6)-symmetric wave functions for their 3-quark component but with specific corrections from relativism and from additional quark-antiquark pairs. For the exotic antidecuplet baryons we obtain the 5-quark wave function.
Energy Spectrum Symmetry of Heisenberg Model in Fock Space
WANG An-Min; ZHU Ren-Gui
2006-01-01
@@ We extend the BCS paring model with equally spaced energy levels to a general one-dimensional spin-l/2 Heisenberg model. The two well-known symmetries of the Heisenberg model, i.e. permutational and spin-inversion symmetries, no longer exist. However, when jointing these two operations together, we find a new symmetry of energy spectrum between its subspace n and subspace L - n of the Fock space. A rigorous proof is presented.
Angular Fock coefficients. Fixing the errors, and further development
Liverts, Evgeny Z
2015-01-01
The angular coefficients $\\psi_{k,p}(\\alpha,\\theta)$ of the Fock expansion characterizing the S-state wave function of the two-electron atomic system, are calculated in hyperspherical angular coordinates $\\alpha$ and $\\theta$. To solve the problem the Fock recurrence relations separated into the independent individual equations associated with definite power $j$ of the nucleus charge $Z$, are applied. The "pure" $j$-components of the angular Fock coefficients, orthogonal to of the hyperspherical harmonics $Y_{kl}$, are found for even values of $k$. To this end, the specific coupling equation is proposed and applied. Effective techniques for solving the individual equations with simplest nonseparable and separable right-hand sides are proposed. Some mistakes/misprints made earlier in representations of $\\psi_{2,0}$, were noted and corrected. All $j$-components of $\\psi_{4,1}$ and the majority of components and subcomponents of $\\psi_{3,0}$ are calculated and presented for the first time. All calculations were ...
Fully discrete Galerkin schemes for the nonlinear and nonlocal Hartree equation
Walter H. Aschbacher
2009-01-01
Full Text Available We study the time dependent Hartree equation in the continuum, the semidiscrete, and the fully discrete setting. We prove existence-uniqueness, regularity, and approximation properties for the respective schemes, and set the stage for a controlled numerical computation of delicate nonlinear and nonlocal features of the Hartree dynamics in various physical applications.
Claudino, D; Gargano, R; Carvalho-Silva, Valter H; E Silva, Geraldo M; da Cunha, W F
2016-07-21
The present paper concludes our series of kinetics studies on the reactions involved in the complex mechanism of nitrogen trifluoride decomposition. Two other related reactions that, along with this mechanism, take part in an efficient boron nitride growth process are also investigated. We report results concerning two abstraction reactions, namely NF2 + N ⇄ 2NF and NF3 + NF ⇄ 2NF2, and two dissociations, N2F4 ⇄ 2NF2 and N2F3 ⇄ NF2 + NF. State-of-the-art electronic structure calculations at the CCSD(T)/cc-pVTZ level of theory were considered to determine geometries and frequencies of reactants, products, and transition states. Extrapolation of the energies to the complete basis set limit was used to obtain energies of all the species. We applied transition state theory to compute thermal rate constants including Wigner, Eckart, Bell, and deformed theory corrections in order to take tunneling effects into account. The obtained results are in good agreement with the experimental data available in the literature and are expected to provide a better phenomenological understanding of the NF3 decomposition role in the boron nitride growth for a wide range of temperature values.
Aerts, Patrick Johan Coenraad
1986-01-01
Computational Theoretical Chemnistry is a research area which, as far as electronic structure problems are concerned, encompasses essentially the development of theoretically sound, yet computionally feasable quantum mechanical models for atoms melecules and the solid state. ... Zie: Introduction
Lewin, Mathieu
2011-01-01
In a recent paper published in Nonlinear Analysis: Theory, Methods & Applications, C. Argaez and M. Melgaard studied excited states for pseudo-relativistic multi-configuration methods. Their paper follows a previous work of mine in the non-relativistic case (Arch. Rat. Mech. Anal., 171, 2004). The main results of the paper of C. Argaez and M. Melgaard are correct, but the proofs are both wrong and incomplete.
Lantri, T.; Bentata, S.; Bouadjemi, B.; Benstaali, W.; Bouhafs, B.; Abbad, A.; Zitouni, A.
2016-12-01
Using the first-principle calculations, we have investigated the structural, elastic, optoelectronic and magnetic properties of Co2MnSi Heusler alloy. Based on the density functional theory (DFT) and hiring the full-potential linearized augmented plane wave (FP-LAPW) method, we have used five approaches: the Hybrid on-site exact exchange, the Local Spin Density Approximation (LSDA), the LSDA+U, the Generalized Gradient Approximation GGA and GGA+U; where the Hubbard on-site Coulomb interaction correction U is calculated by constraint local density approximation for Co and Mn atoms. Our results show that the highly-ordered Co2MnSi alloy is a ductile, stiff and anisotropic material. It has a half-metallic ferromagnetic character with an integer magnetic moment of 5 μB which is in good agreement with the Slater-Pauling rule.
Norman, Patrick; Schimmelpfennig, Bernd; Ruud, Kenneth;
2002-01-01
A systematic investigation of a hierarchy of methods for including relativistic effects in the calculation of linear and nonlinear optical properties was carried out. The simple ECP method and the more involved spin-averaged Douglas-Kroll approximation were compared to benchmark results obtained ...
Lantri, T. [Laboratory of Technology and Solid’s Properties, Faculty of Sciences and Technology, Abdelhamid Ibn Badis University, BP 227, Mostaganem 27000 (Algeria); Bentata, S., E-mail: sam_bentata@yahoo.com [Laboratory of Technology and Solid’s Properties, Faculty of Sciences and Technology, Abdelhamid Ibn Badis University, BP 227, Mostaganem 27000 (Algeria); Bouadjemi, B.; Benstaali, W. [Laboratory of Technology and Solid’s Properties, Faculty of Sciences and Technology, Abdelhamid Ibn Badis University, BP 227, Mostaganem 27000 (Algeria); Bouhafs, B. [Modelling and Simulation in Materials Science Laboratory, Djillali Liabès University of Sidi Bel-Abbès, 22000 Sidi Bel-Abbes (Algeria); Abbad, A. [Laboratory of Technology and Solid’s Properties, Faculty of Sciences and Technology, Abdelhamid Ibn Badis University, BP 227, Mostaganem 27000 (Algeria); Modelling and Simulation in Materials Science Laboratory, Djillali Liabès University of Sidi Bel-Abbès, 22000 Sidi Bel-Abbes (Algeria); Zitouni, A. [Laboratory of Technology and Solid’s Properties, Faculty of Sciences and Technology, Abdelhamid Ibn Badis University, BP 227, Mostaganem 27000 (Algeria)
2016-12-01
Using the first-principle calculations, we have investigated the structural, elastic, optoelectronic and magnetic properties of Co{sub 2}MnSi Heusler alloy. Based on the density functional theory (DFT) and hiring the full-potential linearized augmented plane wave (FP-LAPW) method, we have used five approaches: the Hybrid on-site exact exchange, the Local Spin Density Approximation (LSDA), the LSDA+U, the Generalized Gradient Approximation GGA and GGA+U; where the Hubbard on-site Coulomb interaction correction U is calculated by constraint local density approximation for Co and Mn atoms. Our results show that the highly-ordered Co{sub 2}MnSi alloy is a ductile, stiff and anisotropic material. It has a half-metallic ferromagnetic character with an integer magnetic moment of 5 µB which is in good agreement with the Slater-Pauling rule. - Highlights: • Each approach gives a half magnetic compound. • EECE gives the largest gap. • Elastic properties show a stiff, ductile and anisotropic material. • Electronic properties are similar for the five approaches. • Total magnetic moment is the same for the five approaches (5 µB).
Miranda, R. P.; Fisher, A. J.; Stella, L.; Horsfield, A. P.
2011-06-01
Conjugated polymers have attracted considerable attention in the last few decades due to their potential for optoelectronic applications. A key step that needs optimisation is charge carrier separation following photoexcitation. To understand better the dynamics of the exciton prior to charge separation, we have performed simulations of the formation and dynamics of localised excitations in single conjugated polymer strands. We use a nonadiabatic molecular dynamics method which allows for the coupled evolution of the nuclear degrees of freedom and of multiconfigurational electronic wavefunctions. We show the relaxation of electron-hole pairs to form excitons and oppositely charged polaron pairs and discuss the modifications to the relaxation process predicted by the inclusion of the Coulomb interaction between the carriers. The issue of charge photogeneration in conjugated polymers in dilute solution is also addressed.
Knippenberg, Stefan; Gieseking, Rebecca L; Rehn, Dirk R; Mukhopadhyay, Sukrit; Dreuw, Andreas; Brédas, Jean-Luc
2016-11-08
Third-order nonlinear optical (NLO) properties of polymethine dyes have been widely studied for applications such as all-optical switching. However, the limited accuracy of the current computational methodologies has prevented a comprehensive understanding of the nature of the lowest excited states and their influence on the molecular optical and NLO properties. Here, attention is paid to the lowest excited-state energies and their energetic ratio, as these characteristics impact the figure-of-merit for all-optical switching. For a series of model polymethines, we compare several algebraic diagrammatic construction (ADC) schemes for the polarization propagator with approximate second-order coupled cluster (CC2) theory, the widely used INDO/MRDCI approach and the symmetry-adapted cluster configuration interaction (SAC-CI) algorithm incorporating singles and doubles linked excitation operators (SAC-CI SD-R). We focus in particular on the ground-to-excited state transition dipole moments and the corresponding state dipole moments, since these quantities are found to be of utmost importance for an effective description of the third-order polarizability γ and two-photon absorption spectra. A sum-overstates expression has been used, which is found to quickly converge. While ADC(3/2) has been found to be the most appropriate method to calculate these properties, CC2 performs poorly.
Woldu, Ameha Seyoum; Mai, Joachim
2012-01-01
The present study aims to establish the relationship between the reported radical-scavenging activities of flavonoids and some enthalpy changes that may occur during flavonoids' reactions with free radicals. Eight flavonoids were chosen for the study on the basis of their structural merits and reported 1,1-diphenyl-2-picryl-hydrazyl scavenging activities. Enthalpy changes accompanying interconversions between selected conformations (including spin multiplicities) and homolytic dissociations were estimated. A novel relationship exists between the total enthalpy of reaction for the abstraction of two hydrogen atoms from flavonoids, their reported radical-scavenging activities and the enthalpy of the homolytic dissociation of hydrogen molecule (104.206 kcal mol(-1)). Only those flavonoids which could give up two hydrogen atoms with total enthalpy changes well below 104.206 kcal mol(-1) were active radical scavengers. By appealing to equilibrium dynamics, we demonstrated that, for flavonoids to be able to donate hydrogen atoms, the change in enthalpy accompanying the abstraction of two hydrogen atoms needs to be less than 104.206 kcal mol(-1). This condition does not seem to be restricted to flavonoids only but rather generally applicable to chian-breaking antioxidants. Thermodynamical relationships may be the most important factors governing the radical-scavenging reactions of flavonoids and possibly other compounds as well. Nevertheless, a more complete characterization of antioxidants would necessitate kinetic analysis.
Investigation of Properties of Exotic Nuclei in Non-relativistic and Relativistic Models
2001-01-01
Properties of exotic nuclei are described by non-relativistic and relativistic models. The relativistic mean field theory predicts one proton halo in 26,27,28P and two proton halos in 27,28,29S, recently, one proton halo in 26,27,28P has been found experimentally in MSU lab. The relativistic Hartree-Fock theory has been used to investigate the contribution of Fock term and isovector mesons to the properties of exotic nuclei. It turns out that the influence of the Fock term and isovector mesons on the properties of neutron extremely rich nuclei is very different from that of near stable nuclei. Meanwhile, the deformed Hartree-Fock-Bogoliubov theory has been employed to describe the ground state properties of the isotopes for some light nuclei.
Fission barriers and probabilities of spontaneous fission for elements with Z$\\geq$100
Baran, A; Reinhard, P -G; Robledo, L M; Staszczak, A; Warda, M
2015-01-01
This is a short review of methods and results of calculations of fission barriers and fission half-lives of even-even superheavy nuclei. An approvable agreement of the following approaches is shown and discussed: The macroscopic-microscopic approach based on the stratagem of the shell correction to the liquid drop model and a vantage point of microscopic energy density functionals of Skyrme and Gogny type selfconsistently calculated within Hartree-Fock-Bogoliubov method. Mass parameters are calculated in the Hartree-Fock-Bogoliubov cranking approximation. A short part of the paper is devoted to the nuclear fission dynamics. We also discuss the predictive power of Skyrme functionals applied to key properties of the fission path of $^{266}$Hs. It applies the standard techniques of error estimates in the framework of a $\\chi^2$ analysis.
Strong semiclassical approximation of Wigner functions for the Hartree dynamics
Athanassoulis, Agissilaos
2011-01-01
We consider the Wigner equation corresponding to a nonlinear Schrödinger evolution of the Hartree type in the semiclassical limit h → 0. Under appropriate assumptions on the initial data and the interaction potential, we show that the Wigner function is close in L 2 to its weak limit, the solution of the corresponding Vlasov equation. The strong approximation allows the construction of semiclassical operator-valued observables, approximating their quantum counterparts in Hilbert-Schmidt topology. The proof makes use of a pointwise-positivity manipulation, which seems necessary in working with the L 2 norm and the precise form of the nonlinearity. We employ the Husimi function as a pivot between the classical probability density and the Wigner function, which - as it is well known - is not pointwise positive in general.
A Ansari; P Sharma; U R Jakhar; H L Yadav
2007-01-01
A two-dimensional tilted axis cranking Hartree–Fock–Bogoliubov (CHFB) calculation is performed for 76Kr and 78Kr nuclei up to high spins = 30 employing a pairing-plus-quadrupole (PPQ) model interaction Hamiltonian. Intricate details of the evolution of single particle structures and shapes as a function of spin have been investigated. The results show the existence of energy levels with high quantum numbers lying close to the yrast line in both the nuclei. Such high states should exhibit isomeric characteristics due to the -selection rules for the -decays. Moreover, in 78Kr a new band with = 20–30 lying below the observed ground band is predicted.
