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Journal articles on the topic 'Hamiltonian Calculations'

Author: Grafiati

Published: 7 September 2023

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1

Rai, S., A. Biswas, and B. Mukherjee. "Nuclear structure of low-lying states in 60,62,64,66Zn — A shell model description." International Journal of Modern Physics E 25, no. 11 (November 2016): 1650099. http://dx.doi.org/10.1142/s0218301316500993.

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Shell model calculation has been performed for even–even [Formula: see text]Zn using NuShellX code in [Formula: see text] model space with two different effective Hamiltonians, viz. JUN45 and jj44b. The low-lying structure is studied up to angular momentum, [Formula: see text] = 10[Formula: see text] by calculating level energies, reduced transition probabilities, occupation numbers, lifetimes, and quadrupole moments. The results of the calculations are compared with the available experimental data. It is observed that the inclusion of 1[Formula: see text] orbital in the model space is essential to understand nuclear structure in these isotopes. Shell model calculation with an improved set of effective Hamiltonian parameters and inclusion of [Formula: see text] orbital in the model space are necessary in order to produce finer agreement with the experimental observations.

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2

Elyseeva, Julia. "The Oscillation Numbers and the Abramov Method of Spectral Counting for Linear Hamiltonian Systems." EPJ Web of Conferences 248 (2021): 01002. http://dx.doi.org/10.1051/epjconf/202124801002.

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In this paper we consider linear Hamiltonian differential systems which depend in general nonlinearly on the spectral parameter and with Dirichlet boundary conditions. For the Hamiltonian problems we do not assume any controllability and strict normality assumptions which guarantee that the classical eigenvalues of the problems are isolated. We also omit the Legendre condition for their Hamiltonians. We show that the Abramov method of spectral counting can be modified for the more general case of finite eigenvalues of the Hamiltonian problems and then the constructive ideas of the Abramov method can be used for stable calculations of the oscillation numbers and finite eigenvalues of the Hamiltonian problems.

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3

Coraggio, L., A. Covello, A. Gargano, and N. Itaco. "Core polarization and modern realistic shell-model Hamiltonians." International Journal of Modern Physics E 26, no. 01n02 (January 2017): 1740006. http://dx.doi.org/10.1142/s0218301317400067.

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The understanding of the convergence properties of the shell-model effective Hamiltonian, within the framework of the many-body perturbation theory, is a long-standing problem. The infinite summation of a certain class of diagrams, the so-called “bubble diagrams,” may be provided calculating the Kirson–Babu–Brown induced interaction, and provides a valid instrument to study whether or not the finite summation of the perturbative series is well-grounded. Here, we perform an application of the calculation of the Kirson–Babu–Brown induced interaction to derive the shell-model effective Hamiltonian for [Formula: see text]-shell nuclei starting from a modern nucleon–nucleon potential, obtained by way of the chiral perturbation theory. The outcome of our calculation is compared with a standard calculation of the shell-model Hamiltonian, where the core-polarization effects are calculated only up to third-order in perturbation theory. The results of the two calculations are very close to each other, evidencing that the perturbative approach to the derivation of the shell-model Hamiltonian is still a valid tool for nuclear structure studies.

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4

Polley, Kritanjan, and Roger F. Loring. "Two-dimensional vibronic spectroscopy with semiclassical thermofield dynamics." Journal of Chemical Physics 156, no. 12 (March 28, 2022): 124108. http://dx.doi.org/10.1063/5.0083868.

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Thermofield dynamics is an exactly correct formulation of quantum mechanics at finite temperature in which a wavefunction is governed by an effective temperature-dependent quantum Hamiltonian. The optimized mean trajectory (OMT) approximation allows the calculation of spectroscopic response functions from trajectories produced by the classical limit of a mapping Hamiltonian that includes physical nuclear degrees of freedom and other effective degrees of freedom representing discrete vibronic states. Here, we develop a thermofield OMT (TF-OMT) approach in which the OMT procedure is applied to a temperature-dependent classical Hamiltonian determined from the thermofield-transformed quantum mapping Hamiltonian. Initial conditions for bath nuclear degrees of freedom are sampled from a zero-temperature distribution. Calculations of two-dimensional electronic spectra and two-dimensional vibrational–electronic spectra are performed for models that include excitonically coupled electronic states. The TF-OMT calculations agree very closely with the corresponding OMT results, which, in turn, represent well benchmark calculations with the hierarchical equations of motion method.

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5

Tuszyński, J. A., and J. M. Dixon. "A Quantum Field Theoretical Analysis of Spin-Half Metamagnetism." International Journal of Modern Physics B 11, no. 12 (May 20, 1997): 1445–62. http://dx.doi.org/10.1142/s0217979297000733.

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A number of metallic compounds such as FeRh, Mn3GaC , and FeCl2 exhibit the interesting property of metamagnetism, i.e. the presence of order–order magnetic-phase transitions. The microscopic Hamiltonian that is commonly used to describe this class of system is of Heisenberg type with competing exchange interactions between the nearest- and next-nearest neighbours. Starting from this quantum Hamiltonian, through several transformations, it is possible to obtain an effective second-quantized Hamiltonian which has a two-body interaction term. A recent method of analyzing such Hamiltonians is then applied based on exact calculations for the corresponding nonlinear equation of motion. This is followed by quantization about the classical solutions. Stability conditions imposed on the classical solutions agree with earlier results.

