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1

Wildberger, K., R. Zeller, and P. H. Dederichs. "Screened KKR-Green's-function method for layered systems." Physical Review B 55, no. 15 (April 15, 1997): 10074–80. http://dx.doi.org/10.1103/physrevb.55.10074.

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2

Ebert, H., D. Ködderitzsch, and J. Minár. "Calculating condensed matter properties using the KKR-Green's function method—recent developments and applications." Reports on Progress in Physics 74, no. 9 (August 12, 2011): 096501. http://dx.doi.org/10.1088/0034-4885/74/9/096501.

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3

Ogura, M., H. Akai, and T. Minamisono. "Electric Field Gradients of Fluorides Calculated by the Full Potential KKR Green's Function Method." Hyperfine Interactions 158, no. 1-4 (November 2004): 95–98. http://dx.doi.org/10.1007/s10751-005-9014-6.

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4

Ogura, M., and H. Akai. "Electric Field Gradients of Light Impurities in TiO2 Calculated by the Full Potential KKR Green's Function Method." Hyperfine Interactions 158, no. 1-4 (November 2004): 99–103. http://dx.doi.org/10.1007/s10751-005-9015-5.

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5

Kumar, Sandeep, Surender Kumar, and Prabhakar P. Singh. "First-principles Study of Electronic Properties of FeCrxSe Alloys." MRS Advances 1, no. 24 (2016): 1803–9. http://dx.doi.org/10.1557/adv.2016.256.

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ABSTRACTWe performed first-principles study of electronic properties of FeCrxSe (x=0.0, 0.01, 0.02, 0.04) alloys using the Green’s function-based Korringa-Kohn-Rostoker Atomic Sphere Approximation method within the coherent potential approximation (KKR-ASA-CPA). The KKR-ASA-CPA method is implemented with density function theory (DFT). We find that the excess of Cr into FeSe significantly affects the electronic structure with respect to the parent FeSe. The results have been analyzed in terms of changes in the density of states (DOS), partial DOS, band structures, Fermi surface, bare Sommerfeld constant and the superconducting transition temperature of FeCr0.01Se, FeCr0.02Se and FeCr0.04Se alloys respectively. Our calculations show that calculated Tc for these alloys are close to experimental values, given the nature of approximations used in our calculations.
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6

STEPANYUK, V. S., P. LANG, K. WILDBERGER, R. ZELLER, and P. H. DEDERICHS. "SURFACE ENHANCEMENT OF 3d, 4d, AND 5d IMPURITY MOMENTS AT Cu AND Ag(00l) SURFACES." Surface Review and Letters 01, no. 04 (December 1994): 477–79. http://dx.doi.org/10.1142/s0218625x94000473.

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We present ab initio calculations for the electronic structure of 3d, 4d, and 5d transition metal impurities at the (001) surface of Cu and Ag. Our focus is on the surface enhancement of the local impurity moments. The calculations are performed within local density functional theory and use a KKR Green's function method for impurities at surfaces. For 3d impurities we find a sizeable enhancement of the local moments, being most important for V and Cr. Extremely large effects are found for 4d and 5d impurities, which in general are nonmagnetic in the bulk. On the Ag(001) surface we find that Zr, Nb, Mo, Tc, Ru, Ta, W, Re, and Os are magnetic. Some of adatoms (Nb, Mo, Tc, W, Re) have "giant" magnetic moments between 3 and 4 μB.
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7

Kim, Hyung Sun, Hannah Song, Ji Kwon Jung, Byung-Ki Na, Byung Won Cho, and Yong-Tae Kim. "Codoping effect of Li1.1V0.9O2 anodes for lithium-ion batteries with Mo and W (Li1.1V0.9−2xMoxWxO2): Based on electronic structure calculations using full-potential KKR-Green's function method." Journal of Alloys and Compounds 526 (June 2012): 135–38. http://dx.doi.org/10.1016/j.jallcom.2012.02.073.

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8

Asato, Mitsuhiro, Chang Liu, Nobuhisa Fujima, Toshiharu Hoshino, Ying Chen, and Tetsuo Mohri. "Accuracy of Real Space Cluster Expansion for Total Energies of Pd-rich PdX (X=Rh, Ru) Alloys, based on Full-Potential KKR Calculations for Perfect and Impurity Systems." MATEC Web of Conferences 264 (2019): 03002. http://dx.doi.org/10.1051/matecconf/201926403002.