Nuclear pairing and Coriolis effects in proton emitters
Volya, A; Volya, Alexander; Davids, Cary
2004-01-01
We introduce a Hartree-Fock-Bogoliubov mean-field approach to treat the problem of proton emission from a deformed nucleus. By substituting a rigid rotor in a particle-rotor-model with a mean-field we obtain a better description of experimental data in $^{141}$Ho. The approach also elucidates the softening of kinematic coupling between particle and collective rotation, the Coriolis attenuation problem.
Reflection-asymmetric nuclear deformations within the Density Functional Theory
Olsen, E; Nazarewicz, W; Stoitsov, M; 10.1088/1742-6596/402/1/012034
2013-01-01
Within the nuclear density functional theory (DFT) we study the effect of reflection-asymmetric shapes on ground-state binding energies and binding energy differences. To this end, we developed the new DFT solver AxialHFB that uses an approximate second-order gradient to solve the Hartree-Fock-Bogoliubov equations of superconducting DFT with the quasi-local Skyrme energy density functionals. Illustrative calculations are carried out for even-even isotopes of radium and thorium.
Pairing Field and Moments of Inertia of Superdeformed Nuclei
陈永静; 陈永寿; 陈辅新
2002-01-01
We have systematically analysed the dynamic moments of inertia of the experimental superdeformed (SD)bands observed in the A = 190, 150 and 60-80 mass regions as functions of rotational frequency. By combining the different mass regions, the dramatic features of the dynamic moments of inertia were found and explained based on the calculations of the pairing fields of SD nuclei with the anisotropic harmonic oscillator quadrupole pairing Hartree-Fock-Bogoliubov model.
Approximate particle number projection for finite range density dependent forces
Valor, A; Robledo, L M
1996-01-01
The Lipkin-Nogami method is generalized to deal with finite range density dependent forces. New expressions are derived and realistic calculations with the Gogny force are performed for the nuclei ^{164}Er and ^{168}Er. The sharp phase transition predicted by the mean field approximation is washed out by the Lipkin-Nogami approach; a much better agreement with the experimental data is reached with the new approach than with the Hartree-Fock_Bogoliubov one, specially at high spins.
On the pairing effects in triaxial nuclei
Oudih, M. R. [Laboratoire de Physique Théorique, Faculté de Physique,USTHB BP 32, El Alia, 16111 Bab Ezzouar, Algiers (Algeria); Fellah, M.; Allal, N. H. [Centre de Recherche Nucléaire d' Alger, 2 Bd. Frantz Fanon, BP. 399 Alger-Gare, Algiers, Algeria and Laboratoire de Physique Théorique, Faculté de Physique,USTHB BP 32, El Alia, 16111 Bab Ezzouar, Algiers (Algeria)
2014-03-05
Triaxial deformation effect on the pairing correlations is studied in the framework of the Skyrme Hartree-Fock-Bogoliubov theory. Quantities such as binding energy, gap parameter and particle-number fluctuation are considered in neutron-rich Mo isotopes. The results are compared with those of axially symmetric calculation and with available experimental data. The role played by the particle-number projection is outlined.
Nerlo-Pomorska, B; Kleban, M
2003-01-01
The modern version of the liquid-drop model (LSD) is compared with the macroscopic part of the binding energy evaluated within the Hartree-Fock- Bogoliubov procedure with the Gogny force and the relativistic mean field theory. The parameters of a liquid-drop like mass formula which approximate on the average the self-consistent results are compared with other models. The limits of nuclear stability predicted by these models are discussed.
Systematic Study of Tensor Force Effect on Pseudospin Orbital Splittings in Sn Isotopes
WANG; Yan-zhao; YU; Guo-liang; LI; Zhen-yu; GU; Jian-zhong
2012-01-01
<正>The tensor force is a noncentral and nonlocal spin-spin coupling term of the nucleon-nucleon interaction whose effect on the nuclear structure has been discussed in the framework of the self-consistent mean field approaches and the shell model in the past a few years. Based on the Skyrme Hartree-Fock-Bogoliubov approach, we systematically investigated the role of the tensor force on the
Bulk properties of light deformed nuclei derived from a medium-modified meson-exchange interaction
Grümmer, F; Ma, Z Y; Krewald, S
1996-01-01
Deformed Hartree-Fock-Bogoliubov calculations for finite nuclei are carried out. As residual interaction, a Brueckner G-matrix derived from a meson-exchange potential is taken. Phenomenological medium modifications of the meson masses are introduced. The binding energies, radii, and deformation parameters of the Carbon, Oxygen, Neon, and Magnesium isotope chains are found to be in good agreement with the experimental data.
Microscopic Structure of the Superdeformed Rotational Band in (132) Ce
Tanabe, K.; Sugawara-Tanabe, K.
1990-06-01
The self-consistent cranked Hartree-Fock-Bogoliubov calculation with the monopole- and quadrupole-pairing plus quadrupole-quadrupole interactions, predicts that the superdeformed band in (132) Ce becomes yrast for spins I >= 32. The result indicates that many dissociated nucleon pairs contribute to the ``rigidification'' of the superdeformed system, in contrast to the s-band in which the decoupling of nucleon pairs occurs only in specific high-j orbitals.
A Phenomenological Analysis of Higher Fock State Contributions to the XcJ Decays
HUANG Tao; WU Hui-Fang
2001-01-01
We present a phenomenological analysis of higher Fock state contributions to the XcJ decays by using the recent BES experimental data.It is found that the higher Fock state (cc)8g) makes an important contribution to the inclusive and exclusive processes with respect to that from the valence Fock state cc) of the XcJ and some constraints of these contributions are obtained for the Xco and Xc2 states in order to fit the experimental data.``
THE CODIMENSION FORMULA ON QUASI-INVARIANT SUBSPACES OF THE FOCK SPACE
侯绳照; 胡俊云
2003-01-01
Let M be an approximately finite codimensional quasi-invariant subspace of the Fock space.This paper gives a formula to calculate the codimension of such spaces and uses this formulato study the structure of quasi-invariant subspaces of the Fock space. Especially, as one ofapplications, it is showed that the analogue of Beurling's theorem is not true for the Fock spaceL2a (Cn ) in the case of n ≥ 2.
Polarizability of supported metal nanoparticles: Mehler-Fock approach
Jung, Jesper; Pedersen, Thomas G.
2012-09-01
Using toroidal coordinates and the Mehler-Fock transform, we present an analysis of the polarizability of a complex structure allowing for the study of arbitrarily truncated metal spheres including a dielectric substrate. Our analysis is based on an electrostatic approach, i.e., we are in the quasi-static limit, where we solve the Laplace equation for the potential. The derived method is used to analyze the behavior of localized surface plasmon resonances of truncated metal nanospheres including substrate effects. The method is fast, simple, easy to implement, and useful for analysis of experimental work on supported metal nanoparticles, e.g., within the area of plasmonic photovoltaics.
Quantum turing machine and brain model represented by Fock space
Iriyama, Satoshi; Ohya, Masanori
2016-05-01
The adaptive dynamics is known as a new mathematics to treat with a complex phenomena, for example, chaos, quantum algorithm and psychological phenomena. In this paper, we briefly review the notion of the adaptive dynamics, and explain the definition of the generalized Turing machine (GTM) and recognition process represented by the Fock space. Moreover, we show that there exists the quantum channel which is described by the GKSL master equation to achieve the Chaos Amplifier used in [M. Ohya and I. V. Volovich, J. Opt. B 5(6) (2003) 639., M. Ohya and I. V. Volovich, Rep. Math. Phys. 52(1) (2003) 25.
Poisson process Fock space representation, chaos expansion and covariance inequalities
Last, Guenter
2009-01-01
We consider a Poisson process $\\eta$ on an arbitrary measurable space with an arbitrary sigma-finite intensity measure. We establish an explicit Fock space representation of square integrable functions of $\\eta$. As a consequence we identify explicitly, in terms of iterated difference operators, the integrands in the Wiener-Ito chaos expansion. We apply these results to extend well-known variance inequalities for homogeneous Poisson processes on the line to the general Poisson case. The Poincare inequality is a special case. Further applications are covariance identities for Poisson processes on (strictly) ordered spaces and Harris-FKG-inequalities for monotone functions of $\\eta$.
Proposal for generating Fock states in traveling wave fields
Benmoussa, Adil [Department of Physics and Astronomy, Lehman College, The City University of New York, Bronx, NY 10468-1589 (United States)]. E-mail: adil.benmoussa@lehman.cuny.edu; Gerry, Christopher C. [Department of Physics and Astronomy, Lehman College, The City University of New York, Bronx, NY 10468-1589 (United States)
2007-05-28
We describe a proposal for the generation of a single-mode photonic number state, |N>, in a traveling wave optical field. The state is obtained by state reduction from an input coherent state using Kerr media. Our method is based on a previous scheme used for hole burning in the Fock space by minimizing the Mandel Q parameter. The same method was used by Maia et al., but ours is different, it requires only one single photon injected in the entire setup and one photon detection at the end.
The O(N) linear sigma model at finite temperature beyond the Hartree approximation
Baacke, J
2003-01-01
We study the O(N) linear sigma model with spontaneous symmetry breaking, using a Hartree-like ansatz with a classical field and variational masses. We go beyond the Hartree approximation by including the two-loop contribution, the sunset diagram, using the 2PPI expansion. We have computed numerically the effective potential at finite temperature. We find a phase transition of second order, while it is first order in the one-loop Hartree approximation. We also discuss some implications of the fact that in this order, the decay of the sigma into two pions affects the thermal diagrams.
High-frequency averaging in semi-classical Hartree-type equations
Giannoulis, Johannes; Sparber, Christof
2009-01-01
We investigate the asymptotic behavior of solutions to semi-classical Schroedinger equations with nonlinearities of Hartree type. For a weakly nonlinear scaling, we show the validity of an asymptotic superposition principle for slowly modulated highly oscillatory pulses. The result is based on a high-frequency averaging effect due to the nonlocal nature of the Hartree potential, which inhibits the creation of new resonant waves. In the proof we make use of the framework of Wiener algebras.
Quantum scattering theory of a single-photon Fock state in three-dimensional spaces.
Liu, Jingfeng; Zhou, Ming; Yu, Zongfu
2016-09-15
A quantum scattering theory is developed for Fock states scattered by two-level systems in three-dimensional free space. It is built upon the one-dimensional scattering theory developed in waveguide quantum electrodynamics. The theory fully quantizes the incident light as Fock states and uses a non-perturbative method to calculate the scattering matrix.
Discrete Parametric Oscillation and Nondiffracting Beams in a Glauber-Fock Oscillator
Oztas, Z
2016-01-01
We consider a Glauber-Fock oscillator and show that diffraction can be managed. We show how to design arrays of waveguides where light beams experience zero diffraction. We find an exact analytical family of nondiffracting localized solution. We predict discrete parametric oscillation in the Glauber-Fock oscillator.
Takahashi, Daisuke A
2015-01-01
The matrix-generalized Bogoliubov-de Gennes systems are recently considered by the present author [arXiv:1509.04242], and the time-dependent and self-consistent multi-soliton solutions are constructed based on the ansatz method. In this paper, restricting the problem to the static case, we exhaustively determine the self-consistent solutions using the inverse scattering theory. Solving the gap equation, we rigorously prove that the self-consistent potential must be reflectionless. As a supplementary topic, we elucidate the relation between the stationary self-consistent potentials and the soliton solutions in the matrix nonlinear Schr\\"odinger equation. The asymptotic formulae of multi-soliton solutions for sufficiently isolated solitons are also presented.
Polymer and Fock representations for a Scalar field
Ashtekar, Abhay; Sahlmann, H; Ashtekar, Abhay; Lewandowski, Jerzy; Sahlmann, Hanno
2003-01-01
In loop quantum gravity, matter fields can have support only on the `polymer-like' excitations of quantum geometry, and their algebras of observables and Hilbert spaces of states can not refer to a classical, background geometry. Therefore, to adequately handle the matter sector, one has to address two issues already at the kinematic level. First, one has to construct the appropriate background independent operator algebras and Hilbert spaces. Second, to make contact with low energy physics, one has to relate this `polymer description' of matter fields to the standard Fock description in Minkowski space. While this task has been completed for gauge fields, important gaps remained in the treatment of scalar fields. The purpose of this letter is to fill these gaps.
A Quantum Probability Explanation in Fock Space for Borderline Contradictions
Sozzo, Sandro
2013-01-01
The construction of a consistent theory for structuring and representing how concepts combine and interact is one of the main challenges for the scholars involved in cognitive studies. All traditional approaches are still facing serious hindrances when dealing with combinations of concepts and concept vagueness. One of the main consequences of these difficulties is the existence of borderline cases which is hardly explainable from the point of view of classical (fuzzy set) logic and probability theory. Resting on a quantum-theoretic approach which successfully models conjunctions and disjuncions of two concepts, we propound a quantum probability model in Fock space which faithfully reproduces the experimental data collected by Alxatib and Pelletier (2011) on borderline contradictions. Our model allows one to explain the occurrence of the latter contradictions in terms of genuine quantum effects, such as contextuality, superposition, interference and emergence. In particular, we claim that it is the specific m...
Fock representations of Q-deformed commutation relations
BoŻejko, Marek; Lytvynov, Eugene; Wysoczański, Janusz
2017-07-01
We consider Fock representations of the Q-deformed commutation relations ∂s∂t†=Q (s ,t ) ∂t†∂s+δ (s ,t ) for s ,t ∈T . Here T :=Rd (or more generally T is a locally compact Polish space), the function Q :T2→C satisfies |Q (s ,t ) |≤1 and Q (s ,t ) =Q (t ,s ) ¯ , and ∫T2h (s ) g (t ) δ (s ,t ) σ (d s ) σ (d t ) :=∫Th (t ) g (t ) σ (d t ) , σ being a fixed reference measure on T. In the case, where |Q (s ,t ) |≡1 , the Q-deformed commutation relations describe a generalized statistics studied by Liguori and Mintchev. These generalized statistics contain anyon statistics as a special case (with T =R2 and a special choice of the function Q). The related Q-deformed Fock space F (H ) over H :=L2(T →C ,σ ) is constructed. An explicit form of the orthogonal projection of H⊗n onto the n-particle space Fn(H ) is derived. A scalar product in Fn(H ) is given by an operator Pn≥0 in H⊗n which is strictly positive on Fn(H ) . We realize the smeared operators ∂t† and ∂t as creation and annihilation operators in F (H ) , respectively. Additional Q-commutation relations are obtained between the creation operators and between the annihilation operators. They are of the form ∂s†∂t†=Q (t ,s ) ∂t†∂s†, ∂s∂t=Q (t ,s ) ∂t∂s, valid for those s ,t ∈T for which |Q(s, t)| = 1.