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6

MARTIN, RICHARD M. "Derivation of Models for the Interacting Electrons in Cu-O Superconductors." International Journal of Modern Physics C 02, no. 01 (March 1991): 105–14. http://dx.doi.org/10.1142/s0129183191000111.

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Key questions for theory of high temperature superconductors involve the nature of the electronic system: the minimum essential Hamiltonian and the low energy states of such Hamiltonians. To attempt to answer these questions we are carrying out studies using constrained density functional (CDF) methods to identify the relevant electronic states and realistic values of the parameters, combined with exact calculations on the reduced model Hamiltonians. The CDF calculations lead to a 3-band Hubbard model for Cu-O planes with parameters in general agreement with high energy spectroscopies and low energy magnetic excitations. We describe a modified Lanczos method to carry out large many-body calculations and give a representative result, where we find the spectra are described by the 1-band Hubbard model in regimes which imply spin interactions beyond the usual Heisenberg form.

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7

Seke, J., A. V. Soldatov, and N. N. Bogolubov. "Novel Technique for Quantum-Mechanical Eigenstate and Eigenvalue Calculations based on Seke's Self-Consistent Projection-Operator Method." Modern Physics Letters B 11, no. 06 (March 10, 1997): 245–58. http://dx.doi.org/10.1142/s0217984997000311.

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Seke's self-consistent projection-operator method has been developed for deriving non-Markovian equations of motion for probability amplitudes of a relevant set of state vectors. This method, in a Born-like approximation, leads automatically to an Hamiltonian restricted to a subspace and thus enables the construction of effective Hamiltonians. In the present paper, in order to explain the efficiency of Seke's method in particular applications, its algebraic operator structure is analyzed and a new successive approximation technique for the calculation of eigenstates and eigenvalues of an arbitrary quantum-mechanical system is developed. Unlike most perturbative techniques, in the present case each order of the approximation determines its own effective (approximating) Hamiltonian ensuring self-consistency and formal exactness of all results in the corresponding approximation order.

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8

Li, Yanting, Gediminas Gaigalas, Wenxian Li, Chongyang Chen, and Per Jönsson. "Fine-Tuning of Atomic Energies in Relativistic Multiconfiguration Calculations." Atoms 11, no. 4 (April 8, 2023): 70. http://dx.doi.org/10.3390/atoms11040070.

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Ab initio calculations sometimes do not reproduce the experimentally observed energy separations at a high enough accuracy. Fine-tuning of diagonal elements of the Hamiltonian matrix is a process which seeks to ensure that calculated energy separations of the states that mix are in agreement with experiment. The process gives more accurate measures of the mixing than can be obtained in ab initio calculations. Fine-tuning requires the Hamiltonian matrix to be diagonally dominant, which is generally not the case for calculations based on jj-coupled configuration state functions. We show that this problem can be circumvented by a method that transforms the Hamiltonian in jj-coupling to a Hamiltonian in LSJ-coupling for which fine-tuning applies. The fine-tuned matrix is then transformed back to a Hamiltonian in jj-coupling. The implementation of the method into the General Relativistic Atomic Structure Package is described and test runs to validate the program operations are reported. The new method is applied to the computation of the 2s21S0−2s2p1,3P1 transitions in C III and to the computation of Rydberg transitions in B I, for which the 2s2p22S1/2 perturber enters the 2s2ns2S1/2 series. Improved convergence patterns and results are found compared with ab initio calculations.

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9

S. Almeida, Nuno M., Timothé R. L. Melin, Sasha C. North, Bradley K. Welch, and Angela K. Wilson. "Ab initio composite strategies and multireference approaches for lanthanide sulfides and selenides." Journal of Chemical Physics 157, no. 2 (July 14, 2022): 024105. http://dx.doi.org/10.1063/5.0094367.

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The f-block ab initio correlation consistent composite approach was used to predict the dissociation energies of lanthanide sulfides and selenides. Geometry optimizations were carried out using density functional theory and coupled cluster singles, doubles, and perturbative triples with one- and two-component Hamiltonians. For the two-component calculations, relativistic effects were accounted for by utilizing a third-order Douglas–Kroll–Hess Hamiltonian. Spin–orbit coupling was addressed with the Breit–Pauli Hamiltonian within a multireference configuration interaction approach. The state averaged complete active space self-consistent field wavefunctions obtained for the spin–orbit coupling energies were used to assign the ground states of diatomics, and several diagnostics were used to ascertain the multireference character of the molecules.

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10

Xia, Rongxin, Teng Bian, and Sabre Kais. "Electronic Structure Calculations and the Ising Hamiltonian." Journal of Physical Chemistry B 122, no. 13 (November 3, 2017): 3384–95. http://dx.doi.org/10.1021/acs.jpcb.7b10371.

