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Journal articles on the topic 'Coulomb operator'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Frei, B. J., S. Ernst, and P. Ricci. "Numerical implementation of the improved Sugama collision operator using a moment approach." Physics of Plasmas 29, no. 9 (September 2022): 093902. http://dx.doi.org/10.1063/5.0091244.

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The numerical implementation of the linearized gyrokinetic and drift-kinetic improved Sugama (IS) collision operators, recently introduced by Sugama et al. [Phys. Plasmas 26, 102108 (2019)], is reported. The IS collision operator extends the validity of the widely used original Sugama (OS) operator [Sugama et al., Phys. Plasmas 16, 112503 (2009)] to the Pfirsch–Schlüter collisionality regime. Using a Hermite–Laguerre velocity–space decomposition of the perturbed gyrocenter distribution function that we refer to as the gyro-moment approach, the IS collision operator is written in a form of algebraic coefficients that depend on the mass and temperature ratios of the colliding species and perpendicular wavenumber. A comparison between the IS, OS, and Coulomb collision operators is performed, showing that the IS collision operator is able to approximate the Coulomb collision operator in the case of trapped electron mode in H-mode pedestal conditions better than the OS operator. In addition, the IS operator leads to a level of zonal flow residual which has an intermediate value between the Coulomb and the OS collision operators. The IS operator is also shown to predict a parallel electrical conductivity that approaches the one of the Coulomb operator within less than 1%, while the OS operator can underestimate the parallel electron current by at least 10%. Finally, closed analytical formulas of the lowest order gyro-moments of the IS, OS, and Coulomb operators are given, which are ready to use to describe the collisional effects in reduced gyro-moment fluid models.

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2

ESPOSITO, GIAMPIERO. "A SPECTRAL APPROACH TO YANG-MILLS THEORY." International Journal of Modern Physics A 17, no. 06n07 (March 20, 2002): 926–35. http://dx.doi.org/10.1142/s0217751x02010327.

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Yang–Mills theory in four dimensions is studied by using the Coulomb gauge. The Coulomb gauge Hamiltonian involves integration of matrix elements of an operator [Formula: see text] built from the Laplacian and from a first-order differential operator. The operator [Formula: see text] is studied from the point of view of spectral theory of pseudo-differential operators on compact Riemannian manifolds, both when self-adjointness holds and when it is not fulfilled. In both cases, well-defined matrix elements of [Formula: see text] are evaluated as a first step towards the more difficult problems of quantized Yang–Mills theory.

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3

KHACHIDZE, TAMARI T., and ANZOR A. KHELASHVILI. "AN "ACCIDENTAL" SYMMETRY OPERATOR FOR THE DIRAC EQUATION IN THE COULOMB POTENTIAL." Modern Physics Letters A 20, no. 30 (September 28, 2005): 2277–81. http://dx.doi.org/10.1142/s0217732305018505.

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On the basis of the generalization of the theorem about K-odd operators (K is the Dirac's operator), certain linear combination is constructed, which appears to commute with the Dirac Hamiltonian for Coulomb field. This operator coincides with the Johnson and Lippmann operator and is closely connected to the familiar Laplace–Runge–Lenz vector. Our approach guarantees not only derivation of Johnson–Lippmann operator, but simultaneously commutativity with the Dirac Hamiltonian.

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4

Hogreve, H. "The overcritical Dirac–Coulomb operator." Journal of Physics A: Mathematical and Theoretical 46, no. 2 (December 10, 2012): 025301. http://dx.doi.org/10.1088/1751-8113/46/2/025301.

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5

Varganov, Sergey A., Andrew T. B. Gilbert, Evelyne Deplazes, and Peter M. W. Gill. "Resolutions of the Coulomb operator." Journal of Chemical Physics 128, no. 20 (May 28, 2008): 201104. http://dx.doi.org/10.1063/1.2939239.

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6

Schmidt, Karl Michael. "Dense point spectrum for the one-dimensional Dirac operator with an electrostatic potential." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 126, no. 5 (1996): 1087–96. http://dx.doi.org/10.1017/s0308210500023271.

