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Journal articles on the topic 'Hartree-Fock-Bogoliubov'

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Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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1

Flocard, H., B. Q. Chen, B. Gall, P. Bonche, J. Dobaczewski, P. H. Heenen, and M. S. Weiss. "Hartree-Fock and Hartree-Fock-Bogoliubov calculations of superdeformed bands." Nuclear Physics A 557 (May 1993): 559–72. http://dx.doi.org/10.1016/0375-9474(93)90569-j.

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2

BARAN, A., J. A. SHEIKH, A. STASZCZAK, and W. NAZAREWICZ. "FISSION QUADRUPOLE MASS PARAMETERS IN HF+BCS AND HFB METHODS." International Journal of Modern Physics E 18, no. 04 (April 2009): 1049–53. http://dx.doi.org/10.1142/s0218301309013221.

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The self-consistent Hartree-Fock+BCS and Hartree-Fock-Bogoliubov methods are compared at large nuclear deformations. The calculations are carried out for the fission pathway and quadrupole mass parameter of 252 Fm .

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3

Samyn, M., S. Goriely, P. H. Heenen, J. M. Pearson, and F. Tondeur. "A Hartree–Fock–Bogoliubov mass formula." Nuclear Physics A 700, no. 1-2 (March 2002): 142–56. http://dx.doi.org/10.1016/s0375-9474(01)01316-1.

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4

Sheikh, Javid A., and Peter Ring. "Symmetry-projected Hartree–Fock–Bogoliubov equations." Nuclear Physics A 665, no. 1-2 (February 2000): 71–91. http://dx.doi.org/10.1016/s0375-9474(99)00424-8.

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5

Bao, Nguyen Dien Quoc. "Using DIRHB package to calculate the properties of some nuclei." Science and Technology Development Journal - Natural Sciences 3, no. 4 (February 23, 2020): 252–58. http://dx.doi.org/10.32508/stdjns.v3i4.725.

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In this work, the relativistic Hartree-Bogoliubov method is studied for calculating of nuclear properties such as binding energy per nucleon, charge radii, and single-particle energies of proton and neutron for some nuclei like O16, Ca40, Sn132 and Pb208. This method is the relativistic case of the Hartree-Fock-Bogoliubov method, which is a generalization of the Hartree-Fock method, and the method includes short-range correlations such as pairing force. In addition, the energy functional DD-ME2 is used to describe the effective interactions in equations of the relativistic Hartree-Bogoliubov method. The DIRHB package, which was written in Fortran, is utilized to calculate and get the results. The results are compared with experimental ones, except the single-particle energies of Ca40 due to the lack of data. The comparisons show well agreements between the calculation results and the experimental values of binding energy per nucleon as well as charge radii, for parameters of the DD-ME2 which were fitted based on the experimental data of nuclear mass. However, the results of single-particle levels do not agree with experimental ones in some cases. This means the relativistic Hartree-Bogoliubov method should be studied further in the future.

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6

WARDA, M., A. STASZCZAK, and L. PRÓCHNIAK. "COMPARISON OF SELF-CONSISTENT SKYRME AND GOGNY CALCULATIONS FOR LIGHT Hg ISOTOPES." International Journal of Modern Physics E 19, no. 04 (April 2010): 787–93. http://dx.doi.org/10.1142/s0218301310015230.

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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 have also applied the Hartree-Fock+BCS model with the state-dependent δ-pairing interaction. Potential energy surfaces and pairing properties have been compared for the both types of forces.

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7

KVASIL, J., R. K. SHELINE, and P. ALEXA. "A MICROSCOPIC VIEW OF THE SYMMETRY PROPERTIES OF REFLECTION-ASYMMETRIC NUCLEI." International Journal of Modern Physics E 04, no. 02 (June 1995): 457–75. http://dx.doi.org/10.1142/s0218301395000171.

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The symmetry properties of reflection-asymmetric nuclei are discussed in the framework of the Hartree-Fock-Bogoliubov method. A comparison of reflection-symmetric and reflection-asymmetric approaches is made.

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8

Bassem, Y. El, and M. Oulne. "Ground state properties of even–even and odd Nd, Ce and Sm isotopes in Hartree–Fock–Bogoliubov method." International Journal of Modern Physics E 24, no. 10 (October 2015): 1550073. http://dx.doi.org/10.1142/s0218301315500731.

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In this work, we have studied the 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 binding 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.