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Rashev, Svetoslav, Isak Bivas, and David C. Moule. "Large scale vibrational Hamiltonian calculations on thiophosgene." Chemical Physics Letters 438, no. 4-6 (April 2007): 153–56. http://dx.doi.org/10.1016/j.cplett.2007.02.067.

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12

Banerjee, J. R., A. J. Sobey, H. Su, and J. P. Fitch. "Use of computer algebra in Hamiltonian calculations." Advances in Engineering Software 39, no. 6 (June 2008): 521–25. http://dx.doi.org/10.1016/j.advengsoft.2007.03.013.

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13

Aroca, J. M., and H. Fort. "Hamiltonian loop calculations for 2 + 1 QED." Physics Letters B 317, no. 4 (November 1993): 604–8. http://dx.doi.org/10.1016/0370-2693(93)91379-2.

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14

Wang, Cai-Zhuang, Wen-Cai Lu, Yong-Xin Yao, Ju Li, Sidney Yip, and Kai-Ming Ho. "Tight-binding Hamiltonian from first-principles calculations." Scientific Modeling and Simulation SMNS 15, no. 1-3 (April 2008): 81–95. http://dx.doi.org/10.1007/s10820-008-9108-y.

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15

Lam, Yi Hua, and Nadezda A. Smirnova. "Isospin Non-Conservation in Shell Model Approach and Applications*." EPJ Web of Conferences 178 (2018): 05006. http://dx.doi.org/10.1051/epjconf/201817805006.

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Up to now, empirical shell-model Hamiltonians for valence space calculations provide the most accurate description of the low-energy spectra and individual transitions of sd- and pf-shell nuclei. These features made them of particular importance for the description of the isospin-symmetry-breaking phenomena, such as energy splitting of the isobaric multiplets or isospin-forbidden transition rates. In this contribution, we demonstrate the applications of a recently constructed isospin non-conserving (INC) Hamiltonian in sd shell [Lam et al. Phys. Rev. C 87, 054304 (2013)]. First, we explore the partial decay scheme of 24Si and discuss the states affected by the Thomas-Ehrman shift. Second, we show the accuracy of the INC Hamiltonian for the description of the mirror energy differences.

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16

Michalski, Rafal, and Ryszard J. Radwanski. "Computer Calculations of the Thermally-Induced Magnetic and Electronic Properties of the Rare Earth Compounds RERu₂Si₂." Materials Science Forum 480-481 (March 2005): 617–22. http://dx.doi.org/10.4028/www.scientific.net/msf.480-481.617.

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The aim of this paper is to demonstrate the effectiveness of the calculation method, which takes into consideration the electrostatic ligands field as well as the the magnetic interactions. Our calculations method based on crystal field (CEF) together with the Zeeman effect in one Hamiltonian and allows calculating many of the temperature dependencies of the magnetic and electronic properties of the rare earth compounds. The result of the calculations shows the accuracy of the approach even for the intermetallic compounds. The obtained results for calculations of the compounds of the family in RERu2Si2 (RE – rare-earth element) are fully confirmed the experimental data such as: the easy magnetic direction of all the analyzed compounds, the thermal dependencies of magnetic properties; in particular the giant magnetocrystalline anisotropy of PrRu2S2 with the calculated anisotropy field BA>400T, in-plain anisotropy of ErRu2Si2, the cause of difficulty in magnetic ordering of compounds TmRu2Si2 and YbRu2Si2 as well as effects and dependencies not foreseen before. In this paper we have put together the elementary calculated magnetic properties for the chosen compounds of RERu2Si2 in the paramagnetic region. All Calculations are on the basis of the calculating computer package BIREC 1.51.

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17

Vasileiou, Polytimos, Theo J. Mertzimekis, Eirene Mavrommatis, and Aikaterini Zyriliou. "Nuclear Structure Investigations of Even–Even Hf Isotopes." Symmetry 15, no. 1 (January 9, 2023): 196. http://dx.doi.org/10.3390/sym15010196.

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The mass region of rare-earth nuclei in the nuclear chart is riddled with well-deformed nuclei, exhibiting rotational properties and many interesting nuclear structure-related phenomena. The scarcity of experimental data as the neutron number increases and the exotic phenomena such as shape coexistence, which are strongly connected with the underlying symmetries of the Hamiltonian and are predicted to take place in this region, make this mass region a fertile ground for experimental and theoretical studies of nuclear structure. In this work, we investigate the structure of the even–even 162–184Hf (hafnium) isotopes through a calculation of various observables such as B(E2;01+→21+) reduced transition matrix elements and quadrupole moments. Six different nuclear models are employed in the calculations of the observables for these nuclei, the shapes of which deviate from spherical symmetry, and as such, are characterized by Hamiltonians, which break the rotational invariance of the exact nuclear many-body Hamiltonian. The results of the present study are expected to establish some concrete guidelines for current and future experimental endeavors. Along these lines, the results for the 162–180Hf isotopes are compared with existing experimental data where available, showing an overall good agreement.

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18

Carlson, J., V. R. Pandharipande, and R. Schiavilla. "Variational Monte Carlo calculations ofH3andHe4with a relativistic Hamiltonian." Physical Review C 47, no. 2 (February 1, 1993): 484–97. http://dx.doi.org/10.1103/physrevc.47.484.