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We study the accuracy and convergence of the real space cluster expansion (RSCE) for the total energies of the Pd-rich PdX (X=Ru, Rh) alloys, which are used to study the phase stability and phase equilibria of the Pd-rich PdX alloys. In the present RSCE, the X atoms of minor element are treated as impurities in Pd. The n-body interaction energies (IEs) among X impurities in Pd, being used in the expansion of the total energies of the Pd-rich PdX alloys, are determined uniquely and successively from the low body to high body, by the full-potential Korringa-Kohn-Rostoker (FPKKR) Green's function method (FPKKR) for the perfect and impurity systems (Pd-host and Xn in Pd, n=1~4), combined with the generalized gradient approximation in the density functional theory. In the previous paper, we showed that the RSCE, in which the perturbed potentials due to the insertion of Xn impurities in Pd were redetermined self-consistently up to the first-nearest neighboring (nn) host atoms around Xn impurities, reproduce fairly well (the error of ~ 0.2mRy per atom) the FPKKR-band-calculation result of the ordered Pd3Rh alloy in L12 structure, but a little wrongly (the error of ~ 0.7mRy per atom) for the ordered Pd3Ru alloy in L12 structure. In the present paper, we show that this small RSCE error for the Pd3Ru alloy is corrected very well (from ~ 0.7mRy to ~ 0.1mRy per atom) by enlarging the self-consistent region for the perturbed potentials up to the 2nd-nn host atoms around Run impurities in Pd. We also clarify the correction for each value of the n-body (n=1~ 4) IEs.
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9

Asato, Mitsuhiro, and Toshiharu Hoshino. "Impurity-Impurity Interaction Energies in Cu, Ni, Ag, and Pd and Fundamental Features of Phase Diagrams of Binary Alloys and Solid Solubility Limit of Impurities: KKR-Green’s Function Method and Cluster Variation Method." Journal of the Japan Institute of Metals 63, no. 6 (1999): 676–84. http://dx.doi.org/10.2320/jinstmet1952.63.6_676.

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10

Schadler, G., R. C. Albers, A. M. Boring, and P. Weinberger. "The relativistic spin-polarized KKR-green's function - applications to the bandstructure of plutonium." Journal of Magnetism and Magnetic Materials 63-64 (January 1987): 655–57. http://dx.doi.org/10.1016/0304-8853(87)90695-0.

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11

Pendry, J. B., A. Prêtre, P. J. Rous, and Luis Martín-Moreno. "Causal-surface Green's function method." Surface Science 244, no. 1-2 (March 1991): 160–76. http://dx.doi.org/10.1016/0039-6028(91)90179-v.

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12

Pendry, J. B., A. Prêtre, P. J. Rous, and Luis Martín-Moreno. "Causal-surface Green's function method." Surface Science Letters 244, no. 1-2 (March 1991): A112—A113. http://dx.doi.org/10.1016/0167-2584(91)90743-b.

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13

MINÁR, J., and H. EBERT. "CALCULATION OF THE RESONANT MAGNETO-OPTICAL PROPERTIES OF TRANSITION METALS AND DISORDERED ALLOYS IN THE X-RAY REGIME." Surface Review and Letters 09, no. 02 (April 2002): 1179–83. http://dx.doi.org/10.1142/s0218625x02003482.

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A version of the Kubo formula is presented, which allows one to calculate the resonant magneto-optical properties in the X-ray regime for arbitrary materials. This is achieved by representing the underlying electronic structure in terms of the electronic Green's function. Calculating the Green's function within the framework of spin-polarized relativistic multiple scattering theory (SPR-KKR) in particular gives access to spin–orbit-induced resonant magneto-optical properties. Results obtained for the Faraday effect and for the magnetic dichroic part of the complex reflective index n at the K-edge of Co and L 2,3-edges of Fe are found in very good agreement with recent experimental findings. The relation of n with the local magnetic moment is discussed on the basis of the calculated results for the L 3-edges of Pt in fcc-Co x Pt 1-x disordered alloy.
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14

Barbieri, Renato, Pablo Andrés Muñoz R, and Roberto Dalledone Machado. "Modified Local Green's Function Method (MLGFM)." Engineering Analysis with Boundary Elements 22, no. 2 (September 1998): 141–51. http://dx.doi.org/10.1016/s0955-7997(97)00109-4.

