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Journal articles on the topic 'Feynman-Hellmann'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Howson, T. L., R. Horsley, W. Kamleh, Y. Nakamura, H. Perlt, P. E. L. Rakow, G. Schierholz, H. Stüben, R. D. Young, and J. M. Zanotti. "Directly calculating the glue component of the nucleon in lattice QCD: QCDSF–UKQCD–CSSM Collaborations." EPJ Web of Conferences 245 (2020): 06031. http://dx.doi.org/10.1051/epjconf/202024506031.

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We are investigating the direct determination and non-perturbative renormalisation of gluon matrix elements. Such quantities are sensitive to ultra– violet fluctuations, and are in general statistically noisy. To obtain statistically significant results, we extend an earlier application of the Feynman–Hellmann theorem to gluonic matrix elements to calculate a renormalisation factor in the RI – MOM scheme, in the quenched case. This work demonstrates that the Feynman–Hellmann method is capable of providing a feasible option for calculating gluon quantities.

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2

Esteve, J. G., Fernando Falceto, and C. García Canal. "Generalization of the Hellmann–Feynman theorem." Physics Letters A 374, no. 6 (January 2010): 819–22. http://dx.doi.org/10.1016/j.physleta.2009.12.005.

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3

Pupyshev, Vladimir I. "Hellmann-Feynman theorem near the threshold." International Journal of Quantum Chemistry 88, no. 4 (April 26, 2002): 380–91. http://dx.doi.org/10.1002/qua.10175.

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4

Fernández, Francisco M. "The extended Hellmann-Feynman theorem revisited." Chemical Physics Letters 233, no. 5-6 (February 1995): 651–52. http://dx.doi.org/10.1016/0009-2614(94)01505-p.

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5

Pons, Marina, Bruno Juliá-Díaz, Artur Polls, Arnau Rios, and Isaac Vidaña. "The Hellmann–Feynman theorem at finite temperature." American Journal of Physics 88, no. 6 (June 2020): 503–10. http://dx.doi.org/10.1119/10.0001233.

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6

Sun, Xin. "Generalized Hellmann—Feynman Theorem and Its Applications." Chinese Physics Letters 33, no. 12 (December 2016): 123601. http://dx.doi.org/10.1088/0256-307x/33/12/123601.

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7

Fernández, Francisco M. "The Hellmann–Feynman theorem for statistical averages." Journal of Mathematical Chemistry 52, no. 8 (June 7, 2014): 2128–32. http://dx.doi.org/10.1007/s10910-014-0368-3.

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8

Lehmann, D., and P. Ziesche. "Hellmann-Feynman forces on and between jellia." physica status solidi (b) 135, no. 2 (June 1, 1986): 651–60. http://dx.doi.org/10.1002/pssb.2221350224.

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9

Feng, Chen, Cheng Wei, Bao-long Fang, and Hong-yi Fan. "A Deduction of the Hellmann-Feynman Theorem." International Journal of Theoretical Physics 59, no. 5 (March 28, 2020): 1396–401. http://dx.doi.org/10.1007/s10773-019-04362-7.

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10

Gáspár, R., and Á. Nagy. "Generalized Hellmann-Feynman theorem in theXα method." International Journal of Quantum Chemistry 31, no. 4 (April 1987): 639–47. http://dx.doi.org/10.1002/qua.560310409.

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11

Hirao, K. "Analytic derivative theory based on the Hellmann–Feynman theorem." Canadian Journal of Chemistry 70, no. 2 (February 1, 1992): 434–42. http://dx.doi.org/10.1139/v92-063.

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General formulae for the second, third, and fourth derivatives of the energy with respect to the nuclear coordinates of a molecule are derived from the Hellmann–Feynman theorem. Hurley's condition is used to obtain approximations to the first-order wavefunction, from which the second, third, and fourth energies can be obtained, leading to quadratic, cubic, and quartic force constants. The procedure is equivalent to minimizing the derivative energy by perturbed variation techniques. The expressions for these higher energy derivatives are much simpler than those of the direct analytic derivative method. The electrostatic calculation involves only one-electron integrals. The coupled Hartree–Fock equations to obtain the wavefunction derivatives become much simpler. The present theory provides a great conceptual simplification. However, the theory is correct only if the basis set is complete or basis functions are independent of the perturbation. Keywords: analytic derivative theory, Hellmann–Feynman theorem, force constants, the curvature theorem.