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19

Semay, Claude. "Fourier grid Hamiltonian method and Lagrange-mesh calculations." Physical Review E 62, no. 6 (December 1, 2000): 8777–81. http://dx.doi.org/10.1103/physreve.62.8777.

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20

Forest, J. L., V. R. Pandharipande, J. Carlson, and R. Schiavilla. "Variational Monte Carlo calculations ofH3andHe4with a relativistic Hamiltonian." Physical Review C 52, no. 2 (August 1, 1995): 576–77. http://dx.doi.org/10.1103/physrevc.52.576.

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21

Baretty, Reinaldo, and Carmelo Garcia. "Modified breit-pauli hamiltonian suitable for variational calculations." International Journal of Quantum Chemistry 34, S22 (March 12, 1988): 425–30. http://dx.doi.org/10.1002/qua.560340845.

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22

Olszewski, S., T. Roliński, M. Baszczak, and R. Kozak. "Phase-space Symmetry and the Action Function of the Pendulum Problem." Zeitschrift für Naturforschung A 57, no. 11 (November 1, 2002): 888–96. http://dx.doi.org/10.1515/zna-2002-1108.

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An approach to the pendulum problem, which is an alternative to the well-known traditional treatment of that problem, has been formulated. An advantage of the new approach is provided by a full symmetry in the position and momentum variables of the Hamiltonian expression for the energy of the system. A similar symmetry holds for the Hamilton equations describing the motion of a pendulum-like point mass. Calculations of the action function forthe two kinds of pendulum Hamiltonians - the traditional one and the new one - are presented.

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23

Wang, F., and EI von Nagy-Felsobuki. "Ab Initio Ro-Vibrational Structure of the C2? Isotopes of H2O+." Australian Journal of Physics 45, no. 5 (1992): 651. http://dx.doi.org/10.1071/ph920651.

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The ro-vibrational structures of the C2" isotopes ofH20+ have been calculated from variational solution of the normal coordinate Eckart-Watson Hamiltonian. The calculations use the discrete ab initio potential energy surface of Weis et al. (1989). Where comparisons can be made, the assignment of the vibrational states is in excellent agreement with experiment and with the ab initio variational calculation of Weis et al., who utilised a different force field and an internal coordinate nuclear Hamiltonian (instead of the Eckart-Watson amiltonian). Furthermore, the calculated rotational levels of the ground and the first excited vibrational states of H20+ and D20+ are in excellent agreement with experiment.

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24

Taqi, Ali H., R. A. Radhi, and Adil M. Hussein. "Low excitations of 16O using generalized density matrix random phase approximation GDRPA." International Journal of Modern Physics E 23, no. 08 (August 2014): 1450038. http://dx.doi.org/10.1142/s0218301314500384.

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The random phase approximation (RPA) equations based on the generalized density matrix (GDM), the so-called GDRPA are reformulated in a more compact matrix form, which renders the method especially suitable for realistic nuclear structure calculations. The GDRPA Hamiltonian is expressed in terms of the one-body particle–particle (pp) and hole–hole (hh) density matrices, and the nuclear force contributes not only in the particle–hole (ph) channel, as in normal ph-RPA, but also in the pp and hh channels. The Hamiltonian is diagonalized iteratively starting from initial guess values and the iterating process is carried out until self-consistency is achieved. The calculation in the model space 1p, 1d and 2s using Warburton and Brown interaction WBP is performed for 16 O . The GDRPA in the ph shell model calculations is tested, by comparing the energy eigenvalues and the electron scattering form factors with the results of the normal RPA and with the available experimental data.

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25

Medina-Dozal, Luis, Irán Ramos-Prieto, and José Récamier. "Approximate Evolution for A Hybrid System—An Optomechanical Jaynes-Cummings Model." Entropy 22, no. 12 (December 5, 2020): 1373. http://dx.doi.org/10.3390/e22121373.

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In this work, we start from a phenomenological Hamiltonian built from two known systems: the Hamiltonian of a pumped optomechanical system and the Jaynes-Cummings Hamiltonian. Using algebraic techniques we construct an approximate time evolution operator U^(t) for the forced optomechanical system (as a product of exponentials) and take the JC Hamiltonian as an interaction. We transform the later with U^(t) to obtain a generalized interaction picture Hamiltonian which can be linearized and whose time evolution operator is written in a product form. The analytic results are compared with purely numerical calculations using the full Hamiltonian and the agreement between them is remarkable.

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26

Chávez, Matías, Thomas Wiegand, Alexander A. Malär, Beat H. Meier, and Matthias Ernst. "Residual dipolar line width in magic-angle spinning proton solid-state NMR." Magnetic Resonance 2, no. 1 (July 1, 2021): 499–509. http://dx.doi.org/10.5194/mr-2-499-2021.