Alejandro Cabo Montes de Oca
2010-03-01
Full Text Available This work expands the results and derivations presented in a recent letter. It is argued that symmetry breaking Hartree-Fock (HF solutions of a simple model of the Cu-O planes in La2CuO4, are able to describe the insulator and antiferromagnetic characters of this material. Then, this classical primer of a Mott insulator is alternatively obtained here as an exact Slater insulator within the simplest of the first principles schemes. Moreover, pseudogap HF states are also predicted. The maximal energy gap of 100 meV over the Fermi surface of this wavefunction, reasonably well matches the ARPES upper pseudogap measurements for La2CuO4 in the zero doping limit. These surprising results followed after eliminating spin and crystal symmetry constraints usually imposed on the HF orbitals. The discussion helps to clarify the role of the antiferromagnetism and pseudogaps in the physics of the HTSC materials and indicates a promising way to start conciliating the Mott and Slater pictures for the description of the transition metal oxides.
Fock model and Segal-Bargmann transform for minimal representations of Hermitian Lie groups
Hilgert, Joachim; Kobayashi, Toshiyuki; Möllers, Jan;
2012-01-01
For any Hermitian Lie group G of tube type we construct a Fock model of its minimal representation. The Fock space is defined on the minimal nilpotent K_C-orbit X in p_C and the L^2-inner product involves a K-Bessel function as density. Here K is a maximal compact subgroup of G, and g_C=k_C+p_C i...... intertwines the Schroedinger and Fock model. Its kernel involves the same I-Bessel function. Using the Segal--Bargmann transform we also determine the integral kernel of the unitary inversion operator in the Schroedinger model which is given by a J-Bessel function....
Heisenberg-limited quantum sensing and metrology with superpositions of twin-Fock states
Gerry, Christopher C.; Mimih, Jihane
2011-03-01
We discuss the prospects of performing Heisenberg-limited quantum sensing and metrology using a Mach-Zehnder interferometer with input states that are superpositions of twin-Fock states and where photon number parity measurements are made on one of the output beams of the interferometer. This study is motivated by the experimental challenge of producing twin-Fock states on opposite sides of a beam splitter. We focus on the use of the so-called pair coherent states for this purpose and discuss a possible mechanism for generating them. We also discuss the prospect of using other superstitions of twin-Fock states, for the purpose of interferometry.
The trajectory-coherent approximation and the system of moments for the Hartree type equation
V. V. Belov
2002-01-01
Full Text Available The general construction of semiclassically concentrated solutions to the Hartree type equation, based on the complex WKB-Maslov method, is presented. The formal solutions of the Cauchy problem for this equation, asymptotic in small parameter ℏ (ℏ→0, are constructed with a power accuracy of O(ℏ N/2, where N is any natural number. In constructing the semiclassically concentrated solutions, a set of Hamilton-Ehrenfest equations (equations for centered moments is essentially used. The nonlinear superposition principle has been formulated for the class of semiclassically concentrated solutions of Hartree type equations. The results obtained are exemplified by a one-dimensional Hartree type equation with a Gaussian potential.
Uniqueness of the Fock quantization of Dirac fields in 2+1 dimensions
Cortez, Jerónimo; Martín-Benito, Mercedes; Marugán, Guillermo A Mena; Velhinho, José M
2016-01-01
We study the Fock quantization of a free Dirac field in 2+1-dimensional backgrounds which are conformally ultrastatic, with a time-dependent conformal factor. As it is typical for field theories, there is an infinite ambiguity in the Fock representation of the canonical anticommutation relations. Different choices may lead to unitarily inequivalent theories that describe different physics. To remove this ambiguity one usually requires that the vacuum be invariant under the unitary transformations that implement the symmetries of the equations of motion. However, in non-stationary backgrounds, where time translation is not a symmetry transformation, the requirement of vacuum invariance is in general not enough to fix completely the Fock representation. We show that this problem is overcome in the considered scenario by demanding, in addition, a unitarily implementable quantum dynamics. The combined imposition of these conditions selects a unique family of equivalent Fock representations. Moreover, one also obt...
The origin of linear scaling Fock matrix calculation with density prescreening
Mitin, Alexander V., E-mail: mitin@phys.chem.msu.ru [Chemistry Department, Moscow State University, Moscow, 119991 (Russian Federation)
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.
Fock space resolutions of the Virasoro highest weight modules with c<=1
Bouwknegt, P; Pilch, K; Bouwknegt, Peter; Carthy, Jim Mc; Pilch, Krzysztof
1991-01-01
We extend Felder's construction of Fock space resolutions for the Virasoro minimal models to all irreducible modules with $c\\leq 1$. In particular, we provide resolutions for the representations corresponding to the boundary and exterior of the Kac table.
Heisenberg Algebra in the Bargmann-Fock Space with Natural Cutoffs
Maryam Roushan
2014-01-01
Full Text Available We construct a Heisenberg algebra in Bargmann-Fock space in the presence of natural cutoffs encoded as minimal length, minimal momentum, and maximal momentum through a generalized uncertainty principle.
The Light-Cone Fock Expansion in Quantum Chromodynamics
Brodsky, S J
2000-01-01
A fundamental question in QCD is the non-perturbative structure of hadrons at the amplitude level--not just the single-particle flavor, momentum, and helicity distributions of the quark constituents, but also the multi-quark, gluonic, and hidden-color correlations intrinsic to hadronic and nuclear wavefunctions. The light-cone Fock-state representation of QCD encodes the properties of a hadrons in terms of frame-independent wavefunctions. A number of applications are discussed, including semileptonic B decays, deeply virtual Compton scattering, and dynamical higher twist effects in inclusive reactions. A new type of jet production reaction, "self-resolving diffractive interactions" can provide direct information on the light-cone wavefunctions of hadrons in terms of their quark and gluon degrees of freedom as well as the composition of nuclei in terms of their nucleon and mesonic degrees of freedom. The relation of the intrinsic sea to the light-cone wavefunctions is discussed. The physics of light-cone wavef...
Quantum stopping times stochastic integral in the interacting Fock space
Kang, Yuanbao, E-mail: kangyuanb@163.com [College of Mathematics Science, Chong Qing Normal University, Chongqing 400047 (China)
2015-08-15
Following the ideas of Hudson [J. Funct. Anal. 34(2), 266-281 (1979)] and Parthasarathy and Sinha [Probab. Theory Relat. Fields 73, 317-349 (1987)], we define a quantum stopping time (QST, for short) τ in the interacting Fock space (IFS, for short), Γ, over L{sup 2}(ℝ{sup +}), which is actually a spectral measure in [0, ∞] such that τ([0, t]) is an adapted process. Motivated by Parthasarathy and Sinha [Probab. Theory Relat. Fields 73, 317-349 (1987)] and Applebaum [J. Funct. Anal. 65, 273-291 (1986)], we also develop a corresponding quantum stopping time stochastic integral (QSTSI, for abbreviations) on the IFS over a subspace of L{sup 2}(ℝ{sup +}) equipped with a filtration. As an application, such integral provides a useful tool for proving that Γ admits a strong factorisation, i.e., Γ = Γ{sub τ]} ⊗ Γ{sub [τ}, where Γ{sub τ]} and Γ{sub [τ} stand for the part “before τ” and the part “after τ,” respectively. Additionally, this integral also gives rise to a natural composition operation among QST to make the space of all QSTs a semigroup.
The Fock Space of Loopy Spin Networks for Quantum Gravity
Charles, Christoph
2016-01-01
In the context of the coarse-graining of loop quantum gravity, we introduce loopy and tagged spin networks, which generalize the standard spin network states to account explicitly for non-trivial curvature and torsion. Both structures relax the closure constraints imposed at the spin network vertices. While tagged spin networks merely carry an extra spin at every vertex encoding the overall closure defect, loopy spin networks allow for an arbitrary number of loops attached to each vertex. These little loops can be interpreted as local excitations of the quantum gravitational field and we discuss the statistics to endow them with. The resulting Fock space of loopy spin networks realizes new truncation of loop quantum gravity, allowing to formulate its graph-changing dynamics on a fixed background graph plus local degrees of freedom attached to the graph nodes. This provides a framework for re-introducing a non-trivial background quantum geometry around which we would study the effective dynamics of perturbatio...
Nonperturbative solution of scalar Yukawa model in two- and three-body Fock space truncations
Karmanov, Vladimir A; Smirnov, Alexander V; Vary, James P
2016-01-01
The Light-Front Tamm-Dancoff method of finding the nonperturbative solutions in field theory is based on the Fock decomposition of the state vector, complemented with the sector-dependent nonperturbative renormalization scheme. We show in detail how to implement the renormalization procedure and to solve the simplest nontrivial example of the scalar Yukawa model in the two- and three-body Fock space truncations incorporating scalar "nucleon" and one or two scalar "pions".
Spectrum of the [Formula: see text]-Neumann Laplacian on the Fock space.
Haslinger, Friedrich
2013-06-15
The spectrum of the [Formula: see text]-Neumann Laplacian on the Fock space [Formula: see text] is explicitly computed. It turns out that it consists of positive integer eigenvalues, each of which is of infinite multiplicity. Spectral analysis of the [Formula: see text]-Neumann Laplacian on the Fock space is closely related to Schrödinger operators with magnetic fields and to the complex Witten Laplacian.
Fock-exchange for periodic structures in the real-space formalism and the KLI approximation.
Natan, Amir
2015-12-21
The calculation of Fock-exchange interaction is an important task in the computation of molecule and solid properties. In this work we describe how we implement the Fock exchange in the real-space formalism using the KLI approximation for the OEP equation for 3D periodic systems. The implementation is demonstrated within the PARSEC real-space pseudopotential code that uses a discrete uniform grid and norm conserving pseudopotentials for the ionic potentials.
O(N) linear sigma model beyond the Hartree approximation at finite temperature
Baacke, J; Michalski, Stefan
2003-01-01
We study the O(N) linear sigma model with spontaneous symmetry breaking at finite temperature in the framework of the two-particle point-irreducible (2PPI) effective action. We go beyond the Hartree approximation by including the two-loop contribution, i.e., the sunset diagram. A phase transition of second order is found, whereas it is of first order in the one-loop Hartree approximation. Furthermore, we show the temperature-dependence of the variational mass parameters and comment on their relation to the physical sigma and pion masses.
ON THE DECAY AND SCATTERING FOR THE KLEIN-GORDON-HARTREE EQUATION WITH RADIAL DATA
Wu Haigen; Zhang Junyong
2012-01-01
In this paper,we study the decay estimate and scattering theory for the Klein-Gordon-Hartree equation with radial data in space dimension d ≥ 3.By means of a compactness strategy and two Morawetz-type estimates which come from the linear and nonlinear parts of the equation,respectively,we obtain the corresponding theory for energy subcritical and critical cases.The exponent range of the decay estimates is extended to 0 ＜ γ ≤ 4 and γ＜ d with Hartree potential V(x) =|x|-γ.
Rezania, Hamed; Abdi, Ameneh
2017-04-01
We study the behaviors of both Hartree and correlation energies of undoped gapped armchair graphene nanoribbon using random phase approximation in the context of Hubbard model Hamiltonian. Specially, the effects of spin polarization and gap parameter on electron density dependence of Hartree and correlation energies of armchair graphene nanoribbon has been addressed. Our results show the variation of gap parameter leads to considerable effect on correlation and Hartree energy behavior of spin unpolarized gapped graphene in the middle electron density region. However local Hubbard interaction parameter affects the behaviors of Hartree and correlation energy on the whole range of electron density in zero magnetization case. We also show that a considerable reduction has been observed for density dependence of Hartree and correlation energies of spin polarized gapped graphene nanoribbon.
GEOMETRIC OPTICS FOR 3D-HARTREE-TYPE EQUATION WITH COULOMB POTENTIAL
无
2006-01-01
This article considers a family of 3D-Hartree-type equation with Coulomb potential |x|-1, whose initial data oscillates so that a caustic appears. In the linear geometric optics case, by using the Lagrangian integrals, a uniform description of the solution outside the caustic, and near the caustic are obtained.
Bose-Einstein Condensation in Linear Sigma Model at Hartree Approximation
M. Agop; SHU Song; Camelia Popa; LI Jia-Rong; Anca Harabagiu
2008-01-01
The BEC of charged pions is investigated in the framework of O(4) linear sigma model. By using Cornwall Jackiw Tomboulis formalism, we have derived the gap equations for the effective masses of the mesons at finite tempera-ture and finite isospin density. The critical temperature and phase diagram of BEC are discussed in the non-chiral limit at Hartree approximation.
Level-0 action of $U_{q}(\\widehat{sl}_{n})$ on the q-deformed Fock spaces
Takemura, K; Takemura, Kouichi; Uglov, Denis
1996-01-01
On the level-1 Fock space modules of the algebra $U_q(\\hat{sl_n})$ we define a level-0 action $U_0$ of the $U_q(\\hat{sl_n})$, and an action of an abelian algebra of conserved Hamiltonians commuting with the $U_0$. An irreducible decomposition of the Fock space with respect to the level-0 action is derived by constructing a base of the Fock space in terms of the Non-symmetric Macdonald Polynomials.
Qureshi, Mumnuna A.; Zhong, Johnny; Betouras, Joseph J.; Zagoskin, Alexandre M.