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For the one-dimensional Dirac operator, examples of electrostatic potentials with decay behaviour arbitrarily close to Coulomb decay are constructed for which the operator has a prescribed set of eigenvalues dense in the whole or part of its essential spectrum. A simple proof that the essential spectrum of one-dimensional Dirac operators with electrostatic potentials is never empty is given in the appendix.

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7

KHABIBRAKHMANOV, I. K., and D. SUMMERS. "Spectral representation of the isotropic Coulomb collisional operator." Journal of Plasma Physics 58, no. 3 (October 1997): 475–84. http://dx.doi.org/10.1017/s0022377897005904.

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A spectral representation for the isotropic part of the Coulomb collisional operator is given. The particle distribution function is expanded in a series of generalized Laguerre polynomials, and the Coulomb collisional operator is expressed in terms of the spectral amplitudes. When the spectral representation is applied to the Fokker–Planck equation, a system of coupled ordinary differential equations for the spectral amplitudes is obtained. The spectral coefficients related to the Coulomb operator are defined through recurrence relations, which we reduce to simplified form. This makes possible accurate and efficient analytical and numerical evaluations of the interaction matrices. The results presented can be used in analytical investigations of the properties of the Coulomb collisional operator as well as in numerical calculations for plasmas far from thermal equilibrium. The method can also be generalized to include angular dependencies for non-isotropic particle distributions.

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8

Seri, Marcello, Andreas Knauf, Mirko Degli Esposti, and Thierry Jecko. "Resonances in the two-center Coulomb systems." Reviews in Mathematical Physics 28, no. 07 (August 2016): 1650016. http://dx.doi.org/10.1142/s0129055x16500161.

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We investigate the existence of resonances for two-center Coulomb systems with arbitrary charges in two dimensions, defining them in terms of generalized complex eigenvalues of a non-selfadjoint deformation of the two-center Schrödinger operator. We construct the resolvent kernels of the operators and prove that they can be extended analytically to the second Riemann sheet. The resonances are then analyzed by means of perturbation theory and numerical methods.

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9

Lee, Aaron M., Stephen W. Taylor, Jeremy P. Dombroski, and Peter M. W. Gill. "Optimal partition of the Coulomb operator." Physical Review A 55, no. 4 (April 1, 1997): 3233–35. http://dx.doi.org/10.1103/physreva.55.3233.

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10

Kyniene, A., and R. Karazija. "Standard Atomic Operators and Coulomb Interaction Operator in the Quasispin Space." Physica Scripta 60, no. 5 (November 1, 1999): 407–13. http://dx.doi.org/10.1238/physica.regular.060a00407.

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11

KHAN, SOHAIL A. "PROJECTION OPERATOR TREATMENT FOR SUB-COULOMB WIDTHS." International Journal of Modern Physics E 13, no. 06 (December 2004): 1217–24. http://dx.doi.org/10.1142/s0218301304002624.

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An exact expression using the projection operator method to extract widths and spectroscopic factors is derived. It is applied to sub-Coulomb resonances as they occur in α-decay. A number of α-decaying nuclei are investigated. The widths and spectroscopic factors extracted using the proposed expression are found to be in excellent agreement with those obtained by other methods. Earlier equations of the projection operator for widths and spectroscopic factors would give unrealistic results in this region.

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12

Cassano, Biagio, Matteo Gallone, and Fabio Pizzichillo. "Dirac–Coulomb operators with infinite mass boundary conditions in sectors." Journal of Mathematical Physics 63, no. 7 (July 1, 2022): 071503. http://dx.doi.org/10.1063/5.0089526.

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We investigate the properties of self-adjointness of a two-dimensional Dirac operator on an infinite sector with infinite mass boundary conditions and in the presence of a Coulomb-type potential with the singularity placed on the vertex. In the general case, we prove the appropriate Dirac–Hardy inequality and exploit the Kato–Rellich theory. In the explicit case of a Coulomb potential, we describe the self-adjoint extensions for all the intensities of the potential relying on a radial decomposition in partial wave subspaces adapted to the infinite-mass boundary conditions. Finally, we integrate our results, giving a description of the spectrum of these operators.