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12

Del Debbio, Luigi, and Roman Zwicky. "Renormalisation group, trace anomaly and Feynman–Hellmann theorem." Physics Letters B 734 (June 2014): 107–10. http://dx.doi.org/10.1016/j.physletb.2014.05.038.

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13

Balasubramanian, S. "A note on the generalized Hellmann–Feynman theorem." American Journal of Physics 58, no. 12 (December 1990): 1204–5. http://dx.doi.org/10.1119/1.16254.

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14

Amore, Paolo, and Francisco M. Fernández. "On the Hellmann-Feynman theorem in statistical mechanics." Physics Letters A 384, no. 22 (August 2020): 126531. http://dx.doi.org/10.1016/j.physleta.2020.126531.

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15

Fan, Hong-yi, and Bo-zhan Chen. "Generalized Feynman-Hellmann theorem for ensemble average values." Physics Letters A 203, no. 2-3 (July 1995): 95–101. http://dx.doi.org/10.1016/0375-9601(95)00385-g.

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16

Novák, Matyáš, Jiří Vackář, and Robert Cimrman. "Evaluating Hellmann–Feynman forces within non-local pseudopotentials." Computer Physics Communications 250 (May 2020): 107034. http://dx.doi.org/10.1016/j.cpc.2019.107034.

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17

Venkatesan, R. C., and A. Plastino. "Hellmann–Feynman connection for the relative Fisher information." Annals of Physics 359 (August 2015): 300–316. http://dx.doi.org/10.1016/j.aop.2015.04.021.

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18

FAN, HONG-YI, XUE-XIANG XU, and LI-YUN HU. "CALCULATION OF ENTROPY FOR SOME COUPLED OSCILLATORS BY USING THE GENERALIZED HELLMANN–FEYNMAN THEOREM." Modern Physics Letters B 24, no. 03 (January 30, 2010): 271–76. http://dx.doi.org/10.1142/s0217984910022342.

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The entropies of several typical coupled bosonic oscillators are calculated by virtue of the generalized Hellmann–Feynman theorem (GHFT). The relation between GHFT and entropy-variation is construct by using von Neumann entropy, which provides us with a new approach for deriving entropy of some complicated systems.

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19

LIANG, BAO-LONG, JI-SUO WANG, and XIANG-GUO MENG. "QUANTIZATION FOR THE MESOSCOPIC RLC CIRCUIT AND ITS THERMAL EFFECT BY VIRTUE OF GHFT." Modern Physics Letters B 23, no. 30 (December 10, 2009): 3621–30. http://dx.doi.org/10.1142/s0217984909021661.

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The mesoscopic single RLC (resistance-inductance-capacitance) circuit and the RLC circuit including complicated coupling are quantized by employing Dirac's standard canonical quantization method. The thermal effects for the systems are investigated by virtue of GHFT (the generalized Hellmann–Feynman theorem). The results distinctly show the effect of temperature on the quantum fluctuation.

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20

Sa-yakanit, V., and S. Boonchui. "Magnus force and Hellmann–Feynman force: path integral approach." Journal of Physics A: Mathematical and General 34, no. 50 (December 19, 2001): 11301–5. http://dx.doi.org/10.1088/0305-4470/34/50/311.

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21

Fantoni, Riccardo. "Hellmann and Feynman theorem versus diffusion Monte Carlo experiment." Solid State Communications 159 (April 2013): 106–9. http://dx.doi.org/10.1016/j.ssc.2013.01.028.

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22

Ziesche, P., K. Kunze, and B. Milek. "Generalisation of the Hellmann-Feynman theorem to Gamow states." Journal of Physics A: Mathematical and General 20, no. 10 (July 11, 1987): 2859–64. http://dx.doi.org/10.1088/0305-4470/20/10/030.

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23

Marushko, I. A., and O. P. Bugaets. "Hellmann-Feynman Theorem and the Theory of Force Constants." physica status solidi (b) 131, no. 1 (September 1, 1985): K15—K17. http://dx.doi.org/10.1002/pssb.2221310143.