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15

Barbieri, Renato, and Pablo Andrés Muñoz R. "Modified Local Green's Function Method (MLGFM)." Engineering Analysis with Boundary Elements 22, no. 2 (September 1998): 153–59. http://dx.doi.org/10.1016/s0955-7997(97)00110-0.

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16

Naumov, N. D. "Green's function method in classical electrodynamics." Soviet Physics Journal 34, no. 2 (February 1991): 155–59. http://dx.doi.org/10.1007/bf00940958.

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17

Ohori, M., and Y. Hisada. "Comparison of the Empirical Green's Spatial Derivative Method and Empirical Green's Function Method." Bulletin of the Seismological Society of America 101, no. 6 (December 1, 2011): 2872–86. http://dx.doi.org/10.1785/0120100114.

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18

Hong, Yuan, and Zhang Xiang-wei. "Method of Green's function of corrugated shells." Applied Mathematics and Mechanics 26, no. 7 (July 2005): 830–37. http://dx.doi.org/10.1007/bf02464231.

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19

Gao, Rouxing, Leung Tsang, Shurun Tan, and Tien-Hao Liao. "Band calculations using broadband Green’s functions and the KKR method with applications to magneto-optics and photonic crystals." Journal of the Optical Society of America B 37, no. 12 (November 24, 2020): 3896. http://dx.doi.org/10.1364/josab.400824.

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20

Suzuki, Y., W. Horiuchi, and D. Baye. "Green's Function Method for Strength Function in Three-Body Continuum." Progress of Theoretical Physics 123, no. 3 (March 1, 2010): 547–68. http://dx.doi.org/10.1143/ptp.123.547.

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21

NAKAYAMA, Junichi, and Yasuhiko TAMURA. "Method of Image Green's Function in Grating Theory." IEICE Transactions on Electronics E95-C, no. 1 (2012): 93–96. http://dx.doi.org/10.1587/transele.e95.c.93.

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22

Feng-Ming, Liu, Cai Hao, Liu Zheng-You, and Huang Nian-Ning. "Green's Function Method for Perturbed sine-Gordon Equation." Communications in Theoretical Physics 41, no. 6 (June 15, 2004): 907–10. http://dx.doi.org/10.1088/0253-6102/41/6/907.

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23

SUN, TingTing. "Green's function method in covariant density functional theory." SCIENTIA SINICA Physica, Mechanica & Astronomica 46, no. 1 (December 14, 2015): 012006. http://dx.doi.org/10.1360/sspma2015-00371.

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24

Yamashita, Jiro, and Seturo Asano. "Band structure of KCl by green's function method." International Journal of Quantum Chemistry 1, S1 (June 18, 2009): 611–14. http://dx.doi.org/10.1002/qua.560010663.

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25

Morimatsu, Osamu, and Koichi Yazaki. "A Green's function method for hadrons in nuclei." Progress in Particle and Nuclear Physics 33 (January 1994): 679–728. http://dx.doi.org/10.1016/0146-6410(94)90051-5.

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26

KUNIBA, ATSUO, and REIHO SAKAMOTO. "COMBINATORIAL BETHE ANSATZ AND GENERALIZED PERIODIC BOX-BALL SYSTEM." Reviews in Mathematical Physics 20, no. 05 (June 2008): 493–527. http://dx.doi.org/10.1142/s0129055x08003365.

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We reformulate the Kerov–Kirillov–Reshetikhin (KKR) map in the combinatorial Bethe ansatz from paths to rigged configurations by introducing local energy distribution in crystal base theory. Combined with an earlier result on the inverse map, it completes the crystal interpretation of the KKR bijection for [Formula: see text]. As an application, we solve an integrable cellular automaton, a higher spin generalization of the periodic box-ball system, by an inverse scattering method and obtain the solution of the initial value problem in terms of the ultradiscrete Riemann theta function.
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27

Ponomarenko, Nikolajs, Tatjana Solovjova, and Juris Grizans. "The Use of Kramers-Kronig Relations for Verification of Quality of Ferrite Magnetic Spectra." Electrical, Control and Communication Engineering 9, no. 1 (December 1, 2015): 30–35. http://dx.doi.org/10.1515/ecce-2015-0009.