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Abstract. Magic-angle spinning is routinely used to average anisotropic interactions in solid-state nuclear magnetic resonance (NMR). Due to the fact that the homonuclear dipolar Hamiltonian of a strongly coupled spin system does not commute with itself at different time points during the rotation, second-order and higher-order terms lead to a residual dipolar line broadening in the observed resonances. Additional truncation of the residual broadening due to isotropic chemical-shift differences can be observed. We analyze the residual line broadening in coupled proton spin systems based on theoretical calculations of effective Hamiltonians up to third order using Floquet theory and compare these results to numerically obtained effective Hamiltonians in small spin systems. We show that at spinning frequencies beyond 75 kHz, second-order terms dominate the residual line width, leading to a 1/ωr dependence of the second moment which we use to characterize the line width. However, chemical-shift truncation leads to a partial ωr-2 dependence of the line width which looks as if third-order effective Hamiltonian terms are contributing significantly. At slower spinning frequencies, cross terms between the chemical shift and the dipolar coupling can contribute in third-order effective Hamiltonians. We show that second-order contributions not only broaden the line, but also lead to a shift of the center of gravity of the line. Experimental data reveal such spinning-frequency-dependent line shifts in proton spectra in model substances that can be explained by line shifts induced by the second-order dipolar Hamiltonian.

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27

Морозов, С. В., and М. С. Жолудев. "Применение метода матрицы рассеяния для расчета примесных состояний в полупроводниковых структурах." Письма в журнал технической физики 47, no. 7 (2021): 26. http://dx.doi.org/10.21883/pjtf.2021.07.50795.18663.

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We adapted S-matrix method for calculation of energy levels and carrier wavefunctions near impurity/defect states. We demonstrate the possibility of implying this method for multiband models on the example of Luttinger Hamiltonian with Coulomb acceptor in the spherical symmetry approximation. The obtained energies of discrete levels are in well agreement with results of calculations performed by other methods.

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Türkan, Nurettin, Davut Olgun, and Ýhsan Uluer. "IBM-2 calculations of some even-even selenium nuclei." Open Physics 4, no. 1 (March 1, 2006): 124–54. http://dx.doi.org/10.1007/s11534-005-0011-9.

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AbstractIn this study, we determined the most appropriate Hamiltonian that is needed for present calculations of nuclei in the A≅ 80 region by the view of interacting boson model (IBM-2). Using the best-fitted values of parameters in the Hamiltonian, we have calculated energy levels and B(E2) values for a number of transitions in some doubly even Se nuclei. The results were compared with the previous experimental and theoretical data and it is observed that they are in good agreement. The calculations have been extended to Se isotopes with A < 76 for which some B(E2) values are still not known.

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29

Sokolovsky, A. I. "Realization of the Landau definitions of effective Hamiltonian and nonequilibrium free energy in microscopic theory." Journal of Physics and Electronics 28, no. 2 (December 9, 2020): 63–74. http://dx.doi.org/10.15421/332022.

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Equilibrium fluctuations of some set of parameters in the states described by the canonical Gibbs distribution are investigated. In the theory of phase transitions of the second kind, these parameters are components of the order parameter. The microscopic realization of the Landau definition of the effective Hamiltonian of the system for studying the equilibrium fluctuations of the specified system of parameters is discussed in the terms of the probability density of their values. A general formula for this function is obtained and it is expressed through the equilibrium correlation functions of these parameters. An expression for the effective Hamiltonian in terms of deviations of the parameters from their equilibrium values is obtained. The deviations are considered small for conducting the calculations. The possibility of calculating the exact free energy of the system using the found effective Hamiltonian is discussed. In the microscopic theory, the implementation of the Landau definition of nonequilibrium thermodynamic potentials introduced in his phenomenological theory of phase transitions of the second kind is investigated. Nonequilibrium states of a fluctuating system described with some sets of parameters are considered. A general formula for nonequilibrium free energy expressed through the correlation functions of these parameters is obtained as for the effective Hamiltonian above. Like the previous case, the free energy expression via parameter deviations from the equilibrium values is obtained and small deviations are considered for calculations. The idea of the identity of the effective Hamiltonian of the system and its nonequilibrium free energy is discussed in connection with the Boltzmann distribution. The Gaussian approximation of both developed formalisms is considered. A generalization of the constructed theory for the case of spatially inhomogeneous states and the study of long-wave fluctuations are developed.

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30

Gilleron, Franck, and Jean-Christophe Pain. "A global approach to perform large-scale configuration–interaction calculations." Canadian Journal of Physics 95, no. 9 (September 2017): 878–83. http://dx.doi.org/10.1139/cjp-2016-0886.

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We present a global approach that allows one to tackle cumbersome configuration–interaction calculations. The method is based on the use of approximate configuration-averaged Hamiltonian matrix elements that can be expressed in compact form as a combination of Slater integrals. With some assumptions, we show that the Hamiltonian matrix to be diagonalized may be reduced to a size equivalent to the number of configurations in the basis set. The approach can be used to estimate shifts of configuration average energies and changes in the total strength of transition arrays. The method is also well suited to work out roughly difficult configuration–interaction calculations, to determine the minimal set of interacting configurations to be used in actual fine-structure calculations.