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24

Cooney, William A. "Note concerning conclusions from integral hellmann-feynman theorem calculations." International Journal of Quantum Chemistry 4, S3B (June 18, 2009): 381–82. http://dx.doi.org/10.1002/qua.560040705.

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25

Kresse, G., and J. Hafner. "Ab initio Hellmann-Feynman molecular dynamics for liquid metals." Journal of Non-Crystalline Solids 156-158 (May 1993): 956–60. http://dx.doi.org/10.1016/0022-3093(93)90104-6.

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26

FAN, HONG-YI, and XU-BING TANG. "APPLICATION OF GENERALIZED FEYNMAN–HELLMANN THEOREM IN QUANTIZATION OF LC CIRCUIT IN THERMO BATH." International Journal of Modern Physics B 24, no. 27 (October 30, 2010): 5309–17. http://dx.doi.org/10.1142/s0217979210054609.

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For the quantized LC electric circuit, when taking the Joule thermal effect into account, we think that physical observables should be evaluated in the context of ensemble average. We then use the generalized Feynman–Hellmann theorem for ensemble average to calculate them, which seems convenient. Fluctuation of observables in various LC electric circuits in the presence of thermo bath growing with temperature is exhibited.

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27

Hamada, Ikutaro. "Hellmann–Feynman Forces in the DFT+UMethod with Ultrasoft Pseudopotentials." Journal of the Physical Society of Japan 82, no. 10 (October 15, 2013): 105002. http://dx.doi.org/10.7566/jpsj.82.105002.

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28

Balasubramanian, S. "Hellmann–Feynman theorem in a linear superposition of energy eigenstates." American Journal of Physics 62, no. 12 (December 1994): 1116–17. http://dx.doi.org/10.1119/1.17670.

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29

Pederson, Mark R., Barry M. Klein, and Jeremy Q. Broughton. "Simulated annealing with floating Gaussians: Hellmann-Feynman forces without corrections." Physical Review B 38, no. 6 (August 15, 1988): 3825–33. http://dx.doi.org/10.1103/physrevb.38.3825.

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30

Novoselov, D., Dm M. Korotin, and V. I. Anisimov. "Hellmann–Feynman forces within the DFT +Uin Wannier functions basis." Journal of Physics: Condensed Matter 27, no. 32 (July 27, 2015): 325602. http://dx.doi.org/10.1088/0953-8984/27/32/325602.

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31

Hirao, K., and K. Mogi. "Floating functions satisfying the hellmann?feynman theorem: Single floating scheme." Journal of Computational Chemistry 13, no. 4 (May 1992): 457–67. http://dx.doi.org/10.1002/jcc.540130408.

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32

Ao, Jing, Chun Mei Li, Zhi Qian Chen, and Jin Wang. "Effect of Carbon Doped in BN on Electronic Structures and Mechanical Properties." Advanced Materials Research 652-654 (January 2013): 1410–15. http://dx.doi.org/10.4028/www.scientific.net/amr.652-654.1410.

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The structural properties and elastic constants of (B1-xCx)(N1-xCx) (x=0.0, 0.2, 0.4 and 0.6) are calculated by the ultra-soft pseudo-potentials within the generalized gradient approximation and local density approximation in frame of density functional theory with virtual crystal approximation. The elastic constants, the aggregate elastic modulus, poisson’s ratio, energy gap and hardness are computed too. The energy band structure, DOS, and Hellmann-Feynman stresses are also examined in details.

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33

Xu, Qimen, Xin Jing, Boqin Zhang, John E. Pask, and Phanish Suryanarayana. "Real-space density kernel method for Kohn–Sham density functional theory calculations at high temperature." Journal of Chemical Physics 156, no. 9 (March 7, 2022): 094105. http://dx.doi.org/10.1063/5.0082523.