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Abstract The complex initial permeability (CIP) as a function of frequency is one of the main properties of ferrites. This characteristic (CIP) is measured experimentally, therefore there can be found noisy, doubtful or incomplete parts of the spectrum. Thus there is a need for a method of evaluation of quality of CIP. In this article for evaluation of the quality of experimental CIP spectra of polycrystalline ferrite materials the KKR (Kramers-Kronig relations) are used. In order to apply KKR to experimentally measured data (i.e. data with finite limits) the method of transforming these integral relations into summation relations with finite limits is developed and described. This method can be used only for CIP given over the wide frequency rage, so that the imaginary part of CIP is fully presented. Using KKR with the help of CIP spectra model (based on the effects coming from polycrystal grain sizes and defects distribution) partly removes aforementioned limit. Thus with the help of the model we can also make CIP spectra reconstruction (in cases when CIP is noisy or incomplete) and CIP spectra decomposition.
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28

Bolten, Matthias, Alexander Thiess, Irad Yavneh, and Rudolf Zeller. "Preconditioning systems arising from the KKR Green function method using block-circulant matrices." Linear Algebra and its Applications 436, no. 2 (January 2012): 436–46. http://dx.doi.org/10.1016/j.laa.2011.05.019.

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29

NOZU, Atsushi, and Hitoshi MORIKAWA. "An Empirical Green's Function Method Considering Multiple Nonlinear Effects." Zisin (Journal of the Seismological Society of Japan. 2nd ser.) 55, no. 4 (2003): 361–74. http://dx.doi.org/10.4294/zisin1948.55.4_361.

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30

Daryan. "Probabilistic Empirical Green's Function Method in Ground Motion Simulation." American Journal of Engineering and Applied Sciences 2, no. 1 (January 1, 2009): 160–64. http://dx.doi.org/10.3844/ajeas.2009.160.164.

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31

Abdusalam. "Probabilistic Empirical Green's Function Method in Ground Motion Simulation." American Journal of Engineering and Applied Sciences 2, no. 1 (January 1, 2009): 160–64. http://dx.doi.org/10.3844/ajeassp.2009.160.164.

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32

Barbieri, Renato, and Roberto Dalledone Machado. "The Local Formulation for the Modified Green's Function Method." Latin American Journal of Solids and Structures 12, no. 5 (May 2015): 883–904. http://dx.doi.org/10.1590/1679-78251281.

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33

Melnikov, Yu A., and Ye A. Bobylov. "Green's function method solution of the Reissner's plate problem." Engineering Analysis with Boundary Elements 17, no. 4 (June 1996): 255–62. http://dx.doi.org/10.1016/s0955-7997(96)00021-5.

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34

Robert, Jean‐Luc, and Mathias Fink. "Green's function estimation in speckle using the FDORT method." Journal of the Acoustical Society of America 123, no. 5 (May 2008): 3185. http://dx.doi.org/10.1121/1.2933296.

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35

Kumagai-Fuse, I., and Y. Akaishi. "Pionic Decay of Hypernucleus 5 He: Green's Function Method." Progress of Theoretical Physics 92, no. 4 (October 1, 1994): 815–32. http://dx.doi.org/10.1143/ptp/92.4.815.

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36

Hori, Muneo. "Inverse analysis method using spectral decomposition of Green's function." Geophysical Journal International 147, no. 1 (October 2001): 77–87. http://dx.doi.org/10.1046/j.1365-246x.2001.00505.x.

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37

Torabian, A., and Y. L. Chow. "Simulated image method for Green's function of multilayer media." IEEE Transactions on Microwave Theory and Techniques 47, no. 9 (1999): 1777–81. http://dx.doi.org/10.1109/22.788512.