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9

Majid, Mohammed F. "Nuclear structure study of some tin isotopes using the self-consistent mean field method." Iraqi Journal of Physics (IJP) 13, no. 26 (February 10, 2019): 112–20. http://dx.doi.org/10.30723/ijp.v13i26.291.

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Hartree-Fock calculations for even-even Tin isotopes usingSkyrme density dependent effective nucleon-nucleon interaction arediscussed systematically. Skyrme interaction and the general formulafor the mean energy of a spherical nucleus are described. The chargeand matter densities with their corresponding rms radii and thenuclear skin for Sn isotopes are studied and compared with theexperimental data. The potential energy curves obtained withinclusion of the pairing force between the like nucleons in Hartree-Fock-Bogoliubov approach are also discussed.

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10

Hergert, H., R. Roth, and A. Zapp. "Hartree–Fock–Bogoliubov calculations with correlated realistic interactions." Progress in Particle and Nuclear Physics 59, no. 1 (July 2007): 470–72. http://dx.doi.org/10.1016/j.ppnp.2007.01.005.

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11

Guimarães, F. B., B. V. Carlson, and T. Frederico. "Hartree-Fock-Bogoliubov approximation to relativistic nuclear matter." Physical Review C 54, no. 5 (November 1, 1996): 2385–98. http://dx.doi.org/10.1103/physrevc.54.2385.

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12

Lewin, Mathieu, and Séverine Paul. "A numerical perspective on Hartree−Fock−Bogoliubov theory." ESAIM: Mathematical Modelling and Numerical Analysis 48, no. 1 (November 15, 2013): 53–86. http://dx.doi.org/10.1051/m2an/2013094.

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13

Cescato, M. L., Y. Sun, and P. Ring. "Cranked hartree-fock-bogoliubov calculations for Dy isotopes." Nuclear Physics A 533, no. 3 (1991): 455–75. http://dx.doi.org/10.1016/0375-9474(91)90528-e.

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14

Chong, Jacky, Manoussos Grillakis, Matei Machedon, and Zehua Zhao. "Global estimates for the Hartree–Fock–Bogoliubov equations." Communications in Partial Differential Equations 46, no. 10 (May 17, 2021): 2015–55. http://dx.doi.org/10.1080/03605302.2021.1920615.

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15

AO, PING, DAVID J. THOULESS, and X. M. ZHU. "NONLINEAR SCHRÖDINGER EQUATION FOR SUPERCONDUCTORS." Modern Physics Letters B 09, no. 11n12 (May 20, 1995): 755–61. http://dx.doi.org/10.1142/s021798499500070x.

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Using the Hartree–Fock–Bogoliubov factorization of the density matrix and the Born–Oppenheimer approximation we show that the motion of a superconducting condensate satisfies a Schrödinger equation at zero temperature. The Galilean invariance of the equation is explicitly manifested. This equation gives a unified description of the condensate dynamics, such as Josephson effects, vortex dynamics and the Bogoliubov–Anderson mode.

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16

EBATA, SHUICHIRO, T. NAKATSUKASA, T. INAKURA, Y. HASHIMOTO, and K. YABANA. "LINEAR RESPONSE CALCULATION USING CANONICAL-BASIS TDHFB WITH A SCHEMATIC PAIRING FUNCTIONAL." Modern Physics Letters A 25, no. 21n23 (July 30, 2010): 2001–2. http://dx.doi.org/10.1142/s021773231000085x.

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We derive the Canonical-basis Time-Dependent Hartree-Fock-Bogoliubov (CbTDHFB) equations using time-dependent variational principle with a special pairing energy functional. We obtain the isoscalar quadrupole strength functions for Magnesium isotopes with small-amplitude CbTDHFB calculation in the three-dimensional coordinate-space representation.

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17

Li, Jiajie, Wenhui Long, Jérôme Margueron, and Nguyen Van Giai. "Superheavy magic nuclei in Relativistic Hartree-Fock-Bogoliubov theory." Journal of Physics: Conference Series 533 (September 10, 2014): 012002. http://dx.doi.org/10.1088/1742-6596/533/1/012002.

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18

Li, J. J., W. H. Long, J. Margueron, and N. Van Giai. "Relativistic Hartree-Fock-Bogoliubov predictions of superheavy magic nuclei." Journal of Physics: Conference Series 580 (February 9, 2015): 012006. http://dx.doi.org/10.1088/1742-6596/580/1/012006.