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31

Shova, Sergiu, Angelica Vlad, Maria Cazacu, J. Krzystek, Lukas Bucinsky, Martin Breza, Denisa Darvasiová, et al. "A five-coordinate manganese(iii) complex of a salen type ligand with a positive axial anisotropy parameter D." Dalton Transactions 46, no. 35 (2017): 11817–29. http://dx.doi.org/10.1039/c7dt01809f.

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32

Rivero, P., I. de Pr Moreira, and F. Illas. "Spin Hamiltonian effective parameters from periodic electronic structure calculations." Journal of Physics: Conference Series 117 (June 1, 2008): 012025. http://dx.doi.org/10.1088/1742-6596/117/1/012025.

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33

Yung, C. M., C. R. Allton, and C. J. Hamer. "Hamiltonian Monte Carlo calculations on (2+1)-dimensional QED." Physical Review D 39, no. 12 (June 15, 1989): 3778–84. http://dx.doi.org/10.1103/physrevd.39.3778.

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34

Patkos, A., and P. Rujan. "Basis vector importance sampling for Hamiltonian lattice spectrum calculations." Journal of Physics A: Mathematical and General 18, no. 10 (July 11, 1985): 1765–79. http://dx.doi.org/10.1088/0305-4470/18/10/029.

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35

Katsuki, S., and S. Huzinaga. "An effective hamiltonian method for valence-electron molecular calculations." Chemical Physics Letters 152, no. 2-3 (November 1988): 203–6. http://dx.doi.org/10.1016/0009-2614(88)87355-x.

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36

TAO, R. B., X. HU, and M. SUZUKI. "DISCUSSION ON THE MEAN FIELD APPROXIMATION IN THE RVB THEORY." Modern Physics Letters B 02, no. 10 (November 1988): 1205–9. http://dx.doi.org/10.1142/s0217984988001144.

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Baskaran’s mean field approximation of the Hubbard Hamiltonian with strong correlation and half-filling is discussed. Our calculations show that his decoupling of the Hamiltonian is not permissible in the half-filling case and that it destroys the equivalence of the Hubbard model to the Heisenberg magnetic system and violates some spin-spin relations.

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37

Sen, Rupam, Ashim Kalyan, and Ramendu Bhattacharjee. "A study of the stretching vibrational spectroscopy of C120O and C120O2 by u(2) lie algebra." Journal of the Serbian Chemical Society 78, no. 1 (2013): 85–92. http://dx.doi.org/10.2298/jsc120131074s.

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The vibrational energy levels of endohedral fullerene dimers C120O and C120O2 are calculated considering the local Hamiltonian of Morse potential using the algebra. Here each bond of the molecules is replaced by a corresponding Lie algebra and finally the Hamiltonian is constructed considering the interacting Casimir and Majorana operators. The fundamental stretching modes of vibration of both the dimmers C120O and C120O2 are then calculated using this Hamiltonian to compare the results of functional-based tight-binding (DF-TB) calculations.

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38

Pingak, Redi Kristian, Rosara Kolmate, and Bernandus Bernandus. "A Simple Matrix Approach to Determination of the Helium Atom Energies." Jurnal Penelitian Fisika dan Aplikasinya (JPFA) 9, no. 1 (June 30, 2019): 10. http://dx.doi.org/10.26740/jpfa.v9n1.p10-21.

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Calculation of He atomic energy levels using the first order perturbation theory taught in the Basic Quantum Mechanics course has led to relatively large errors. To improve its accuracy, several methods have been developed but most of them are too complicated to be understood by undergraduate students. The purposes of this study are to apply a simple matrix method in calculating some of the lowest energy levels of He atom (1s2, triplet 1s2s, and singlet 1s2s states) and to reduce errors obtained from calculations using the standard perturbation theory. The convergence of solutions as a function of the number of bases is also examined. The calculation is done analytically for 3 bases and computationally with the number of bases using MATHEMATICA. First, the 2-electron wave function of the Helium atom is written as the multiplication of two He+ ion wave functions, which are then expanded into finite dimension bases. These bases are used to calculate the elements of the Hamiltonian matrix, which are then substituted back to the energy eigenvalue equation to determine the energy values of the system. Based on the calculation results, the error obtained for the He ground state energy using 3 bases is 2.51 %, smaller than the errors of the standard perturbation theory (5.28 %). Despite the fact that the error is still relatively large from the analytical calculations for singlet-triplet 1s2s energy splitting of He atom, this error is successfully reduced significantly as more bases were used in the numerical calculations. In particular, for n = 25, the current calculation error for all states is much smaller than the errors obtained from calculations using standard perturbation theory. In conclusion, the analytical calculations for the energy eigenvalue equation for the 3 lowest states of the Helium atom using 3 bases have been carried out. It was also found in this study that increasing the number of bases in our numerical calculations has significantly reduced the errors obtained from the analytical calculations.

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39

Singh, Jagjit, Sunny Aggarwal, A. K. Singh, and Man Mohan. "Breit–Pauli atomic structure calculations for sulphur-like titanium." Canadian Journal of Physics 90, no. 9 (September 2012): 833–47. http://dx.doi.org/10.1139/p2012-074.