2017-03-01
Theoretical description and simulation of large quantum coherent systems out of equilibrium remains a daunting task. Here we are developing an approach to it based on the Pechukas-Yukawa formalism, which is especially convenient in the case of an adiabatically slow external perturbation, though it is not restricted to adiabatic systems. In this formalism the dynamics of energy levels in an externally perturbed quantum system as a function of the perturbation parameter is mapped on that of a fictitious one-dimensional classical gas of particles with cubic repulsion. Equilibrium statistical mechanics of this Pechukas gas allows us to reproduce the random matrix theory of energy levels. In the present work, we develop the nonequilibrium statistical mechanics of the Pechukas gas, starting with the derivation of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) chain of equations for the appropriate generalized distribution functions. Sets of approximate kinetic equations can be consistently obtained by breaking this chain at a particular point (i.e., approximating all higher-order distribution functions by the products of the lower-order ones). When complemented by the equations for the level occupation numbers and interlevel transition amplitudes, they allow us to describe the nonequilibrium evolution of the quantum state of the system, which can describe better a large quantum coherent system than the currently used approaches. In particular, we find that corrections to the factorized approximation of the distribution function scale as 1 /N , where N is the number of the "Pechukas gas particles" (i.e., energy levels in the system).
Loop Quantization Versus Fock Quantization Of P-form Electromagnetism On Static Spacetimes
Carrion Alvarez, M
2004-01-01
As a warmup for studying dynamics and gravitons in loop quantum gravity. Varadajan showed that Wilson loops give operators on the Fock space for electromagnetism in Minkowski spacetime—but only after regularizing the loops by smearing them with a Gaussian. Unregularized Wilson loops are too singular to give densely defined operators. Here we present a rigorous treatment of unsmeared Wilson loops for vacuum electromagnetism on an arbitrary globally hyperbolic static spacetime. Our Wilson loops are not operators, but “quasioperators”: sesquilinear forms on the dense subspace of Fock space spanned by coherent states corresponding to smooth classical solutions. To obtain this result we begin by carefully treating electromagnetism on globally hyperbolic static spacetimes, addressing various issues that are usually ignored, such as the definition of Aharonov-Bohm modes when space is noncompact. We then use a new construction of Fock space based on coherent states to define Wilson loop ...
Quantum Interference between a Single-Photon Fock State and a Coherent State
Windhager, Armin; Pacher, Christoph; Peev, Momtchil; Poppe, Andreas
2010-01-01
We derive analytical expressions for the single mode quantum field state at the individual output ports of a beam splitter when a single-photon Fock state and a coherent state are incident on the input ports. The output states turn out to be a statistical mixture between a displaced Fock state and a coherent state. Consequently we are able to find an analytical expression for the corresponding Wigner function. Because of the generality of our calculations the obtained results are valid for all passive and lossless optical four port devices. We show further how the results can be adapted to the case of the Mach-Zehnder interferometer. In addition we consider the case for which the single-photon Fock state is replaced with a general input state: a coherent input state displaces each general quantum state at the output port of a beam splitter with the displacement parameter being the amplitude of the coherent state.
Quantum interference between a single-photon Fock state and a coherent state
Windhager, A.; Suda, M.; Pacher, C.; Peev, M.; Poppe, A.
2011-04-01
We derive analytical expressions for the single mode quantum field state at the individual output ports of a beam splitter when a single-photon Fock state and a coherent state are incident on the input ports. The output states turn out to be a statistical mixture between a displaced Fock state and a coherent state. Consequently we are able to find an analytical expression for the corresponding Wigner function. Because of the generality of our calculations the obtained results are valid for all passive and lossless optical four port devices. We show further how the results can be adapted to the case of the Mach-Zehnder interferometer. In addition we consider the case for which the single-photon Fock state is replaced with a general input state: a coherent input state displaces each general quantum state at the output port of a beam splitter with the displacement parameter being the amplitude of the coherent state.
Lin, G W; Huang, T; Lin, X M; Wang, Z Y; Gong, S Q
2012-01-01
We propose a technique for quantum nondemolition (QND) measurement and preparation of fock states by dynamics of electromagnetically induced transparency (EIT). An atomic medium trapped in an optical cavity is driven by two continuous-wave classical fields under steady-state EIT. The weak coherent fields are sequently injected into the cavity. During the process of photons passing through the cavity, a measurement on the changes of absorption loss of the probe field will be used for QND measurement of the small photon number, and thus create photon fock states, in particular single-photon states, in a heralded way.
Quantum Interference between a Single-Photon Fock State and a Coherent State
Windhager, Armin; Suda, Martin; Pacher, Christoph; Peev, Momtchil; Poppe, Andreas
2010-01-01
We derive analytical expressions for the single mode quantum field state at the individual output ports of a beam splitter when a single-photon Fock state and a coherent state are incident on the input ports. The output states turn out to be a statistical mixture between a displaced Fock state and a coherent state. Consequently we are able to find an analytical expression for the corresponding Wigner function. Because of the generality of our calculations the obtained results are valid for al...
Prykarpatski, A. K.; Bogolubov, N. N.
2017-01-01
A quantum fermionic massless charged particle self-intercating with its own self-generated bosonic electromagnetic field is reanalyzed in the framework of the Fock many-temporal and Feynman proper time approaches. The self-interaction phenomenon structure is discussed within the renormalized quantum Fock space. The quantum electromagnetic charged particle mass origin is suggested.
Papoulia, A; Ekman, J
2016-01-01
Background: Atomic spectral lines from different isotopes display a small shift in energy, commonly referred to as the line isotope shift. One of the components of the isotope shift is the field shift, which depends on the extent and the shape of the nuclear charge density distribution. Purpose: To investigate how sensitive field shifts are with respect to variations in the nuclear size and shape and what information of nuclear charge distributions that can be extracted from measured field shifts. Methods: Nuclear properties are obtained from nuclear density functional theory calculations based on the Skyrme-Hartree-Fock-Bogoliubov approach. These results are combined with multiconfiguration Dirac-Hartree-Fock methods to obtain realistic field shifts. Results: Phenomena such as nuclear deformation and variations in the diffuseness of nuclear charge distributions give measurable contributions to the field shifts. Using a novel approach, we demonstrate the possibility to extract new information concerning the n...
Mapping the Generator Coordinate Method to the Coupled Cluster Approach
Stuber, Jason L
2015-01-01
The generator coordinate method (GCM) casts the wavefunction as an integral over a weighted set of non-orthogonal single determinantal states. In principle this representation can be used like the configuration interaction (CI) or shell model to systematically improve the approximate wavefunction towards an exact solution. In practice applications have generally been limited to systems with less than three degrees of freedom. This bottleneck is directly linked to the exponential computational expense associated with the numerical projection of broken symmetry Hartree-Fock (HF) or Hartree-Fock-Bogoliubov (HFB) wavefunctions and to the use of a variational rather than a bi-variational expression for the energy. We circumvent these issues by choosing a hole-particle representation for the generator and applying algebraic symmetry projection, via the use of tensor operators and the invariant mean (operator average). The resulting GCM formulation can be mapped directly to the coupled cluster (CC) approach, leading...
Gogny interactions with tensor terms
Anguiano, M.; Lallena, A.M.; Bernard, R.N. [Universidad de Granada, Departamento de Fisica Atomica, Molecular y Nuclear, Granada (Spain); Co' , G. [INFN, Lecce (Italy); De Donno, V. [Universita del Salento, Dipartimento di Matematica e Fisica ' ' E. De Giorgi' ' , Lecce (Italy); Grasso, M. [Universite Paris-Sud, Institut de Physique Nucleaire, IN2P3-CNRS, Orsay (France)
2016-07-15
We present a perturbative approach to include tensor terms in the Gogny interaction. We do not change the values of the usual parameterisations, with the only exception of the spin-orbit term, and we add tensor terms whose only free parameters are the strengths of the interactions. We identify observables sensitive to the presence of the tensor force in Hartree-Fock, Hartree-Fock-Bogoliubov and random phase approximation calculations. We show the need of including two tensor contributions, at least: a pure tensor term and a tensor-isospin term. We show results relevant for the inclusion of the tensor term for single-particle energies, charge-conserving magnetic excitations and Gamow-Teller excitations. (orig.)
Finite-temperature pairing re-entrance in the drip-line nucleus 48Ni
Belabbas, Mohamed; Li, Jia Jie; Margueron, Jérôme
2017-08-01
Finite-temperature Hartree-Fock-Bogoliubov theory using Skyrme interactions and relativistic Hartree-Fock effective Lagrangians predicts 48Ni as being a possible candidate for the finite-temperature pairing re-entrance phenomenon. For this proton-drip-line nucleus, proton resonant states are expected to contribute substantially to pairing correlations and the two predicted critical temperatures are Tc 1˜0.08 -0.2 MeV and Tc 2˜0.7 -0.9 MeV. It is also shown that pairing re-entrance modifies the proton single-particle energies around the Fermi level, as well as occupation numbers and quasiparticle levels. The understanding of pairing re-entrance in 48Ni presently challenges our understanding of exotic matter under extreme conditions.
Controlling single-photon Fock-state propagation through opaque scattering media
Huisman, T.J.; Huisman, S.R.; Mosk, A.P.; Pinkse, P.W.H.
2014-01-01
The control of light scattering is essential in many quantum optical experiments. Wavefront shaping is a technique used for ultimate control over wave propagation through multiple-scattering media by adaptive manipulation of incident waves. We control the propagation of single-photon Fock states thr
Flight test report: Focke wulf PIAGGIO P149D-TP
Barker, D
2015-12-01
Full Text Available and subsequently built under licence by Focke Wulf for the German Air Force. After the fleet was retired from Luftwaffe Service, Heiml’s brother bought one and overhauled it. Several years later, while on a visit to Germany, it was ‘love at first sight’ leaving...
Generation of motional Fock states of a trappedion in the mediate-excitation regime
Zheng Shi-Biao
2004-01-01
We propose a scheme to prepare Fock states for the vibrational motion of a trapped ion. Unlike previous schemes,the present scheme works in the mediate-excitation regime, in which the corresponding Rabi frequency is equal to the trap frequency. Thus, the required time is greatly shortened, which is important in view of decoherence.
Relativistic Dirac-Fock atom properties for Z = 121 to Z = 138
Zhou, Z.; Kas, J. J.; Rehr, J. J.; Ermler, W. C.
2017-03-01
We present relativistic Dirac-Fock calculations of atomic properties for atomic numbers Z = 121- 138, extending a previous tabulation of Desclaux. The calculations assume a single LS ground state configuration and include a correction for finite nuclear size, with an approximation for the mean nuclear mass A(Z) based on the liquid-drop model.
Heavy Quarks Production in Hadronic Processes: Qualitative Study of Higher-Order Fock States
N. Mebarki; K. Benhizia; Z. Belghobsi; D. Bouaziz
2009-01-01
The contribution of the two particles Fock states for the production of a heavy quark in proton-pion and photon-pion collisions is studied. It is shown that the effect depends strongly on the produced heavy quark mass, and the choice of the factorization scale.
Monte Carlo solution of the Schrödinger equation in Fock space representation
Szybisz, L.; Zabolitzky, J. G.
1984-09-01
A new Monte Carlo method to solve the Schrödinger equation when expressed in Fock space is presented. The procedure is applied to two soluble many-body hamiltonians, the quasispin model of Lipkin-Meshkov-Glick and the so-called "static source" limit of the nucleon-scalar-meson interaction in the discrete one-dimensional space.
Monte Carlo solution of the Schroedinger equation in Fock space representation
Szybisz, L.; Zabolitzky, J.G. (Koeln Univ. (Germany, F.R.). Inst. fuer Theoretische Physik)
1984-09-03
A new Monte Carlo method to solve the Schroedinger equation when expressed in Fock space is presented. The procedure is applied to two soluble many-body hamiltonians, the quasispin model of Lipkin-Meshkov-Glick and the so-called 'static source' limit of the nucleon-scalar-meson interaction in the discrete one-dimensional space.
Group classification and conservation laws of the generalized Klein-Gordon-Fock equation
Muatjetjeja, B.
2016-08-01
In the present paper, we perform Lie and Noether symmetries of the generalized Klein-Gordon-Fock equation. It is shown that the principal Lie algebra, which is one-dimensional, has several possible extensions. It is further shown that several cases arise for which Noether symmetries exist. Exact solutions for some cases are also obtained from the invariant solutions of the investigated equation.
Zeros of the Bergman kernel of the Fock-Bargmann-Hartogs domain and the interlacing property
Yamamori, Atsushi
2011-01-01
In this paper we consider the zeros of the Bergman kernel of the Fock-Bargmann-Hartogs domain $D_{n,m}$. We describe how the existence of zeros of the Bergman kernel depends on the integers $m$ and $n$ with the help of the interlacing property.
Statistical signatures of states orthogonal to the Fock-state ladder of composite bosons
Bouvrie, P. Alexander; Tichy, Malte C.; Mølmer, Klaus
2016-11-01
The theory of composite bosons (cobosons) made of two fermions [C. K. Law, Phys. Rev. A 71, 034306 (2005), 10.1103/PhysRevA.71.034306; M. C. Tichy et al., Phys. Rev. Lett. 109, 260403 (2012), 10.1103/PhysRevLett.109.260403] converges to ordinary structureless bosons in the limit of infinitely strong entanglement between the fermionic constituents. For finite entanglement, the annihilation operator c ̂ of a composite boson couples the N -coboson Fock state not only to the (N -1 ) -coboson state—as for ordinary bosons—but also to a component which is orthogonal to the Fock-state ladder of cobosons. Coupling with states orthogonal to the Fock ladder arises also in dynamical processes of cobosons. Here, with a Gedanken experiment involving both mode splitting and collective Hong-Ou-Mandel-like interference, we derive the characteristic physical signature of the states orthogonal to the Fock ladder generated in the splitting process. This allows us to extract the microscopic properties of many-fermion wave functions from the collective coboson behavior. We show that consecutive beam-splitter dynamics increases the deviation from the ideal bosonic behavior pattern, which opens up a rigorous approach to the falsification of coboson theory.