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19

Samyn, M., S. Goriely, and J. M. Pearson. "Further explorations of Skyrme–Hartree–Fock–Bogoliubov mass formulas." Nuclear Physics A 725 (September 2003): 69–81. http://dx.doi.org/10.1016/s0375-9474(03)01578-1.

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20

Yamaki, Daisuke, Tadafumi Ohsaku, Hidemi Nagao, and Kizashi Yamaguchi. "Formulation of unrestricted and restricted Hartree-Fock-Bogoliubov equations." International Journal of Quantum Chemistry 96, no. 1 (2003): 10–16. http://dx.doi.org/10.1002/qua.10788.

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21

Goriely, S., N. Chamel, and J. M. Pearson. "Latest results of Skyrme-Hartree-Fock-Bogoliubov mass formulas." Journal of Physics: Conference Series 665 (January 5, 2016): 012038. http://dx.doi.org/10.1088/1742-6596/665/1/012038.

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22

Tommasini, Paolo, E. J. V. de Passos, M. O. C. Pires, and A. F. R. de Toledo Piza. "Extended Hartree–Fock–Bogoliubov theory for degenerate Bose systems." Journal of Physics: Condensed Matter 17, no. 21 (May 13, 2005): 3165–81. http://dx.doi.org/10.1088/0953-8984/17/21/012.

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23

Lin, Lin, and Xiaojie Wu. "Numerical solution of large scale Hartree–Fock–Bogoliubov equations." ESAIM: Mathematical Modelling and Numerical Analysis 55, no. 3 (May 2021): 763–87. http://dx.doi.org/10.1051/m2an/2020074.

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The Hartree–Fock–Bogoliubov (HFB) theory is the starting point for treating superconducting systems. However, the computational cost for solving large scale HFB equations can be much larger than that of the Hartree–Fock equations, particularly when the Hamiltonian matrix is sparse, and the number of electrons N is relatively small compared to the matrix size Nb. We first provide a concise and relatively self-contained review of the HFB theory for general finite sized quantum systems, with special focus on the treatment of spin symmetries from a linear algebra perspective. We then demonstrate that the pole expansion and selected inversion (PEXSI) method can be particularly well suited for solving large scale HFB equations. For a Hubbard-type Hamiltonian, the cost of PEXSI is at most 𝒪(Nb2) for both gapped and gapless systems, which can be significantly faster than the standard cubic scaling diagonalization methods. We show that PEXSI can solve a two-dimensional Hubbard-Hofstadter model with Nb up to 2.88 × 106, and the wall clock time is less than 100 s using 17 280 CPU cores. This enables the simulation of physical systems under experimentally realizable magnetic fields, which cannot be otherwise simulated with smaller systems.

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24

BARAN, A., J. A. SHEIKH, and W. NAZAREWICZ. "ADIABATIC MASS PARAMETERS FOR SPONTANEUS FISSION." International Journal of Modern Physics E 18, no. 04 (April 2009): 1054–57. http://dx.doi.org/10.1142/s0218301309013233.

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The collective mass tensor derived from the adiabatic time-dependent Hartree-Fock-Bogoliubov theory, perturbative cranking approximation, and the Gaussian overlap approximation to the generator coordinate method is discussed. Illustrative calculations are carried out for 252 Fm using the nuclear density functional theory with Skyrme interaction SkM* and seniority pairing.

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25

NERLO–POMORSKA, BOŻENA, KRZYSZTOF POMORSKI, and MONIKA ZWIERZCHOWSKA. "PREDICTIONS OF NUCLEAR MASSES IN DIFFERENT MODELS." International Journal of Modern Physics E 16, no. 02 (February 2007): 474–82. http://dx.doi.org/10.1142/s0218301307005909.

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The modern version of the liquid-drop model is compared to the macroscopic Thomas-Fermi (TF) energy and the macroscopic part of the binding energy evaluated within the Hartree-Fock-Bogoliubov theory with the Gogny force and the relativistic mean field theory. The limits of nuclear stability predicted by these models are discussed.

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26

OBA, HIROSHI, and MASAYUKI MATSUO. "CONTINUUM COUPLING AND PAIR CORRELATION IN WEAKLY BOUND DEFORMED NUCLEI." International Journal of Modern Physics E 18, no. 10 (November 2009): 2015–19. http://dx.doi.org/10.1142/s0218301309014202.

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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.

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27

KHAN, E., and N. SANDULESCU. "MICROSCOPIC DESCRIPTION OF TEMPERATURE AND PAIRING EFFECTS IN NUCLEI." International Journal of Modern Physics E 20, no. 02 (February 2011): 387–92. http://dx.doi.org/10.1142/s0218301311017764.