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13

Zaitsev, F. S. "Difference approximation of the coulomb collision operator." Computational Mathematics and Modeling 2, no. 3 (1991): 232–36. http://dx.doi.org/10.1007/bf01128329.

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14

SLOBODENYUK, V. A. "ON THE EVOLUTION OPERATOR KERNEL FOR THE COULOMB AND COULOMB-LIKE POTENTIALS." Modern Physics Letters A 11, no. 21 (July 10, 1996): 1729–35. http://dx.doi.org/10.1142/s0217732396001715.

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With the help of the Schwinger-DeWitt expansion analytical properties of the evolution operator kernel for the Schrödinger equation in time variable t are studied for the Coulomb and Coulomb-like potentials (which becomes 1/|q| as |q|→0). It turned out that the Schwinger-DeWitt expansion for them is divergent. So, the kernels for these potentials have additional (beyond δ-like) singularities at t=0. Hence, the initial condition is fulfilled only in asymptotic sense. It is established that the potentials considered do not belong to the class of potentials, which have exactly δ-like singularity at t=0 and for which the initial condition is fulfilled in rigorous sense (such as [Formula: see text] for integer λ).

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15

Limpanuparb, Taweetham, and Peter M. W. Gill. "Resolutions of the Coulomb Operator: V. The Long-Range Ewald Operator." Journal of Chemical Theory and Computation 7, no. 8 (June 28, 2011): 2353–57. http://dx.doi.org/10.1021/ct200305n.

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16

Henheik, Joscha, and Roderich Tumulka. "Interior-boundary conditions for the Dirac equation at point sources in three dimensions." Journal of Mathematical Physics 63, no. 12 (December 1, 2022): 122302. http://dx.doi.org/10.1063/5.0104675.

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A recently proposed approach for avoiding the ultraviolet divergence of Hamiltonians with particle creation is based on interior-boundary conditions (IBCs). The approach works well in the non-relativistic case, i.e., for the Laplacian operator. Here, we study how the approach can be applied to Dirac operators. While this has successfully been done already in one space dimension, and more generally for codimension-1 boundaries, the situation of point sources in three dimensions corresponds to a codimension-3 boundary. One would expect that, for such a boundary, Dirac operators do not allow for boundary conditions because they are known not to allow for point interactions in 3D, which also correspond to a boundary condition. Indeed, we confirm this expectation here by proving that there is no self-adjoint operator on a (truncated) Fock space that would correspond to a Dirac operator with an IBC at configurations with a particle at the origin. However, we also present a positive result showing that there are self-adjoint operators with an IBC (on the boundary consisting of configurations with a particle at the origin) that are away from those configurations, given by a Dirac operator plus a sufficiently strong Coulomb potential.

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17

DEGOND, P., and B. LUCQUIN-DESREUX. "THE FOKKER-PLANCK ASYMPTOTICS OF THE BOLTZMANN COLLISION OPERATOR IN THE COULOMB CASE." Mathematical Models and Methods in Applied Sciences 02, no. 02 (June 1992): 167–82. http://dx.doi.org/10.1142/s0218202592000119.

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The Fokker-Planck collision operator is usually considered as an approximation of the Boltzmann collision operator when the collisions become grazing. A mathematical framework to this approach has recently been given in Ref. 2, by assuming that the scattering cross-section is smooth and depends upon a small parameter ε which tends to zero. However, the connection between ε and the physical quantities is unclear. In the present paper, our main concern is the Boltzmann operator for Coulomb collisions and its Fokker-Planck approximation. In the case of Coulomb collisions, the scattering cross-section has a non-integrable singularity when the relative velocity of the colliding particles tends to zero and a careful analysis is required. Furthermore, by a scaling of the collision operator, the small parameter which is involved in the Fokker-Planck asymptotics is clearly identified to the plasma parameter, and an expansion which is consistent with the physical observations is derived.

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18

Ji, Jeong-Young, and Eric D. Held. "Full Coulomb collision operator in the moment expansion." Physics of Plasmas 16, no. 10 (October 2009): 102108. http://dx.doi.org/10.1063/1.3234253.