Wigner spectrum and coherent feedback control of continuous-mode single-photon Fock states
Dong, Zhiyuan; Cui, Lei; Zhang, Guofeng; Fu, Hongchen
2016-10-01
Single photons are very useful resources in quantum information science. In real applications it is often required that the photons have a well-defined spectral (or equivalently temporal) modal structure. For example, a rising exponential pulse is able to fully excite a two-level atom while a Gaussian pulse cannot. This motivates the study of continuous-mode single-photon Fock states. Such states are characterized by a spectral (or temporal) pulse shape. In this paper we investigate the statistical property of continuous-mode single-photon Fock states. Instead of the commonly used normal ordering (Wick order), the tool we proposed is the Wigner spectrum. The Wigner spectrum has two advantages: (1) it allows to study continuous-mode single-photon Fock states in the time domain and frequency domain simultaneously; (2) because it can deal with the Dirac delta function directly, it has the potential to provide more information than the normal ordering where the Dirac delta function is always discarded. We also show how various control methods in particular coherent feedback control can be used to manipulate the pulse shapes of continuous-mode single-photon Fock states.
Accardi, Luigi
2007-01-01
The identification of the $*$--Lie algebra of the renormalized higher powers of white noise (RHPWN) and the analytic continuation of the second quantized Virasoro--Zamolodchikov--$w_{\\infty}$ $*$--Lie algebra of conformal field theory and high-energy physics, was recently established in \\cite{id} based on results obtained in [1] and [2]. In the present paper we show how the RHPWN Fock kernels must be truncated in order to be positive definite and we obtain a Fock representation of the two algebras. We show that the truncated renormalized higher powers of white noise (TRHPWN) Fock spaces of order $\\geq 2$ host the classical continuous binomial process.
Constantin, Lucian A; Fabiano, Eduardo; Della Sala, Fabio
2017-09-12
Using the semiclassical neutral atom theory, we developed a modified fourth-order kinetic energy (KE) gradient expansion (GE4m) that keeps unchanged all the linear-response terms of the uniform electron gas and gives a significant improvement with respect to the known semilocal functionals for both large atoms and jellium surfaces. On the other hand, GE4m is not accurate for light atoms; thus, we modified the GE4m coefficients making them dependent on a novel ingredient, the reduced Hartree potential, recently introduced in the Journal of Chemical Physics 2016, 145, 084110, in the context of exchange functionals. The resulting KE gradient expansion functional, named uGE4m, belongs to the novel class of u-meta-generalized-gradient-approximations (uMGGA) whose members depend on the conventional ingredients (i.e., the reduced gradient and Laplacian of the density) as well as on the reduced Hartree potential. To test uGE4m, we defined an appropriate benchmark (including total KE and KE differences for atoms, molecules and jellium clusters) for gradient expansion functionals, that is, including only those systems which are mainly described by a slowly varying density regime. While most of the GGA and meta-GGA KE functionals (we tested 18 of them) are accurate for some properties and inaccurate for others, uGE4m shows a consistently good performance for all the properties considered. This represents a qualitative boost in the KE functional development and highlights the importance of the reduced Hartree potential for the construction of next-generation KE functionals.
Wang, Haobin; Thoss, Michael
2016-10-01
The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method is implemented in the interaction picture to allow a more effective description of correlation effects. It is shown that the artificial correlation present in the original Schrödinger picture can be removed with an appropriate choice of the zeroth-order Hamiltonian. Thereby, operators in the interaction picture are obtained through time-dependent unitary transformations, which have negligible computational cost compared with other parts of the ML-MCTDH algorithm. The efficiency of the method is demonstrated by application to a model of vibrationally coupled charge transport in molecular junctions.
A Hartree–Fock study of the confined helium atom: Local and global basis set approaches
Young, Toby D., E-mail: tyoung@ippt.pan.pl [Zakład Metod Komputerowych, Instytut Podstawowych Prolemów Techniki Polskiej Akademia Nauk, ul. Pawińskiego 5b, 02-106 Warszawa (Poland); Vargas, Rubicelia [Universidad Autónoma Metropolitana Iztapalapa, División de Ciencias Básicas e Ingenierías, Departamento de Química, San Rafael Atlixco 186, Col. Vicentina, Iztapalapa, D.F. C.P. 09340, México (Mexico); Garza, Jorge, E-mail: jgo@xanum.uam.mx [Universidad Autónoma Metropolitana Iztapalapa, División de Ciencias Básicas e Ingenierías, Departamento de Química, San Rafael Atlixco 186, Col. Vicentina, Iztapalapa, D.F. C.P. 09340, México (Mexico)
2016-02-15
Two different basis set methods are used to calculate atomic energy within Hartree–Fock theory. The first is a local basis set approach using high-order real-space finite elements and the second is a global basis set approach using modified Slater-type orbitals. These two approaches are applied to the confined helium atom and are compared by calculating one- and two-electron contributions to the total energy. As a measure of the quality of the electron density, the cusp condition is analyzed. - Highlights: • Two different basis set methods for atomic Hartree–Fock theory. • Galerkin finite element method and modified Slater-type orbitals. • Confined atom model (helium) under small-to-extreme confinement radii. • Detailed analysis of the electron wave-function and the cusp condition.
Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization
Cortez, Jerónimo; Martín-Benito, Mercedes; Marugán, Guillermo A Mena; Velhinho, José M
2016-01-01
We address the issue of the infinite ambiguity that affects the construction of a Fock quantization of a Dirac field propagating in a cosmological spacetime with flat compact sections. In particular, we discuss a physical criterion that restricts to a unique possibility (up to unitary equivalence) the infinite set of available vacua. We prove that this desired uniqueness is guaranteed, for any possible choice of spin structure on the spatial sections, if we impose two conditions. The first one is that the symmetries of the classical system must be implemented quantum mechanically, so that the vacuum is invariant under the symmetry transformations. The second and more important condition is that the constructed theory must have a quantum dynamics that is implementable as a (non-trivial) unitary operator in Fock space. Actually, this unitarity of the quantum dynamics leads us to identify as explicitly time dependent some very specific contributions of the Dirac field. In doing that, we essentially characterize ...
Fock-space localization of polaritons in the Jaynes-Cummings dimer model
Shapourian, Hassan; Sadri, Darius
2016-01-01
We present a method to study the semiclassical dynamics of the Jaynes-Cummings dimer model, describing two coupled cavities, each containing a two-level system (qubit). We develop a Fock-space WKB approach in the polariton basis where each site is treated exactly while the intersite polariton hopping is treated semiclassically. We show that the self-trapped states can be viewed as Fock-space localized states. We find that this picture yields the correct critical value of interaction strength at which the delocalization-localization transition occurs. Moreover, the validity of our WKB approach is supported by showing that the quantum spectrum can be derived from a set of Bohr-Sommerfeld quantization conditions and by confirming that the quantum eigenstates are consistent with the classical orbital motion in the polariton band picture. The underlying idea of our method is quite general and can be applied to other interacting spin-boson models.
Relativity with Respect to Measurement: Collapse and Quantum Events from Fock to Cramer
Leonardo Chiatti
2014-10-01
Full Text Available Some observations are presented starting with the well-known article by Vladimir Fock “Quantum Physics and Philosophical Problems”, published in 1971. In this article, which summarizes for Western readers a long and complicated reflection of the foundations of quantum mechanics (QM, Fock illustrates his “minimal” interpretation of this theory. By minimal, we mean that it only uses concepts related to the operational aspects of the measurement procedures, avoiding any mention of definite quantum ontologies (Bell’s beables. It is argued that, by taking into account the time reversal invariance of the microscopic processes and introducing the notion of irreversibility in an appropriate manner, Fock’s description becomes an anticipation of the “transaction” notion introduced by Cramer a decade later. So, the concept of “collapse” does retain the features of a QM “freak” postulate to become a new way to look at the elementary quantum processes.
A semiclassical approach to many-body interference in Fock-space
Engl, Thomas
2015-11-01
Many-body systems draw ever more physicists' attention. Such an increase of interest often comes along with the development of new theoretical methods. In this thesis, a non-perturbative semiclassical approach is developed, which allows to analytically study many-body interference effects both in bosonic and fermionic Fock space and is expected to be applicable to many research areas in physics ranging from Quantum Optics and Ultracold Atoms to Solid State Theory and maybe even High Energy Physics. After the derivation of the semiclassical approximation, which is valid in the limit of large total number of particles, first applications manifesting the presence of many-body interference effects are shown. Some of them are confirmed numerically thus verifying the semiclassical predictions. Among these results are coherent back-/forward-scattering in bosonic and fermionic Fock space as well as a many-body spin echo, to name only the two most important ones.
The light-cone Fock state expansion and hadron physics phenomenology
Brodsky, S.J.
1997-06-01
The light-cone Fock expansion is defined in the following way: one first constructs the light-cone time evolution operator and the invariant mass operator in light-cone gauge from the QCD Lagrangian. The total longitudinal momentum and transverse momenta are conserved, i.e. are independent of the interactions. The matrix elements of the invariant mass operator on the complete orthonormal basis of the free theory can then be constructed. The matrix elements connect Fock states differing by 0, 1, or 2 quark or gluon quanta, and they include the instantaneous quark and gluon contributions imposed by eliminating dependent degrees of freedom in light-cone gauge. Applications of light-cone methods to QCD phenomenology are briefly described.
Uniqueness of the Fock quantization of scalar fields in a Bianchi I cosmology with unitary dynamics
Cortez, Jerónimo; Martín-Benito, Mercedes; Marugán, Guillermo A Mena; Olmedo, Javier; Velhinho, José M
2016-01-01
The Fock quantization of free scalar fields is subject to an infinite ambiguity when it comes to choosing a set of annihilation and creation operators, choice that is equivalent to the determination of a vacuum state. In highly symmetric situations, this ambiguity can be removed by asking vacuum invariance under the symmetries of the system. Similarly, in stationary backgrounds, one can demand time-translation invariance plus positivity of the energy. However, in more general situations, additional criteria are needed. For the case of free (test) fields minimally coupled to a homogeneous and isotropic cosmology, it has been proven that the ambiguity is resolved by introducing the criterion of unitary implementability of the quantum dynamics, as an endomorphism in Fock space. This condition determines a specific separation of the time dependence of the field, so that this splits into a very precise background dependence and a genuine quantum evolution. Furthermore, together with the condition of vacuum invaria...
The Mehler-Fock transform of general order and arbitrary index and its inversion
Cyril Nasim
1984-01-01
Full Text Available An integral transform involving the associated Legendre function of zero order, P−12+iτ(x, x∈[1,∞, as the kernel (considered as a function of τ, is called Mehler-Fock transform. Some generalizations, involving the function P−12+iτμ(x, where the order μ is an arbitrary complex number, including the case when μ=0,1,2,… have been known for some time. In this present note, we define a general Mehler-Fock transform involving, as the kernel, the Legendre function P−12+tμ(x, of general order μ and an arbitrary index −12+t, t=σ+iτ, −∞<τ<∞. Then we develop a symmetric inversion formulae for these transforms. Many well-known results are derived as special cases of this general form. These transforms are widely used for solving many axisymmetric potential problems.
El-Ganainy, Ramy; Christodoulides, Demetrios N
2013-01-01
We investigate the dynamics of nonclassical states of light in coupled optical structures and we demonstrate a number of intriguing features associated with such arrangements. By diagonalizing the system's Hamiltonian, we show that these geometries can support eigenstates having anomalous optical intensity distribution with no classical counterpart. These features may provide new avenues towards manipulating light flow at the quantum level. By projecting the Hamiltonian operator on Hilbert subspaces spanning different numbers of photon excitations, we demonstrate that processes such as coherent transport, state localization and surface Bloch oscillations can take place in Fock space. Furthermore, we show that Hamiltonian representations of Fock space manifolds differing by one photon obey a discrete supersymmetry relation
Gomar, Laura Castelló; Blas, Daniel Martín-de; Marugán, Guillermo A Mena; Velhinho, José M
2012-01-01
We study the Fock quantization of scalar fields with a time dependent mass in cosmological scenarios with flat compact spatial sections. This framework describes physically interesting situations like, e.g., cosmological perturbations in flat Friedmann-Robertson-Walker spacetimes, generally including a suitable scaling of them by a background function. We prove that the requirements of vacuum invariance under the spatial isometries and of a unitary quantum dynamics select (a) a unique canonical pair of field variables among all those related by time dependent canonical transformations which scale the field configurations, and (b) a unique Fock representation for the canonical commutation relations of this pair of variables. Though the proof is generalizable to other compact spatial topologies in three or less dimensions, we focus on the case of the three-torus owing to its relevance in cosmology, paying a especial attention to the role played by the spatial isometries in the determination of the representatio...
Manipulating Fock states of a harmonic oscillator while preserving its linearity
Juliusson, K.; Bernon, S.; Zhou, X.; Schmitt, V.; le Sueur, H.; Bertet, P.; Vion, D.; Mirrahimi, M.; Rouchon, P.; Esteve, D.
2016-12-01
We present a scheme for controlling the quantum state of a harmonic oscillator by coupling it to an anharmonic multilevel system (MLS) with first- to second-excited-state transition on resonance with the oscillator. In this scheme, which we call ef-resonant, the spurious oscillator Kerr nonlinearity inherited from the MLS is very small, while its Fock states can still be selectively addressed via an MLS transition at a frequency that depends on the number of photons. We implement this concept in a circuit-QED setup with a microwave three-dimensional cavity (the oscillator, with frequency 6.4 GHz and quality factor QO=2 ×106 ) embedding a frequency tunable transmon qubit (the MLS). We characterize the system spectroscopically and demonstrate selective addressing of Fock states and a Kerr nonlinearity below 350 Hz. At times much longer than the transmon coherence times, a nonlinear cavity response with driving power is also observed and explained.
Partial-wave Coulomb transition matrices for attractive interaction by Fock's method
Kharchenko, V F
2016-01-01
Leaning upon the Fock method of the stereographic projection of the three-dimensional momentum space onto the four-dimensional unit sphere the possibility of the analytical solving of the Lippmann-Schwinger integral equation for the partial wave two-body Coulomb transition matrix at the ground bound state energy has been studied. In this case new expressions for the partial p-, d- and f-wave two-body Coulomb transition matrices have been obtained in the simple analytical form. The developed approach can also be extended to determine analytically the partial wave Coulomb transition matrices at the energies of excited bound states. Keywords: Partial wave Coulomb transition matrix; Lippmann-Schwinger equation; Fock method; Analytical solution PACS Nos. 03.65.-w; 03.65.Nk; 34.20.Cf
Symmetry conserving configuration mixing method with cranked states
Borrajo, Marta; Egido, J Luis
2015-01-01
We present the first calculations of a symmetry conserving configuration mixing method (SCCM) using time-reversal symmetry breaking Hartree-Fock-Bogoliubov (HFB) states with the Gogny D1S interaction. The method includes particle number and tridimensional angular momentum symmetry restorations as well as configuration mixing within the generator coordinate method (GCM) framework. The nucleus $^{32}$Mg is chosen to show the performance and reliability of the calculations. Additionally, $0^{+}_{1}$, $2^{+}_{1}$ and $4^{+}_{1}$ states are computed for the magnesium isotopic chain, where a noticeable compression of the spectrum is obtained by including cranked states, leading to a very good agreement with the known experimental data.