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Finite temperature Hartree-Fock-Bogoliubov calculations are performed in finite nuclei using Skyrme and zero-range, density-dependent pairing interactions. The value of the critical temperature follows approximatively the empirical rule Tc ≃ 0.5 ΔT=0. The specific heat is calculated within the FT-HFB framework. Preliminary results obtained with the FT-QRPA are discussed.

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28

SCHUNCK, N., P. OLBRATOWSKI, J. DUDEK, and J. DOBACZEWSKI. "ROTATION OF TETRAHEDRAL NUCLEI IN THE CRANKING MODEL." International Journal of Modern Physics E 15, no. 02 (March 2006): 490–94. http://dx.doi.org/10.1142/s0218301306004417.

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The three-dimensional cranking model is used to investigate the microscopic aspects of the rotation of nuclei with the tetrahedral symmetry. Two classes of rotation axes are studied corresponding to two different discrete symmetries of the rotating hamiltonian. Self-consistent Hartree-Fock-Bogoliubov calculations show that the tetrahedral minimum remains remarkably stable until the first single-particle crossing.

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29

AVOGADRO, PAOLO, and TAKASHI NAKATSUKASA. "THE FINITE AMPLITUDE METHOD FOR THE QRPA." Modern Physics Letters A 25, no. 21n23 (July 30, 2010): 1999–2000. http://dx.doi.org/10.1142/s0217732310000848.

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We present the finite amplitude method (FAM) for the Quasi Particle Random Phase Approximation (QRPA). This method allows to extract a QRPA code starting from a Hartree-Fock-Bogoliubov (HFB) code. The code obtained is fully self consistent, moreover since the FAM is not restricted to spherical symmetry it can be used to obtain deformed QRPA codes.

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30

BAYRAM, TUNCAY. "AN INVESTIGATION ON SHAPE EVOLUTION OF Ti ISOTOPES WITH HARTREE–FOCK–BOGOLIUBOV THEORY." Modern Physics Letters A 27, no. 28 (September 4, 2012): 1250162. http://dx.doi.org/10.1142/s0217732312501623.

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Constrained Hartree–Fock–Bogoliubov theory with SLy4 and SLy5 Skyrme forces is used to investigate the shape transition between spherical and γ-unstable nuclei in 38–66 Ti . By examining potential energy curves and neutron single-particle levels of even–even Ti isotopes, 46,52,60 Ti are suggested as possible candidates of the nuclei with E(5) symmetry.

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31

Li, Jia Jie, Wen Hui Long, Jérôme Margueron, and Nguyen Van Giai. "Superheavy magic structures in the relativistic Hartree–Fock–Bogoliubov approach." Physics Letters B 732 (May 2014): 169–73. http://dx.doi.org/10.1016/j.physletb.2014.03.031.

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32

Bulgac, Aurel. "Time-dependent Hartree-Fock-Bogoliubov approximation and nonintegrable quantum phase." Physical Review C 41, no. 5 (May 1, 1990): 2333–39. http://dx.doi.org/10.1103/physrevc.41.2333.

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33

Bach, Volker, Sébastien Breteaux, Hans Konrad Knörr, and Edmund Menge. "Generalization of Lieb's variational principle to Bogoliubov–Hartree–Fock theory." Journal of Mathematical Physics 55, no. 1 (January 2014): 012101. http://dx.doi.org/10.1063/1.4853875.

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34

AVEZ, B., C. SIMENEL, and Ph CHOMAZ. "PAIRING VIBRATIONS STUDY FROM TIME-DEPENDENT HARTREE-FOCK-BOGOLIUBOV FORMALISM." International Journal of Modern Physics E 18, no. 10 (November 2009): 2103–7. http://dx.doi.org/10.1142/s0218301309014378.

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We study pairing vibrations in 18,20,22 O and 42,44,46 Ca nuclei solving the time-dependent Hartree-Fock-Bogoliubov equation in coordinate space with spherical symmetry. We use the SLy4 Skyrme functional in the particle-hole part of the energy density functional and a local, density-dependent pairing functional in its particle-particle (hole-hole) part. Pairing vibrations are excited by a two-neutrons transfer operator. The Fourier analysis of the time-dependent response of the expectation value of this operator in the linear regime is used to extract strength functions. The presence of the giant pairing vibration is discussed.