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Kohn–Sham density functional theory calculations using conventional diagonalization based methods become increasingly expensive as temperature increases due to the need to compute increasing numbers of partially occupied states. We present a density matrix based method for Kohn–Sham calculations at high temperatures that eliminates the need for diagonalization entirely, thus reducing the cost of such calculations significantly. Specifically, we develop real-space expressions for the electron density, electronic free energy, Hellmann–Feynman forces, and Hellmann–Feynman stress tensor in terms of an orthonormal auxiliary orbital basis and its density kernel transform, the density kernel being the matrix representation of the density operator in the auxiliary basis. Using Chebyshev filtering to generate the auxiliary basis, we next develop an approach akin to Clenshaw–Curtis spectral quadrature to calculate the individual columns of the density kernel based on the Fermi operator expansion in Chebyshev polynomials and employ a similar approach to evaluate band structure and entropic energy components. We implement the proposed formulation in the SPARC electronic structure code, using which we show systematic convergence of the aforementioned quantities to exact diagonalization results, and obtain significant speedups relative to conventional diagonalization based methods. Finally, we employ the new method to compute the self-diffusion coefficient and viscosity of aluminum at 116 045 K from Kohn–Sham quantum molecular dynamics, where we find agreement with previous more approximate orbital-free density functional methods.

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34

Semay, Claude. "The Hellmann–Feynman theorem, the comparison theorem, and the envelope theory." Results in Physics 5 (2015): 322–23. http://dx.doi.org/10.1016/j.rinp.2015.11.004.

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35

Szmytkowski, Radosław. "Analogs of the Hellmann–Feynman theorem in the R-matrix theory." Physics Letters A 280, no. 3 (February 2001): 105–13. http://dx.doi.org/10.1016/s0375-9601(01)00034-2.

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36

Xu, Xue-Xiang, Li-Yun Hu, and Hong-Chun Yuan. "Generalized Hellmann-Feynman Theorem for Coupled Anisotropic Two-Mode Boson System." International Journal of Theoretical Physics 49, no. 6 (March 19, 2010): 1200–1211. http://dx.doi.org/10.1007/s10773-010-0300-y.

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37

Bakken, VebjØSRN, Trygve Helgaker, Wim Klopper, and Kenneth Ruud. "The calculation of molecular geometrical properties in the Hellmann—Feynman approximation." Molecular Physics 96, no. 4 (February 1999): 653–71. http://dx.doi.org/10.1080/00268979909483002.

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38

BAKKEN, VEBJORN. "The calculation of molecular geometrical properties in the Hellmann-Feynman approximation." Molecular Physics 96, no. 4 (February 20, 1999): 653–71. http://dx.doi.org/10.1080/002689799165512.

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39

Flego, S. P., A. Plastino, and A. R. Plastino. "Fisher information, the Hellmann–Feynman theorem, and the Jaynes reciprocity relations." Annals of Physics 326, no. 10 (October 2011): 2533–43. http://dx.doi.org/10.1016/j.aop.2011.07.009.

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40

Vianna, Reinaldo O., Rog�rio Cust�dio, H�lio Chacham, and Jos� Rachid Mohallem. "Reliable Hellmann-Feynman forces for nuclei-centeredGTO basis of standard size." International Journal of Quantum Chemistry 44, S26 (March 14, 1992): 311–18. http://dx.doi.org/10.1002/qua.560440827.

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41

Kryachko, Eugene S. "On wave-function correction to Hellmann-Feynman force: Hartree-fock method." International Journal of Quantum Chemistry 56, no. 1 (October 5, 1995): 3–7. http://dx.doi.org/10.1002/qua.560560103.

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42

Liolios, T., and M. Grypeos. "Application of the hypervirial theorem scheme to the potential -D/cosh^2(r/R)." HNPS Proceedings 4 (February 19, 2020): 51. http://dx.doi.org/10.12681/hnps.2874.

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The well known potential -D/cosh^2(r/R)is studied with the aim of obtaining approximate analytic expressions mainly for the energies of the excited states with l≠0. Use is made of the Hypervirial Theorems (HVT) in conjunction with the Hellmann-Feynman Theorem (HFT) which provide a very powerful scheme especially for the treatment of 'Oscillator-like' potentials,as previous studies have shown. The energy eigenvalues are calculated in the form of an expansion, the first terms of which, in many cases, yield very satisfactory results.