Toroidal Nuclear Matter Distributions of Superheavy Nuclei from Constrained Skyrme-HFB Calculations
Kosior, Amelia [Maria Curie-Sklodowska University, Poland; Staszczak, A. [Maria Curie-Sklodowska University, Poland; Wong, Cheuk-Yin [ORNL
2017-01-01
Using the Hartree Fock Bogoliubov (HFB) self-consistent mean-field theory with the SkM* Skyrme energy-density functional, we study nuclear structure properties of even even superheavy nuclei (SHN) of Z = 120 isotopes and N = 184 isotones. The shape of the nucleus along the lowest energy curve as a function of the quadrupole moment Q20 makes a sud- den transition from the oblate spheroids (biconcave discs) to the toroidal shapes, in the region of large oblate quadrupole moments.
Self-Consistent Description of Multipole Strength in Exotic Nuclei I: Method
Terasaki, J; Bender, M; Dobaczewski, J; Nazarewicz, W; Stoitsov, M V
2004-01-01
We use the canonical Hartree-Fock-Bogoliubov basis to implement a completely self-consistent quasiparticle-random-phase approximation with arbitrary Skyrme energy density functionals and density-dependent pairing functionals. The point of the approach is to accurately describe multipole strength functions in spherical even-even nuclei, including weakly-bound drip-line systems. We describe the method and carefully test its accuracy, particularly in handling spurious modes. To illustrate our approach, we calculate isoscalar and isovector monopole, dipole, and quadrupole strength functions in several Sn isotopes, both in the stable region and at the drip lines.
Augmented Lagrangian Method for Constrained Nuclear Density Functional Theory
Staszczak, A; Baran, A; Nazarewicz, W
2010-01-01
The augmented Lagrangiam method (ALM), widely used in quantum chemistry constrained optimization problems, is applied in the context of the nuclear Density Functional Theory (DFT) in the self-consistent constrained Skyrme Hartree-Fock-Bogoliubov (CHFB) variant. The ALM allows precise calculations of multidimensional energy surfaces in the space of collective coordinates that are needed to, e.g., determine fission pathways and saddle points; it improves accuracy of computed derivatives with respect to collective variables that are used to determine collective inertia; and is well adapted to supercomputer applications.
Linear response calculation using the canonical-basis TDHFB with a schematic pairing functional
Ebata, Shuichiro; Yabana, Kazuhiro
2010-01-01
A canonical-basis formulation of the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory is obtained with an approximation that the pair potential is assumed to be diagonal in the time-dependent canonical basis. The canonical-basis formulation significantly reduces the computational cost. We apply the method to linear-response calculations for even-even nuclei. E1 strength distributions for proton-rich Mg isotopes are systematically calculated. The calculation suggests strong Landau damping of giant dipole resonance for drip-line nuclei.
Matsuo, Masayuki
2014-01-01
We formulate a many-body theory to calculate the cross section of direct radiative neutron capture reaction by means of the Hartree-Fock-Bogoliubov mean-field model and the continuum quasiparticle random phase approximation (QRPA). A focus is put on very neutron-rich nuclei and low-energy neutron kinetic energy in the range of O(1 keV) - O(1 MeV), relevant for the rapid neutron-capture process of nucleosynthesis. We begin with the photo-absorption cross section and the E1 strength function, t...
Structure of high spin states of 76Kr and 78Kr nuclei
U R Jakhar; H L Yadav; A Ansari
2005-12-01
Following a fully self-consistent cranked Hartree-Fock-Bogoliubov (CHFB) approach with a pairing+quadrupole+hexadecapole model interaction Hamiltonian the structure of the yrast states of 76,78Kr nuclei is studied up to angular momentum = 24. Evolution of the shape with spin, and rotation alignment of proton as well as neutron 0g9/2 orbitals is investigated along with the inter- and intra-nucleus variations of the factors as a function of . We find that the shape of 78Kr remains prolate all through up to = 24, whereas 76Kr becomes triaxial beyond = 12.
Interplay between tensor force and deformation in even-even nuclei
Bernard, Rémi N.; Anguiano, Marta
2016-09-01
In this work we study the effect of the nuclear tensor force on properties related with deformation. We focus on isotopes in the Mg, Si, S, Ar, Sr and Zr chains within the Hartree-Fock-Bogoliubov theory using the D1ST2a Gogny interaction. Contributions to the tensor energy in terms of saturated and unsaturated subshells are analyzed. Like-particle and proton-neutron parts of the tensor term are independently examinated. We found that the tensor term may considerably modify the potential energy landscapes and change the ground state shape. We analyze too how the pairing characteristics of the ground state change when the tensor force is included.
Critical temperature for shape transitions in excited nuclei
Martin, V. [Analisis Numerico, Facultad de Informatica, Universidad Politecnica de Madrid, E-28660, Madrid (Spain); Egido, J.L.; Robledo, L.M. [Departamento de Fisica Teorica, Universidad Autonoma de Madrid, E-28049, Madrid (Spain)
2004-04-01
The behavior of shell effects with temperature is studied within the framework of the finite-temperature Hartree-Fock-Bogoliubov theory with the Gogny force. Thermal shape fluctuations in the quadrupole degree of freedom are taken into account in the frame of the Landau theory. Numerical results for the superfluid-to-normal and deformed-to-spherical phase transitions are presented for the nucleus {sup 164}Er. We find that the critical temperature for the deformed-spherical shape transition is much lowered when the thermal shape fluctuations are considered. (orig.)
Martin, V. [Analisis Numerico, Facultad de Informatica, Universidad Politecnica de Madrid, E-28660 Madrid (Spain); Egido, J.L. [Departamento de Fisica Teorica C-XI, Universidad Autonoma de Madrid, E-28049 Madrid (Spain)
1995-06-01
Using the finite-temperature Hartree-Fock-Bogoliubov formalism we analyze the properties of the nuclei {sup 152,154,156}Dy at the quasicontinuum region from {ital I}=0{h_bar} to 70{h_bar} and excitation energy up to approximately 16 MeV. We discuss energy gaps, shapes, moments of inertia, and entropy among others. The role of shape fluctuations is studied in the frame of classical statistics and we find large effects on several observables. A very rich structure is found in terms of excitation energy and angular momentum.
Zhuravlev, Vladimir; Duan, Wenye; Maniv, Tsofar
2017-01-01
A self-consistent Bogoliubov-de Gennes theory of the vortex lattice state in a 2D strong type-II superconductor at high magnetic fields reveals a novel quantum mixed state around the semiclassical Hc 2, characterized by a well-defined Landau-Bloch band structure in the quasiparticle spectrum and suppressed order-parameter amplitude, which sharply crossover into the well-known semiclassical (Helfand-Werthamer) results upon decreasing magnetic field. Application to the 2D superconducting state observed recently on the surface of the topological insulator Sb2Te3 accounts well for the experimental data, revealing a strong type-II superconductor, with unusually low carrier density and very small cyclotron mass, which can be realized only in the strong coupling superconductor limit.
Schatten-p Class (0 Fock
Lian Hua XIAO; Xiao Feng WANG; Jin XIA
2015-01-01
In this paper, we discuss the Schatten-p class (0 < p ≤ ∞ ) of Toeplitz operators on generalized Fock space with the symbol in positive Borel measure. It makes a great diff erence from other papers by using the estimates of the kernel and the weight together instead of separately estimating each other. We also get the equivalent conditions when a Toeplitz operator is in the Schatten-p class.
The Fock-Kemmer approach to precursor shock waves in relativistic field theory
Abdullah, Rawand H
2016-01-01
We use distribution theory (generalized functions) to extend and justify the Fock-Kemmer approach to the propagation of precursor shock wave discontinuities in classical and quantum field theory. We apply lightcone causality arguments to propose that shock wave singularities in non-linear classical field theories and in Maxwell's equations for responsive media require a form of classical renormalization analogous to Wilson operator product expansions in quantum field theories.
Evolution of Arbitrary States under Fock-Darwin Hamiltonian and a Time-Dependent Electric Field
徐晓飞; 杨涛; 翟智远; 潘孝胤
2012-01-01
The method of path integral is employed to calculate the time evolution of the eigenstates of a charged particle under the Fock-Darwin （FD） Hamiltonian subjected to a time-dependent electric field in the plane of the system. An exact analytical expression is established for the evolution of the eigenstates. This result then provides a general solution to the time-dependent Schrodinger equation.
Higher-order Schrödinger and Hartree–Fock equations
Carles, Rémi, E-mail: Remi.Carles@math.cnrs.fr [IMAG, UMR5149, CNRS and University Montpellier, CC051, 34095 Montpellier (France); Lucha, Wolfgang, E-mail: Wolfgang.Lucha@oeaw.ac.at [Institute for High Energy Physics, Austrian Academy of Sciences, Nikolsdorfergasse 18, A-1050 Vienna (Austria); Moulay, Emmanuel, E-mail: emmanuel.moulay@univ-poitiers.fr [XLIM (UMR-CNRS 7252), University Poitiers, 11 Blvd. Marie et Pierre Curie, BP 30179, 86962 Futuroscope Chasseneuil Cedex (France)
2015-12-15
The domain of validity of the higher-order Schrödinger equations is analyzed for harmonic-oscillator and Coulomb potentials as typical examples. Then, the Cauchy theory for higher-order Hartree–Fock equations with bounded and Coulomb potentials is developed. Finally, the existence of associated ground states for the odd-order equations is proved. This renders these quantum equations relevant for physics.
Can X-ray constrained Hartree–Fock wavefunctions retrieve electron correlation?
Alessandro Genoni
2017-03-01
Full Text Available The X-ray constrained wavefunction (XC-WF method proposed by Jayatilaka [Jayatilaka & Grimwood (2001, Acta Cryst. A57, 76–86] has attracted much attention because it represents a possible third way of theoretically studying the electronic structure of atoms and molecules, combining features of the more popular wavefunction- and DFT-based approaches. In its original formulation, the XC-WF technique extracts statistically plausible wavefunctions from experimental X-ray diffraction data of molecular crystals. A weight is used to constrain the pure Hartree–Fock solution to the observed X-ray structure factors. Despite the wavefunction being a single Slater determinant, it is generally assumed that its flexibility could guarantee the capture, better than any other experimental model, of electron correlation effects, absent in the Hartree–Fock Hamiltonian but present in the structure factors measured experimentally. However, although the approach has been known for long time, careful testing of this fundamental hypothesis is still missing. Since a formal demonstration is impossible, the validation can only be done heuristically and, to accomplish this task, X-ray constrained Hartree–Fock calculations have been performed using structure factor amplitudes computed at a very high correlation level (coupled cluster for selected molecules in isolation, in order to avoid the perturbations due to intermolecular interactions. The results show that a single-determinant XC-WF is able to capture the electron correlation effects only partially. The largest amount of electron correlation is extracted when: (i a large external weight is used (much larger than what has normally been used in XC-WF calculations using experimental data; and (ii the high-order reflections, which carry less information on the electron correlation, are down-weighted (or even excluded, otherwise they would bias the fitting towards the unconstrained Hartree–Fock wavefunction.
Can X-ray constrained Hartree–Fock wavefunctions retrieve electron correlation?
Genoni, Alessandro; Dos Santos, Leonardo H. R.; Meyer, Benjamin; Macchi, Piero
2017-01-01
The X-ray constrained wavefunction (XC-WF) method proposed by Jayatilaka [Jayatilaka & Grimwood (2001) ▸, Acta Cryst. A57, 76–86] has attracted much attention because it represents a possible third way of theoretically studying the electronic structure of atoms and molecules, combining features of the more popular wavefunction- and DFT-based approaches. In its original formulation, the XC-WF technique extracts statistically plausible wavefunctions from experimental X-ray diffraction data of molecular crystals. A weight is used to constrain the pure Hartree–Fock solution to the observed X-ray structure factors. Despite the wavefunction being a single Slater determinant, it is generally assumed that its flexibility could guarantee the capture, better than any other experimental model, of electron correlation effects, absent in the Hartree–Fock Hamiltonian but present in the structure factors measured experimentally. However, although the approach has been known for long time, careful testing of this fundamental hypothesis is still missing. Since a formal demonstration is impossible, the validation can only be done heuristically and, to accomplish this task, X-ray constrained Hartree–Fock calculations have been performed using structure factor amplitudes computed at a very high correlation level (coupled cluster) for selected molecules in isolation, in order to avoid the perturbations due to intermolecular interactions. The results show that a single-determinant XC-WF is able to capture the electron correlation effects only partially. The largest amount of electron correlation is extracted when: (i) a large external weight is used (much larger than what has normally been used in XC-WF calculations using experimental data); and (ii) the high-order reflections, which carry less information on the electron correlation, are down-weighted (or even excluded), otherwise they would bias the fitting towards the unconstrained Hartree–Fock wavefunction. PMID:28250952
Representations of coherent and squeezed states in an extended two-parameter Fock space
M. K. Tavassoly; M. H. Lake
2012-01-01
Recently an f-deformed Fock space which is spanned by ｜n〉λ was introduced.These bases are the eigenstates of a deformed non-Hermitian Hamiltonian.In this contribution,we will use rather new nonorthogonal basis vectors for the construction of coherent and squeezed states,which in special case lead to the earlier known states.For this purpose,we first generalize the previously introduced Fock space spanned by ｜n〉λ bases,to a new one,spanned by extended two-parameters bases ｜n〉λ1,λ2.These bases are now the eigenstates of a non-Hermitian Hamiltonian Hλ1,λ2 =a(+)1,λ2a +1/2,where a(+)λ1,λ2 =a(+) + λ1a + λ2 and a are,respectively,the deformed creation and ordinary bosonic annihilation operators.The bases ｜n〉λ1,λ2 are nonorthogonal (squeezed states),but normalizable.Then,we deduce the new representations of coherent and squeezed states in our two-parameter Fock space.Finally,we discuss the quantum statistical properties,as well as the non-classical properties of the obtained states numerically.