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35

Goodman, Alan L. "Finite-temperature Hartree-Fock-Bogoliubov calculations in rare earth nuclei." Physical Review C 34, no. 5 (November 1, 1986): 1942–49. http://dx.doi.org/10.1103/physrevc.34.1942.

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36

Ashok, Nithu, Deepthy Maria Joseph, and Antony Joseph. "Cluster decay in osmium isotopes using Hartree–Fock–Bogoliubov theory." Modern Physics Letters A 31, no. 07 (March 2, 2016): 1650045. http://dx.doi.org/10.1142/s0217732316500450.

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Cluster radioactivity is a rare cold nuclear process which is intermediate between alpha decay and spontaneous fission. The present work is a theoretical investigation of the feasibility of alpha decay and cluster radioactivity from proton rich Osmium (Os) isotopes with mass number ranging from 162–190. Osmium forms a part of the transition region between highly deformed and spherical nuclei. Calculations have been done using unified fission model and Hartree–Fock–Bogoliubov (HFB) theory. We have chosen only those decays with half-lives falling in measurable range. Geiger–Nuttall plot has been successfully reproduced. The isotope which is most favorable to each decay mode has a magic daughter nucleus.

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37

Egido, J. L., P. Ring, and H. J. Mang. "Temperature-dependent Hartree-Fock-Bogoliubov calculations in hot rotating nuclei." Nuclear Physics A 451, no. 1 (March 1986): 77–90. http://dx.doi.org/10.1016/0375-9474(86)90242-3.

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38

Saha Sarkar, M., and S. Sen. "Cranked Hartree-Fock-Bogoliubov calculations in the Xe-Ba region." Physical Review C 56, no. 6 (December 1, 1997): 3140–51. http://dx.doi.org/10.1103/physrevc.56.3140.

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39

Puddu, G. "Functional integrals for Hartree Fock Bogoliubov many-body matrix elements." Journal of Physics A: Mathematical and General 35, no. 37 (September 5, 2002): 7919–27. http://dx.doi.org/10.1088/0305-4470/35/37/304.

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40

Dobaczewski, J., W. Nazarewicz, and T. R. Werner. "Neutron radii and skins in the Hartree-Fock-Bogoliubov calculations." Zeitschrift für Physik A: Hadrons and Nuclei 354, no. 1 (December 1996): 27–35. http://dx.doi.org/10.1007/s002180050009.

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41

RODRÍGUEZ, T. R., J. L. EGIDO, L. M. ROBLEDO, and R. R. RODRÍGUEZ-GUZMÁN. "ON THE STABILITY OF PROJECTION AFTER VARIATION SOLUTIONS." International Journal of Modern Physics E 13, no. 01 (February 2004): 165–68. http://dx.doi.org/10.1142/s0218301304001898.

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We have performed angular momentum projection with double-constrained Hartree-Fock-Bogoliubov wave functions with the Gogny interaction for the 32 Mg . We show that the more relevant degree of freedom is the quadrupole deformation. Minima of the ground state obtained in single-constrained calculations with this operator are hardly modified in double-constrained calculations insuring thereby the stability of the solution.

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42

Shimizu, Noritaka, Takahiro Mizusaki, and Makito Oi. "Recent progress of the sign problem in the Onishi formula." EPJ Web of Conferences 178 (2018): 02004. http://dx.doi.org/10.1051/epjconf/201817802004.

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The Hartree-Fock-Bogoliubov (HFB) method is one of the major methods to study a nuclear wave function. We discuss the sign problem in the Onishi formula, which emerges in calculating the overlap between two HFB wave functions. The origin of this problem is elucidated by expanding the overlap as a polynomial function. This article is based on Ref.[1].

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43

MORIKAWA, TSUNEYASU, EIJI IDEGUCHI, SHINSUKE OTA, MASUMI OSHIMA, MITSUO KOIZUMI, YOSUKE TOH, ATSUSHI KIMURA, et al. "SUPERDEFORMED BAND IN ASYMMETRIC N > Z NUCLEUS 40Ar." Modern Physics Letters A 25, no. 21n23 (July 30, 2010): 1792–95. http://dx.doi.org/10.1142/s0217732310000344.

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A rotational band with five cascade γ-ray transitions was newly found in 40 Ar . The deduced transition quadrupole moment of [Formula: see text] has demonstrated this band as having a superdeformed shape of β2 ~ 0.5. The structure of the band was discussed in the framework of cranked Hartree-Fock-Bogoliubov calculations and the assignment of multiparticle–multihole configuration has been made.