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Configuration interaction calculation has been performed for excitation energies, oscillator strengths, and transition probabilities of 114 fine-structure levels of sulphur-like titanium. The relativistic effects are included in Breit–Pauli approximation by adding mass-correction, Darwin, and spin–orbit interaction terms to the nonrelativistic Hamiltonian. We have adjusted the diagonal elements of Hamiltonian matrices (fine-tuning) before the calculation of oscillator strength and transition probabilities for the electric dipole allowed transitions. Our calculated data are in close agreement with data listed in National Institute of Standards and Technology and other available results. Correct identification of some of the levels become very difficult because of strong mixing among several fine-structure levels. We predict new energy levels, oscillator strength, and transition probability data, where no other theoretical or experimental results are available, which will form the basis for future experimental work.

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40

HORN, D. "THE t-EXPANSION AND HAMILTONIAN LATTICE QCD." International Journal of Modern Physics A 04, no. 09 (May 20, 1989): 2147–72. http://dx.doi.org/10.1142/s0217751x89000856.

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The t-expansion is a tool designed to improve on any variational calculation of a quantum theory. It is designed to produce the correct volume behavior of operators appearing in lattice models. We review its formulation and discuss the techniques used for its analysis by testing it on the solvable Heisenberg model in 1+1 dimensions. We discuss its application to the SU(3) lattice gauge theory in 3+1 space-time dimensions. Starting with strong coupling wave functions we investigate the pure glue sector. We review the calculations of the energy-density, the string-tension and several glueball masses. The scalar 0++ glueball follows from the same calculation as the energy-density. The other glueballs which. we study, with the JPC quantum numbers of 1+−, 0−−, 1−− and 2−− are constructed by using wave-functions corresponding to appropriate representations of the cubic symmetry group. Estimates of their physical masses, as obtained from studies of scaling ratios, are presented and discussed. It is quite straightforward to incorporate dynamical quarks in the model. We point out some qualitative features of the structure of the vacuum and the phase transition at high baryon density. Spectra of hadrons including quarks have not yet been calculated with these techniques but the glueball results indicate that this is a viable analytic method for the study of lattice QCD.

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BYLANDER, D. M., and LEONARD KLEINMAN. "THE OPTIMIZED EFFECTIVE POTENTIAL FOR ATOMS AND SEMICONDUCTORS." International Journal of Modern Physics B 10, no. 04 (February 15, 1996): 399–425. http://dx.doi.org/10.1142/s0217979296000167.

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Given an n-electron Hamiltonian containing a potential operator such as the Fock operator, the optimized effective potential (OEP) is that simple multiplicative potential whose n lowest eigenfunctions minimize the expectation value of the Hamiltonian. Thus it is the exact Kohn-Sham potential for that Hamiltonian. We discuss OEP calculations and the KLI approximation to it for atoms and semiconductors. Because the Fock operator treats exchange exactly, all deviations from experimental energies are attributable to the use of approximate correlation energy density functionals whose shortcomings are discussed.

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42

Batagin-Neto, Augusto, Erika Soares Bronze-Uhle, and Carlos Frederico de Oliveira Graeff. "Electronic structure calculations of ESR parameters of melanin units." Physical Chemistry Chemical Physics 17, no. 11 (2015): 7264–74. http://dx.doi.org/10.1039/c4cp05256k.

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Electronic structure calculations were employed to evaluate spin hamiltonian parameters of distinct monomers and dimers of melanin. The results bring valuable insights regarding the nature of the sub-structures responsible for the intrinsic paramagnetism observed in this biomaterial and their roles in electrical conductivity.

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43

BARTON, GABRIEL. "VAN DER WAALS FRICTION: A HAMILTONIAN TEST-BED." International Journal of Modern Physics: Conference Series 14 (January 2012): 16–26. http://dx.doi.org/10.1142/s2010194512007209.

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In the van der Waals regime (neglecting relativity and retardation), we find the power P generated by friction between two Drude-modelled dissipative half-spaces, at fixed separation and relative speed u, admitting only low u and low temperatures. This requires only elementary quantum mechanics; but the results can serve as partial checks on calculations in the fully retarded Casimir regime. They also raise questions regarding (i) the frequency-distribution of P; (ii) the status of predictions about Casimir forces generally, insofar as they feature parameters like conductivities with their empirical temperature-dependence; and (iii) calculations of heat transfer, insofar as they assume fluctuations in the two bodies to be uncorrelated.

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44

BARTON, GABRIEL. "VAN DER WAALS FRICTION: A HAMILTONIAN TEST-BED." International Journal of Modern Physics A 27, no. 15 (June 14, 2012): 1260002. http://dx.doi.org/10.1142/s0217751x12600020.

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In the van der Waals regime (neglecting relativity and retardation), we find the power P generated by friction between two Drude-modelled dissipative half-spaces, at fixed separation and relative speed u, admitting only low u and low temperatures. This requires only elementary quantum mechanics; but the results can serve as partial checks on calculations in the fully retarded Casimir regime. They also raise questions regarding (i) the frequency-distribution of P; (ii) the status of predictions about Casimir forces generally, insofar as they feature parameters like conductivities with their empirical temperature-dependence; and (iii) calculations of heat transfer, insofar as they assume fluctuations in the two bodies to be uncorrelated.