Uniqueness of the Fock quantization of scalar fields in spatially flat cosmological spacetimes
Gomar, Laura Castelló [Facultad de Ciencias Físicas, Universidad Complutense de Madrid, Ciudad Universitaria, 28040 Madrid (Spain); Cortez, Jerónimo [Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico D.F. 04510 (Mexico); Blas, Daniel Martín-de; Marugán, Guillermo A. Mena [Instituto de Estructura de la Materia, CSIC, Serrano 121, 28006 Madrid (Spain); Velhinho, José M., E-mail: laucaste@estumail.ucm.es, E-mail: jacq@ciencias.unam.mx, E-mail: daniel.martin@iem.cfmac.csic.es, E-mail: jvelhi@ubi.pt [Departamento de Física, Faculdade de Ciências, Universidade da Beira Interior, R. Marquês D' Ávila e Bolama, 6201-001 Covilhã (Portugal)
2012-11-01
We study the Fock quantization of scalar fields in (generically) time dependent scenarios, focusing on the case in which the field propagation occurs in –either a background or effective– spacetime with spatial sections of flat compact topology. The discussion finds important applications in cosmology, like e.g. in the description of test Klein-Gordon fields and scalar perturbations in Friedmann-Robertson-Walker spacetime in the observationally favored flat case. Two types of ambiguities in the quantization are analyzed. First, the infinite ambiguity existing in the choice of a Fock representation for the canonical commutation relations, understandable as the freedom in the choice of inequivalent vacua for a given field. Besides, in cosmological situations, it is customary to scale the fields by time dependent functions, which absorb part of the evolution arising from the spacetime, which is treated classically. This leads to an additional ambiguity, this time in the choice of a canonical pair of field variables. We show that both types of ambiguities are removed by the requirements of (a) invariance of the vacuum under the symmetries of the three-torus, and (b) unitary implementation of the dynamics in the quantum theory. In this way, one arrives at a unique class of unitarily equivalent Fock quantizations for the system. This result provides considerable robustness to the quantum predictions and renders meaningful the confrontation with observation.
Uniqueness of the Fock quantization of scalar fields in a Bianchi I cosmology with unitary dynamics
Cortez, Jerónimo; Navascués, Beatriz Elizaga; Martín-Benito, Mercedes; Mena Marugán, Guillermo A.; Olmedo, Javier; Velhinho, José M.
2016-11-01
The Fock quantization of free scalar fields is subject to an infinite ambiguity when it comes to choosing a set of annihilation and creation operators, a choice that is equivalent to the determination of a vacuum state. In highly symmetric situations, this ambiguity can be removed by asking vacuum invariance under the symmetries of the system. Similarly, in stationary backgrounds, one can demand time-translation invariance plus positivity of the energy. However, in more general situations, additional criteria are needed. For the case of free (test) fields minimally coupled to a homogeneous and isotropic cosmology, it has been proven that the ambiguity is resolved by introducing the criterion of unitary implementability of the quantum dynamics, as an endomorphism in Fock space. This condition determines a specific separation of the time dependence of the field, so that this splits into a very precise background dependence and a genuine quantum evolution. Furthermore, together with the condition of vacuum invariance under the spatial Killing symmetries, unitarity of the dynamics selects a unique Fock representation for the canonical commutation relations, up to unitary equivalence. In this work, we generalize these results to anisotropic spacetimes with shear, which are therefore not conformally symmetric, by considering the case of a free scalar field in a Bianchi I cosmology.
Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization
Cortez, Jerónimo, E-mail: jacq@ciencias.unam.mx [Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, México D.F. 04510 (Mexico); Elizaga Navascués, Beatriz, E-mail: beatriz.elizaga@iem.cfmac.csic.es [Instituto de Estructura de la Materia, IEM-CSIC, Serrano 121, 28006 Madrid (Spain); Martín-Benito, Mercedes, E-mail: m.martin@hef.ru.nl [Radboud University Nijmegen, Institute for Mathematics, Astrophysics and Particle Physics, Heyendaalseweg 135, NL-6525 AJ Nijmegen (Netherlands); Mena Marugán, Guillermo A., E-mail: mena@iem.cfmac.csic.es [Instituto de Estructura de la Materia, IEM-CSIC, Serrano 121, 28006 Madrid (Spain); Velhinho, José M., E-mail: jvelhi@ubi.pt [Universidade da Beira Interior, Rua Marquês d’Ávila e Bolama, 6201-001, Covilhã (Portugal)
2017-01-15
We address the issue of the infinite ambiguity that affects the construction of a Fock quantization of a Dirac field propagating in a cosmological spacetime with flat compact sections. In particular, we discuss a physical criterion that restricts to a unique possibility (up to unitary equivalence) the infinite set of available vacua. We prove that this desired uniqueness is guaranteed, for any possible choice of spin structure on the spatial sections, if we impose two conditions. The first one is that the symmetries of the classical system must be implemented quantum mechanically, so that the vacuum is invariant under the symmetry transformations. The second and more important condition is that the constructed theory must have a quantum dynamics that is implementable as a (non-trivial) unitary operator in Fock space. Actually, this unitarity of the quantum dynamics leads us to identify as explicitly time dependent some very specific contributions of the Dirac field. In doing that, we essentially characterize the part of the dynamics governed by the Dirac equation that is unitarily implementable. The uniqueness of the Fock vacuum is attained then once a physically motivated convention for the concepts of particles and antiparticles is fixed.
Entanglement of remote transmon qubits by concurrent measurement using Fock states
Narla, A.; Hatridge, M.; Shankar, S.; Leghtas, Z.; Sliwa, K. M.; Vlastakis, B.; Zalys-Geller, E.; Mirrahimi, M.; Devoret, M. H.
2015-03-01
A requirement of any modular quantum computer is the ability to maintain individual qubits in isolated environments while also being able to entangle arbitrary distant qubits on demand. For superconducting qubits, such a protocol can be realized by first entangling the qubits with flying microwave coherent states which are then concurrently detected by a parametric amplifier. This protocol has a 50% success probability but is vulnerable to losses between the qubits and the amplifier which reduce the entanglement fidelity. An alternative is to use itinerant Fock states, since losses now tend to reduce the success probability of creating an entangled state but not its fidelity. Such single-photon protocols have been implemented in trapped-ion and NV-center experiments. We present such a protocol tailored for entangling two transmon qubits in the circuit QED architecture. Each qubit is entangled with a Fock state of its cavity using sideband pulses. The Fock states leak out of the cavity, interfere on a beam-splitter which erases their which-path information, and are subsequently detected using a novel photo-detector realized by another qubit-cavity system. Simulations suggest that we can realize a high-fidelity entangled state with a success probability as large as 1%.
Semi-infinite $q$-wedge construction of the level 2 Fock Space of $U_q(\\widehat{sl}_2)$
Petersen, J U H
1997-01-01
In this proceedings a particular example from \\cite{KMPY} (q-alg/9603025) is presented: the construction of the level 2 Fock space of $\\U_q(\\affsl{2})$. The generating ideal of the wedge relations is given and the wedge space defined. Normal ordering of wedges is defined in terms of the energy function. Normally ordered wedges form a base of the wedge space. The q-deformed Fock space is defined as the space of semi-infinite wedges with a finite number of vectors in the wedge product differing from a ground state sequence, and endowed with a separated q-adic topology . Normally ordered wedges form a base of the Fock space. The action of $\\U_q(\\affsl{2})$ on the Fock space converges in the q-adic topology. On the Fock space the action of bosons, which commute with the $\\U_q(\\affsl{2})$-action, also converges in the q-adic topology. Hence follows the decomposition of the Fock space into irreducible $\\U_q(\\affsl{2})$-modules.
Berski, Slawomir; Gordon, Agnieszka J
2011-09-07
In this paper, the electronic structures of cis- and trans-ClONO and BrONO are studied at the CCSD∕aug-cc-pVTZ, CASSCF(14,12)/aug-cc-pVTZ, and B3LYP/aug-cc-pVTZ computational levels. For the Cl-O bond, topological analysis of the electron density field, ρ(r), shows the prevalence of the shared-electron type bond (∇(2)ρ((3,-1)) 0). Topological analysis of the electron localization function, η(r), and electron localizability indicator (ELI-D), (D) (σ)(r), shows that the electronic structure of the central N-O bond is very sensitive to both electron correlation improvements (coupled-cluster single double (CCSD), CASSCF, density functional theory (DFT)) and bond length alteration. Depending on the method used, the N-O bond can be characterized as a "normal" N-O bond with a disynaptic V(N,O) basin (DFT); a protocovalent N-O bond with two monosynaptic, V(N) and V(O), basins (CCSD, CASSCF); or a new type, first discovered for FONO, characterized by a single monosynaptic, V(N) basin (CCSD, DFT). The total basin population oscillates between 0.46-0.96 e (CCSD) and 0.86-1.02 e (CASSCF). The X-O bond is described by the single disynaptic basin, V(X,O), with a basin population between 0.76 and 0.81 e (CCSD) or 0.77 and 0.85 e (CASSCF). Analysis of the localized electron detector distribution for the cis-Cl-O1-N=O2 shows a manifold in the Cl···O2 region, associated with decreased electron density. © 2011 American Institute of Physics
Deformed Relativistic Hartree Theory in Coordinate Space and in Harmonic Oscillator Basis
ZHOU Shan-Gui; MENG Jie; Shuhei YAMAJI; YANG Si-Chun
2000-01-01
The deformed relativistic Hartree theory (DRH) is solved both in coordinate space (DRH-c) and in harmonic oscillator basis (DRH-o). Results obtained from these two methods are compared in details. The DRH-c and DRH-o calculations give similar total binding energies, deformation, level structures and radii for nitrogen iso topes, while their descriptions on the density distributions for drip-line nuclei are very different. The large spatiai istributions of nucleon densities, which is crucial to understand a weakly bound system, can only be obtained by DRH-c calculations. This implies that the DRH theory should be solved in coordinate space in order to describe uclei close to the drip line.
Hernández, E. S.; Capuzzi, P.; Szybisz, L.
2011-02-01
We extend our earlier fluid-dynamical description of fermion superfluids incorporating the particle energy flow together with the equation of motion for the internal kinetic energy of the pairs. The formal scheme combines a set of equations similar to those of classical hydrodynamics with the equations of motion for the anomalous density and for its related momentum density and kinetic energy density. This dynamical frame represents a second order truncation of an infinite hierarchy of equations of motion isomorphic to the full time dependent Hartree-Fock-Bogoliubov equations in coordinate representation. We analyze the equilibrium solutions and fluctuations for a homogeneous, unpolarized fermion system of two species, and show that the collective spectrum presents the well-known Anderson-Bogoliubov low energy mode of homogeneous superfluids and a pairing vibration near the gap energy.
Fock-Darwin-like quantum dot states formed by charged Mn interstitial ions.
Makarovsky, O; Thomas, O; Balanov, A G; Eaves, L; Patanè, A; Campion, R P; Foxon, C T; Vdovin, E E; Maude, D K; Kiesslich, G; Airey, R J
2008-11-28
We report a method of creating electrostatically induced quantum dots by thermal diffusion of interstitial Mn ions out of a p-type (GaMn)As layer into the vicinity of a GaAs quantum well. This approach creates deep, approximately circular, and strongly confined dotlike potential minima in a large (200 microm) mesa diode structure without need for advanced lithography or electrostatic gating. Magnetotunneling spectroscopy of an individual dot reveals the symmetry of its electronic eigenfunctions and a rich energy level spectrum of Fock-Darwin-like states with an orbital angular momentum component |lz| from 0 to 11.
Compactness characterization of operators in the Toeplitz algebra of the Fock space $F_\\alpha ^p$
Bauer, Wolfram
2011-01-01
Let BT be the class of functions $f$ on $\\mathbb{C}^n$ where the Berezin transform $B_\\alpha (|f|)$ associated to the standard weighted Fock space $F_\\alpha ^2$ is bounded, and for $1 < p < \\infty$ let $\\mathcal{T}_p$ be the norm closure of the algebra generated by Toeplitz operators with BT symbols acting on $F_\\alpha ^p$. In this paper, we will show that an operator $A$ is compact on $F_\\alpha ^p$ if and only if $A \\in \\mathcal{T}_p$ and the Berezin transform $B_\\alpha (A)$ of $A$ vanishes at infinity.
Multipartite State Representations in Multi-mode Fock Space and Their Squeezing Transformations
YUAN Hong-Chun; LI Heng-Mei; QI Kai-Guo
2007-01-01
We present the continuous state vector of the total coordinate of multi-particle and the state vector of their total momentum, respectively, which possess completeness relation in multi-mode Fock space by virtue of the integration within an order product (IWOP) technique. We also calculate the transition from classical transformation of variables in the states to quantum unitary operator, deduce a new multi-mode squeezing operator, and discuss its squeezing effect. In progress, it indicates that the IWOP technique provides a convenient way to construct new representation in quantum mechanics.
Flight test report Focke Wulf Piaggio P149D-TP 2015
Barker, D
2015-09-01
Full Text Available stream_source_info Barker_2015.pdf.txt stream_content_type text/plain stream_size 12410 Content-Encoding UTF-8 stream_name Barker_2015.pdf.txt Content-Type text/plain; charset=UTF-8 Flight Test Report Focke Wulf... Piaggio P149D-TP IASSA 2015 Des Barker Flight Test Society of South Africa Scope • Executive Summary of Flight Test Programme: – Background – Objectives of Test Programme – Scope of Modifications – Flight Test Team – Conditions...