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44

BARAN, A., A. STASZCZAK, and W. NAZAREWICZ. "FISSION HALF LIVES OF FERMIUM ISOTOPES WITHIN SKYRME HARTREE-FOCK-BOGOLIUBOV THEORY." International Journal of Modern Physics E 20, no. 02 (February 2011): 557–64. http://dx.doi.org/10.1142/s0218301311018009.

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Nuclear fission barriers, mass parameters and spontaneous fission half lives of fermium isotopes calculated in a framework of the Skyrme Hartree-Fock-Bogoliubov model with the SkM* force are discussed. Zero-point energy corrections in the ground state are determined for each nucleus using the Gaussian overlap approximation of the generator coordinate method and in the cranking formalism. Results of spontaneous fission half lives are compared to experimental data.

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45

WARDA, M. "TOROIDAL STRUCTURE OF SUPER-HEAVY NUCLEI IN THE HFB THEORY." International Journal of Modern Physics E 16, no. 02 (February 2007): 452–58. http://dx.doi.org/10.1142/s0218301307005880.

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Toroidal structure of super-heavy nuclei has been analyzed within the Hartree-Fock-Bogoliubov theory with the Gogny D1S force. The global minimum of the potential energy of systems with Z > 130 has been found for nuclei in the shape of a torus. The binding energy of toroidal super-heavy nuclei is lower than the energy of the spherical nuclei by 180 MeV.

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46

Shelley, Matthew, and Alessandro Pastore. "Comparison between the Thomas–Fermi and Hartree–Fock–Bogoliubov Methods in the Inner Crust of a Neutron Star: The Role of Pairing Correlations." Universe 6, no. 11 (November 11, 2020): 206. http://dx.doi.org/10.3390/universe6110206.

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We investigated the role of a pairing correlation in the chemical composition of the inner crust of a neutron star with the extended Thomas–Fermi method, using the Strutinsky integral correction. We compare our results with the fully self-consistent Hartree–Fock–Bogoliubov approach, showing that the resulting discrepancy, apart from the very low density region, is compatible with the typical accuracy we can achieve with standard mean-field methods.

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47

SHIMODA, YUICHI, TATSUYA NAKAJIMA, and ANJU SAWADA. "GROUND-STATE PROPERTIES OF BILAYER ν=2 QUANTUM HALL STATES." International Journal of Modern Physics B 18, no. 27n29 (November 30, 2004): 3713–16. http://dx.doi.org/10.1142/s0217979204027335.

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We construct a Hartree-Fock-Bogoliubov (HFB) Hamiltonian Haldane-sphere and study excitation spectra and ground-state properties in bilayer ν=2 QH systems. It is found that the HFB approximation can systematically give SU (2) symmetrical excitation spectra spectra well agree with those from exact diagonalization calculations in large tunneling-energy region. In this region, has been considered to be a pseudospin-squeezed ground state is favored theory.

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48

Imamović-Tomasović, Milena, and Allan Griffin. "Coupled Hartree-Fock-Bogoliubov kinetic equations for a trapped Bose gas." Physical Review A 60, no. 1 (July 1, 1999): 494–503. http://dx.doi.org/10.1103/physreva.60.494.

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YANG, Shen, JiaJie LI, and WenHui LONG. "Pairing phase transition within finite-temperature relativistic Hartree-Fock-Bogoliubov approach." SCIENTIA SINICA Physica, Mechanica & Astronomica 46, no. 1 (December 14, 2015): 012009. http://dx.doi.org/10.1360/sspma2015-00393.

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SHIMODA, YUICHI, TATSUYA NAKAJIMA, and ANJU SAWADA. "HARTREE–FOCK–BOGOLIUBOV STUDIES OF BILAYER ν = 2 QUANTUM HALL SYSTEMS." Modern Physics Letters B 19, no. 11 (May 10, 2005): 539–48. http://dx.doi.org/10.1142/s0217984905008517.

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Abstract:

Excitation spectra in bilayer quantum Hall systems at total Landau-level filling ν = 2 are studied by the Hartree–Fock–Bogoliubov (HFB) approximation. The systems have the spin degrees of freedom in addition to the layer degrees of freedom described in terms of pseudospin. On the excitation spectrum from the spin-singlet and pseudospin-polarized ground state, this approximation fully preserves the spin rotational symmetry and thus can give both spin-triplet and spin-singlet excitations systematically. It is also found that the ground state is pseudospin squeezed because of pseudospin correlations and that the HFB approximation can describe ground-state properties better than other approximations.

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