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45

FENG, WEN-LIN, and WEN-CHEN ZHENG. "INVESTIGATION OF THE DEFECT STRUCTURE, OPTICAL AND EPR SPECTRA FOR CdS: Ti2+ AND CdSe: Ti2+ CRYSTAL." International Journal of Modern Physics B 23, no. 27 (October 30, 2009): 5325–31. http://dx.doi.org/10.1142/s0217979209053503.

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The optical spectral band positions and spin-Hamiltonian parameters (g factors g‖, g⊥ and zero-field splitting D) of CdS : Ti 2+ and CdSe : Ti 2+ crystals are calculated from the complete diagonalizaion (of energy matrix) method based on a two-spin-orbit parameter model for 3d2 ions in trigonal symmetry. In the model, both the contribution to spin-Hamiltonian parameters due to the spin-orbit parameter of central 3d2 ions and that of ligand ions are included. The crystal field parameters used in the calculations are obtained from the superposition model which enables correlation of the optical and EPR spectral data with the defect structure of the studied paramagnetic impurity centers in crystals. From the calculations, the defect structures of Ti 2+ centers in CdS : Ti 2+ and CdSe : Ti 2+ are acquired, the signs of zero-field splittings D are suggested, and the optical band positions and spin-Hamiltonian parameters are explained. The results are discussed.

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46

Jiménez-Mejía, Raúl E., Rodrigo Acuna Herrera, and Pedro Torres. "Analysis of Spatially Doped Fused Silica Fiber Optic by Means of a Hamiltonian Formulation of the Helmholtz Equation." Advances in Materials Science and Engineering 2018 (2018): 1–11. http://dx.doi.org/10.1155/2018/5806947.

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This paper discusses an alternative method for calculating modal parameters in optical fibers such as propagation constants, transverse distributions, and anisotropy, due to linear and nonlinear phenomena acting as perturbations caused by doped silica regions. This method is based on a Hamiltonian formulation of the Helmholtz equation and the stationary perturbation theory, which allows a full-vectorial description of the electric field components when linear anisotropic inhomogeneities and Kerr nonlinearity are included. Linear and nonlinear parameters can be found for each propagating mode, and its accuracy has been successfully tested when compared to numerical calculations from the vector finite element method, and the results are published in the literature. This method facilitates the calculation of the spatial-distributed perturbation effects on individual electric field components for each propagating mode.

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47

BRACKEN, PAUL. "DIAGONALIZATION OF A HAMILTONIAN DESCRIBING A SINGLE TWO-LEVEL ATOM INTERACTING WITH A TWO MODE AMPLIFIER." International Journal of Modern Physics B 21, no. 02 (January 20, 2007): 211–20. http://dx.doi.org/10.1142/s0217979207035960.

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A Hamiltonian which describes the interaction of a single atom with two photon modes is introduced. It is shown that the Hamiltonian can be diagonalized in a particular basis. The energies and an eigenvector basis set are obtained. Some quasi-probability densities are calculated using amplitudes determined with respect to the rotated basis. Some of the physical phenomena which are manifested in the calculations are discussed.

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48

Nejad, Arman, and Deborah L. Crittenden. "On the separability of large-amplitude motions in anharmonic frequency calculations." Physical Chemistry Chemical Physics 22, no. 36 (2020): 20588–601. http://dx.doi.org/10.1039/d0cp03515g.

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Nuclear vibrational theories based upon the Watson Hamiltonian are ubiquitous in quantum chemistry, but cannot model molecules with delocalised large-amplitude vibrations. Dropping these is an efficient and effective way of circumventing the problem.

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49

Mead, Lawrence R., Sungwook Lee, and David Garfinkle. "A non-trivial PT-symmetric continuum Hamiltonian and its eigenstates and eigenvalues." Journal of Mathematical Physics 63, no. 7 (July 1, 2022): 072104. http://dx.doi.org/10.1063/5.0096250.

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In this paper, a non-trivial system governed by a continuum PT-symmetric Hamiltonian is discussed. We show that this Hamiltonian is iso-spectral to the simple harmonic oscillator. We find its eigenfunctions and the path in the complex plane along which these functions form an orthonormal set. We also find the hidden symmetry operator, [Formula: see text], for this system. All calculations are performed analytically and without approximation.

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50

Larsson, Jonas. "A new Hamiltonian formulation for fluids and plasmas. Part 3. Multifluid electrodynamics." Journal of Plasma Physics 55, no. 2 (April 1996): 279–300. http://dx.doi.org/10.1017/s0022377800018833.

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The Hamiltonian structure underlying ideal multifluid electrodynamics is formulated in a way that simplifies Hamiltonian perturbation calculations. We consider linear and lowest-order nonlinear theory, and the results in Part 1 of this series of papers are generalized in a satisfactory way. Thus the Hermitian structure of linearized dynamics is derived, and we obtain the coupling coefficients for resonant three-wave interaction in symmetric form, giving the Manley–Rowe relations.

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