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43

Römer, Rudolf A., and Paul Ziesche. "Hellmann-Feynman theorem and correlation-fluctuation analysis for the Calogero-Sutherland model." Journal of Physics A: Mathematical and General 34, no. 7 (February 9, 2001): 1485–506. http://dx.doi.org/10.1088/0305-4470/34/7/320.

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44

İpekoğlu, Y., and S. Turgut. "An elementary derivation of the quantum virial theorem from Hellmann–Feynman theorem." European Journal of Physics 37, no. 4 (June 1, 2016): 045405. http://dx.doi.org/10.1088/0143-0807/37/4/045405.

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45

Moscardó, Federico. "The Hellmann–Feynman theorem and its relation with the universal density functional." Chemical Physics Letters 428, no. 1-3 (September 2006): 187–90. http://dx.doi.org/10.1016/j.cplett.2006.06.086.

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46

Lichtenberg, D. B. "Application of a generalized Feynman-Hellmann theorem to bound-state energy levels." Physical Review D 40, no. 12 (December 15, 1989): 4196–98. http://dx.doi.org/10.1103/physrevd.40.4196.

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47

Ziesche, P., R. Kaschner, and N. Nafari. "Stress theorem and Hellmann-Feynman relations for the jellium model of interfaces." Physical Review B 41, no. 15 (May 15, 1990): 10553–67. http://dx.doi.org/10.1103/physrevb.41.10553.

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48

Hurley, A. C. "Integrated and integral hellmann-feynman formulae II. Construction of super-floating functions." International Journal of Quantum Chemistry 1, S1 (June 18, 2009): 677–85. http://dx.doi.org/10.1002/qua.560010674.

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49

Okon, Ituen, Clement Onate, Ekwevugbe Omugbe, Uduakobong Okorie, Akaninyene Antia, Michael Onyeaju, Chen Wen-Li, and Judith Araujo. "Approximate Solutions, Thermal Properties, and Superstatistics Solutions to Schrödinger Equation." Advances in High Energy Physics 2022 (March 7, 2022): 1–18. http://dx.doi.org/10.1155/2022/5178247.

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In this work, we apply the parametric Nikiforov-Uvarov method to obtain eigensolutions and total normalized wave function of Schrödinger equation expressed in terms of Jacobi polynomial using Coulomb plus Screened Exponential Hyperbolic Potential (CPSEHP), where we obtained the probability density plots for the proposed potential for various orbital angular quantum number, as well as some special cases (Hellmann and Yukawa potential). The proposed potential is best suitable for smaller values of the screening parameter α . The resulting energy eigenvalue is presented in a close form and extended to study thermal properties and superstatistics expressed in terms of partition function Z and other thermodynamic properties such as vibrational mean energy U , vibrational specific heat capacity C , vibrational entropy S , and vibrational free energy F . Using the resulting energy equation and with the help of Matlab software, the numerical bound state solutions were obtained for various values of the screening parameter ( α ) as well as different expectation values via Hellmann-Feynman Theorem (HFT). The trend of the partition function and other thermodynamic properties obtained for both thermal properties and superstatistics were in excellent agreement with the existing literatures. Due to the analytical mathematical complexities, the superstatistics and thermal properties were evaluated using Mathematica 10.0 version software. The proposed potential model reduces to Hellmann potential, Yukawa potential, Screened Hyperbolic potential, and Coulomb potential as special cases.

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50

Momeni, D., Koblandy Yerzhanov, and Ratbay Myrzakulov. "Quantized black hole and Heun function." Canadian Journal of Physics 90, no. 9 (September 2012): 877–81. http://dx.doi.org/10.1139/p2012-078.

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In this paper, following the simple proposal by He and Ma for quantization of a black hole (BH) using Bohr’s method, we discuss the solvability of the wave equation for such a BH. We consequentially solve the associated Schrödinger equation. The eigenfunction problem reduces to the HeunB, H(α, β, γ, δ; z), differential equation, which is a natural generalization of the hypergeometric differential equation. We investigate some physical properties of the wavefunction. We then obtain the expectation value of the kinetic and the potential energies, using Hellmann–Feynman theorem. Our work introduces some new applications of the Heun function.

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