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38

Sadasivam, Sridhar, Yuhang Che, Zhen Huang, Liang Chen, Satish Kumar, and Timothy S. Fisher. "THE ATOMISTIC GREEN'S FUNCTION METHOD FOR INTERFACIAL PHONON TRANSPORT." Annual Review of Heat Transfer 17, N/A (2014): 89–145. http://dx.doi.org/10.1615/annualrevheattransfer.2014006986.

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39

Rozenbaum, V. M., I. V. Shapochkina, and L. I. Trakhtenberg. "Green's function method in the theory of Brownian motors." Physics-Uspekhi 62, no. 5 (May 31, 2019): 496–509. http://dx.doi.org/10.3367/ufne.2018.04.038347.

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40

Nooijen, Marcel, and Jaap G. Snijders. "Coupled cluster Green's function method: Working equations and applications." International Journal of Quantum Chemistry 48, no. 1 (October 5, 1993): 15–48. http://dx.doi.org/10.1002/qua.560480103.

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41

TRKOV, A., M. NAJŽER, and L. ŠKERGET. "Variant of Green's Function Nodal Method for Neutron Diffusion." Journal of Nuclear Science and Technology 27, no. 8 (August 1990): 766–77. http://dx.doi.org/10.1080/18811248.1990.9731251.

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42

Shi, Y., and C. H. Chan. "Improved 3D full-wave multilevel Green's function interpolation method." Electronics Letters 47, no. 3 (2011): 174. http://dx.doi.org/10.1049/el.2010.3109.

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43

Hao, Cai, and Huang Nian-Ning. "Green's Function Method for Perturbed Korteweg-de Vries Equation." Chinese Physics Letters 20, no. 4 (March 26, 2003): 469–72. http://dx.doi.org/10.1088/0256-307x/20/4/308.

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44

Hori, Muneo. "Inverse analysis method using spectral decomposition of Green's function." Geophysical Journal International 147, no. 1 (September 2001): 77–87. http://dx.doi.org/10.1111/j.1365-246x.2001.00505.x.

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45

Molinari, E., G. B. Bachelet, and M. Altarelli. "GREEN'S FUNCTION MATCHING METHOD FOR REALISTIC CALCULATIONS OF INTERFACES." Le Journal de Physique Colloques 46, no. C4 (April 1985): C4–321—C4–329. http://dx.doi.org/10.1051/jphyscol:1985435.

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46

Piva, Renzo, and Luigi Morino. "Vector green's function method for unsteady Navier-Stokes equations." Meccanica 22, no. 2 (June 1987): 76–85. http://dx.doi.org/10.1007/bf01556905.

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47

Shinn, J. L., J. W. Wilson, W. Schimmerling, M. R. Shavers, J. Miller, E. V. Benton, A. L. Frank, and F. F. Badavi. "A Green's function method for heavy ion beam transport." Radiation and Environmental Biophysics 34, no. 3 (August 1995): 155–59. http://dx.doi.org/10.1007/bf01211542.

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48

Mayfield, Jay, Yijin Gao, and Songting Luo. "An asymptotic Green's function method for the wave equation." Journal of Computational Physics 446 (December 2021): 110655. http://dx.doi.org/10.1016/j.jcp.2021.110655.

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49

Torabi, Abdorreza, Amir Ahmad Shishegar, and Reza Faraji-Dana. "An Efficient Closed-Form Derivation of Spatial Green's Function for Finite Dielectric Structures Using Characteristic Green's Function-Rational Function Fitting Method." IEEE Transactions on Antennas and Propagation 62, no. 3 (March 2014): 1282–92. http://dx.doi.org/10.1109/tap.2013.2295243.

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50

Brahim, Benali, Mohammed Tayeb Meftah, and Rai Vandana. "Green's Function for A Piecewise Continous Potential via Integral Equations Method." Journal of the Indonesian Mathematical Society 24, no. 2 (May 18, 2018): 20–35. http://dx.doi.org/10.22342/jims.24.2.387.20-35.

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The aim of this work is to provide Green's function for the Schrodingerequation. The potential part in the Hamiltonian is piecewise continuous operator.It is a zero operator on a disk of radius "a" and a constant V0 outside this disk (intwo dimensions). We have used, to construct the Green's function, the technique ofthe integral equations. We have respected the boundary conditions of the problem.The discrete spectra of the Hamiltonian operator have been also derived.
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