Non-Commutative Fock-Darwin System and Magnetic Field Limits
YU Xiao-Min; LI Kang
2008-01-01
A Fock-Darwin system in noncommutative quantum mechanics is studied. By constructing Heisenberg algebra we obtain the levels on noncommutative space and noncommutative phase space, and give the corrections to the results in usual quantum mechanics. Moreover, to search the difference among the three spaces, the degeneracy is analysed by two ways, the value of (ω)/(ω)c and certain algebra realization (SU(2)and SU(1,1)), and some interesting properties in the magnetic field limit are exhibited, such as totally different degeneracy and magic number distribution for the given frequency or mass of a system in strong magnetic field.
Non-commutative Fock-Darwin system and its magnetism properties
Yu Xiao-Min; Li Kang
2009-01-01
The Fock-Darwin system is studied in noncommutative quantum mechanics. We not only obtain its energy eigenvalues and eigenstates in noncommutative phase space,but also give an electron orbit description as well as the general expressions of the magnetization and the susceptibility in a noncommutative situation. Further,we discuss two particular cases of temperature and present some interesting results different from those obtained from usual quantum mechanics such as the susceptibility dependent on a magnetic field at high temperatures,the occurrence of the magnetization in a zero magnetic field and zero temperature limit,and so on.
Conditional large Fock state preparation and field state reconstruction in cavity QED.
Santos, M F; Solano, E; de Matos Filho, R L
2001-08-27
We propose a scheme for producing large Fock states in cavity QED via the implementation of a highly selective atom-field interaction. It is based on Raman excitation of a three-level atom by a classical field and a quantized field mode. Selectivity appears when one tunes to resonance a specific transition inside a chosen atom-field subspace, while other transitions remain dispersive, as a consequence of the field dependent electronic energy shifts. We show that this scheme can be also employed for reconstructing, in a new and efficient way, the Wigner function of the cavity field state.
Geometry of Vlasov kinetic moments: A bosonic Fock space for the symmetric Schouten bracket
Gibbons, John [Department of Mathematics, Imperial College London, London SW7 2AZ (United Kingdom); Holm, Darryl D. [Department of Mathematics, Imperial College London, London SW7 2AZ (United Kingdom); Computer and Computational Science Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Tronci, Cesare [Department of Mathematics, Imperial College London, London SW7 2AZ (United Kingdom); TERA Foundation for Oncological Hadrontherapy, 11 V. Puccini, Novara 28100 (Italy)], E-mail: cesare.tronci@imperial.ac.uk
2008-06-02
The dynamics of Vlasov kinetic moments is shown to be Lie-Poisson on the dual Lie algebra of symmetric contravariant tensor fields. The corresponding Lie bracket is identified with the symmetric Schouten bracket and the moment Lie algebra is related with a bundle of bosonic Fock spaces, where creation and annihilation operators are used to construct the cold plasma closure. Kinetic moments are also shown to define a momentum map, which is infinitesimally equivariant. This momentum map is the dual of a Lie algebra homomorphism, defined through the Schouten bracket. Finally the moment Lie-Poisson bracket is extended to anisotropic interactions.
QUANTUM FLUCTUATIONS IN A MESOSCOPIC DAMPED LC PARALLEL CIRCUIT IN DISPLACED SQUEEZED FOCK STATE
GU YONG-JIAN
2001-01-01
We study the quantum effects of a damped LC parallel circuit considering its different performance from an RLC series circuit in classical physics. The damped LC parallel circuit with a source is quantized and the quantum fluctuations of magnetic flux and electric charge in the circuit in displaced squeezed Fock state are investigated. It is shown that, as in the RLC series circuit, the fluctuations only depend on the squeezing parameter and the parameters of the circuit components in the damped LC parallel circuit, but the effects of the circuit components on the fluctuations are different in the two circuits.
Fock-Darwin spectrum of a single InAs/GaAs quantum dot
Babinski, A. [Institute of Experimental Physics, Warsaw University, Hoza 69, 00-681 Warsaw (Poland); Grenoble High Magnetic Field Laboratory, CNRS, BP-166, 38042 Grenoble Cedex 9 (France); Potemski, M. [Grenoble High Magnetic Field Laboratory, CNRS, BP-166, 38042 Grenoble Cedex 9 (France); Raymond, S.; Lapointe, J.; Wasilewski, Z.R. [Institute for Microstructural Sciences, NRC, Ottawa, K1A 0R6 (Canada)
2006-07-01
Magnetospectroscopic study of a highly excited single InAs/GaAs quantum dot is reported. Optical emission from the s- and p-shells is identified and investigated in magnetic fields up to 20T. The zero-field splitting and the Zeeman orbital splitting of the p-shell-related emission lines in magnetic field are observed. The evolution of spectra in magnetic field resembles a classical Fock-Darwin energy diagram, although effects of the electron-electron interaction and asymmetry of localizing potential can be clearly observed. (copyright 2006 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Fermion Superfluidity And Confining Interactions
Galal, A A
2004-01-01
We study the pairing of Fermi systems with long-range, confining interparticle interactions. We solve the Cooper problem for a pair of fermions interacting via a regularized harmonic oscillator potential and determine the s-wave spectrum of bound states. Using a model of two interacting species of fermions, we calculate the ground state energy of the normal phase in the Hartree-Fock approximation and find that it is infrared (IR) divergent, due to a combination of the sharpness of the Fermi sea and the long-range nature of the interaction. We calculate the correlation energy in the normal phase using the random phase approximation (RPA) and demonstrate the cancellation of infrared divergences between the Hartree-Fock and RPA contributions. Introducing a variational wavefunction to study the superfluid phase, we solve the BCS equations using a Hartree-Fock-Bogoliubov (HFB) analysis to determine the wave-function, excitation gap, and other parameters of the superfluid phase. We show that the system crosses over...
Urbina, Juan Diego; Engl, Thomas; Richter, Klaus [Institute for Theoretical Physics, University of Regensburg (Germany); Arguelles, Arturo [Department of Physics, University of Liege (Belgium); Institute for Theoretical Physics, University of Regensburg (Germany); Dujardin, Julien; Schlagheck, Peter [Department of Physics, University of Liege (Belgium)
2013-07-01
We present a semiclassical theory of quantum interference effects in interacting bosonic fields. We make special emphasis on the difference between genuine quantum interference (due to the superposition principle in the many-body Hilbert space), and classical interference effects due to the wave character of the classical limit. First, we discuss how the usual approaches to this problem are unable to provide the characteristic sum of oscillatory terms, each asociated with a solution of the classical equations of motion, required to semiclassically address interference effects. We show then how to solve this problems by a formal construction of the van Vleck-Gutzwiller propagator for bosonic fields as a sum over paths in the associated Fock space and we identify the classical limit as a Gross-Pitaevskii equation with boundary conditions and multiple solutions. The theory predicts effects akin to weak localization to take place in Fock space, and in particular the enhancement of quantum probability of return due to interference between time-reversed paths there. We support our claims with extensive numerical calculations for a discrete version of an interacting bosonic field.
General Quantum Modeling of Combining Concepts: A Quantum Field Model in Fock Space
Aerts, Diederik
2007-01-01
We extend a quantum model in Hilbert space developed in Aerts (2007a) into a quantum field theoric model in Fock space for the modeling of the combination of concepts. Items and concepts are represented by vectors in Fock space and membership weights of items are modeled by quantum probabilities. We apply this theory to model the disjunction of concepts and show that the predictions of our theory for the membership weights of items regarding the disjunction of concepts match with great accuracy the complete set of results of an experiment conducted by Hampton (1988b). It are the quantum effects of interference and superposition of that are at the origin of the effects of overextension and underextension observed by Hampton as deviations from a classical use of the disjunction. It is essential for the perfect matches we obtain between the predictions of the quantum field model and Hampton's experimental data that items can be in superpositions of `different numbers states' which proves that the genuine structu...
Representations of Coherent and Squeezed States in an Extended Two-parameters Fock Space
Tavassoly, M K
2012-01-01
Recently a $f$-deformed Fock space which is spanned by $|n>_{\\lambda}$ has been introduced. These bases are indeed the eigen-states of a deformed non-Hermitian Hamiltonian. In this contribution, we will use a rather new non-orthogonal basis vectors for the construction of coherent and squeezed states, which in special case lead to the earlier known states. For this purpose, we first generalize the previously introduced Fock space spanned by $|n>_{\\lambda}$ bases, to a new one, spanned by an extended two-parameters bases $|n>_{\\lambda_{1},\\lambda_{2}}$. These bases are now the eigen-states of a non-Hermitian Hamiltonian $H_{\\lambda_{1},\\lambda_{2}}=a^{\\dagger}_{\\lambda_{1},\\lambda_{2}}a+1/2$, where $a^{\\dagger}_{\\lambda_{1},\\lambda_{2}}=a^{\\dagger}+\\lambda_{1}a + \\lambda_{2}$ and $a$ are respectively, the deformed creation and ordinary bosonic annihilation operators. The bases $|n>_{\\lambda_{1},\\lambda_{2}}$ are non-orthogonal (squeezed states), but normalizable. Then, we deduce the new representations of cohe...
Odd-even mass differences from self-consistent mean-field theory
Bertsch, George F; Nazarewicz, W; Schunck, N; Stoitsov, M V
2008-01-01
We survey odd-even nuclear binding energy staggering using density functional theory with several treatments of the pairing interaction including the BCS, Hartree-Fock-Bogoliubov, and the Hartree-Fock-Bogoliubov with the Lipkin-Nogami approximation. We calculate the second difference of binding energies and compare with 443 measured neutron energy differences in isotope chains and 418 measured proton energy differences in isotone chains. The particle-hole part of the energy functional is taken as the SLy4 Skyrme parametrization and the pairing part of the functional is based on a contact interaction with possible density dependence. An important feature of the data, reproduced by the theory, is the sharp gap quenching at magic numbers. With the strength of the interaction as a free parameter, the theory can reproduce the data to an rms accuracy of about 0.25 MeV. This is slightly better than a single-parameter phenomenological description but slightly poorer than the usual two-parameter phenomenological form ...
Cho, Yonggeun
2016-05-04
This paper is devoted to the mathematical analysis of a class of nonlinear fractional Schrödinger equations with a general Hartree-type integrand. We show the well-posedness of the associated Cauchy problem and prove the existence and stability of standing waves under suitable assumptions on the nonlinearity. Our proofs rely on a contraction argument in mixed functional spaces and the concentration-compactness method. © 2015 World Scientific Publishing Company
Basler, Mathias; Gindensperger, Etienne; Meyer, Hans-Dieter; Cederbaum, Lorenz S.
2008-05-01
We address the nonadiabatic quantum dynamics of (macro)systems involving a vast number of nuclear degrees of freedom (modes) in the presence of conical intersections. The macrosystem is first decomposed into a system part carrying a few, strongly coupled modes, and an environment, comprising the remaining modes. By successively transforming the modes of the environment, a hierarchy of effective Hamiltonians for the environment can be constructed. Each effective Hamiltonian depends on a reduced number of effective modes, which carry cumulative effects. The environment is described by a few effective modes augmented by a residual environment. In practice, the effective modes can be added to the system's modes and the quantum dynamics of the entire macrosystem can be accurately calculated on a limited time-interval. For longer times, however, the residual environment plays a role. We investigate the possibility to treat fully quantum mechanically the system plus a few effective environmental modes, augmented by the dynamics of the residual environment treated by the time-dependent Hartree (TDH) approximation. While the TDH approximation is known to fail to correctly reproduce the dynamics in the presence of conical intersections, it is shown that its use on top of the effective-mode formalism leads to much better results. Two numerical examples are presented and discussed; one of them is known to be a critical case for the TDH approximation.
The exact calculation of the edge components of the angular Fock coefficients
Liverts, Evgeny Z
2016-01-01
The present paper constitutes the development of our previous work devoted to calculations of the angular Fock coefficients, $\\psi_{k,p}(\\alpha,\\theta)$. The explicit analytic representations for the edge components $\\psi_{k,0}^{(0)}$ and $\\psi_{k,0}^{(k)}$ with $k\\leq8$ are derived. The methods developed enable such a calculation for arbitrary $k$. The single-series representation for subcomponent $\\psi_{3,0}^{(2e)}$ missed in the previous paper is developed. It is shown how to express some of the complicated subcomponents through the hypergeometric and the elementary functions, as well. Using the specific operator of the Wolfram Mathematica, the simple explicit representations for some complex mathematical objects under consideration are obtained.
On the Discrete Spectrum of a Model Operator in Fermionic Fock Space
Zahriddin Muminov
2013-01-01
Full Text Available We consider a model operator H associated with a system describing three particles in interaction, without conservation of the number of particles. The operator H acts in the direct sum of zero-, one-, and two-particle subspaces of the fermionic Fock space ℱa(L2(3 over L2(3. We admit a general form for the "kinetic" part of the Hamiltonian H, which contains a parameter γ to distinguish the two identical particles from the third one. (i We find a critical value γ* for the parameter γ that allows or forbids the Efimov effect (infinite number of bound states if the associated generalized Friedrichs model has a threshold resonance and we prove that only for γγ*. (ii In the case γ>γ* , we also establish the following asymptotics for the number N(z of eigenvalues of H below z0, for all γ>γ*.
Fock space expansion of {sigma} meson in leading-N{sub c}
Llanes-Estrada, Felipe J.; Pelaez, Jose Ramon; Ruiz de Elvira, Jacobo [Departamentos de Fisica Teorica I y II, Universidad Complutense de Madrid, 28040 Madrid (Spain)
2010-10-15
We examine the leading-N{sub c} behavior of the masses and transition matrix elements of some low-lying, few-particle configurations in QCD. A truncation of the Fock space produces an effective, symmetric Hamiltonian that we diagonalize. The lowest eigenvalue is identified as the {sigma} meson if the Hamiltonian is chosen to represent the scalar sector. As an application, the coefficients of the N{sub c} powers are then fit to two-loop Unitarized SU(2) Chiral Perturbation Theory results for the {sigma} mass and width as a function of the number of colors, and we show that those results can be accommodated using the QCD N{sub c} dependence previously derived for matrix elements, without the need for unnatural parameters or fine tunings. Finally, we show a very preliminary good quality fit, estimating the proportion of tetraquark/molecule-like (dominant), qq-bar -like (subdominant) and exotic-like (marginal) configurations in the {sigma}.