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19

Reza Ahmadi, G., and Jan Almlöf. "The Coulomb operator in a Gaussian product basis." Chemical Physics Letters 246, no. 4-5 (December 1995): 364–70. http://dx.doi.org/10.1016/0009-2614(95)01127-4.

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20

RAY, RASHMI, and GIL GAT. "EFFECTIVE INTERACTIONS OF PLANAR FERMIONS IN A STRONG MAGNETIC FIELD — THE EFFECT OF LANDAU LEVEL MIXING." Modern Physics Letters B 08, no. 11 (May 10, 1994): 687–98. http://dx.doi.org/10.1142/s0217984994000704.

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We obtain expressions for the current operator in the lowest Landau level (L.L.L.) field theory, where higher Landau level mixing due to various external and interparticle interactions is systematically taken into account. We consider the current operators in the presence of electromagnetic interactions, both Coulomb and time-dependent, as well as local four-Fermi interactions. The importance of Landau level mixing for long range interactions is especially emphasized. We also calculate the edge current for a finite sample.

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21

KÖNENBERG, MARTIN, OLIVER MATTE, and EDGARDO STOCKMEYER. "EXISTENCE OF GROUND STATES OF HYDROGEN-LIKE ATOMS IN RELATIVISTIC QED I: THE SEMI-RELATIVISTIC PAULI–FIERZ OPERATOR." Reviews in Mathematical Physics 23, no. 04 (May 2011): 375–407. http://dx.doi.org/10.1142/s0129055x11004321.

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We consider a hydrogen-like atom in a quantized electromagnetic field which is modeled by means of the semi-relativistic Pauli–Fierz operator and prove that the infimum of the spectrum of the latter operator is an eigenvalue. In particular, we verify that the bottom of its spectrum is strictly less than its ionization threshold. These results hold true, for arbitrary values of the fine-structure constant and the ultraviolet cut-off as long as the Coulomb coupling constant is less than 2/π. For Coulomb coupling constants larger than 2/π, we show that the quadratic form of the Hamiltonian is unbounded below.

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22

MARTÍNEZ, D., M. SALAZAR-RAMÍREZ, R. D. MOTA, and V. D. GRANADOS. "ON THE SUPERSYMMETRY OF THE DIRAC–KEPLER PROBLEM PLUS A COULOMB-TYPE SCALAR POTENTIAL IN (D+1) DIMENSIONS AND THE GENERALIZED LIPPMANN–JOHNSON OPERATOR." Modern Physics Letters A 28, no. 11 (April 10, 2013): 1350042. http://dx.doi.org/10.1142/s0217732313500429.

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We will study the Dirac–Kepler problem plus a Coulomb-type scalar potential by generalizing the Lippmann–Johnson operator to D spatial dimensions. From this operator, we construct the supersymmetric generators to obtain the energy spectrum for discrete excited eigenstates and the radial spinor for the SUSY ground state.

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23

HALLER, KURT, and HAI-CANG REN. "THE COULOMB INTERACTION AND THE INVERSE FADDEEV–POPOV OPERATOR IN QCD." Modern Physics Letters A 18, no. 38 (December 14, 2003): 2749–53. http://dx.doi.org/10.1142/s0217732303012416.

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24

Simulik, V. M., and I. O. Gordievich. "Symmetries of Relativistic Hydrogen Atom." Ukrainian Journal of Physics 64, no. 12 (December 9, 2019): 1148. http://dx.doi.org/10.15407/ujpe64.12.1148.

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The Dirac equation in the external Coulomb field is proved to possess the symmetry determined by 31 operators, which form the 31-dimensional algebra. Two different fermionic realizations of the SO(1,3) algebra of the Lorentz group are found. Two different bosonic realizations of this algebra are found as well. All generators of the above-mentioned algebras commute with the operator of the Dirac equation in an external Coulomb field and, therefore, determine the algebras of invariance of such Dirac equation. Hence, the spin s = (1, 0) Bose symmetry of the Dirac equation for the free spinor field, proved recently in our papers, is extended here for the Dirac equation interacting with an external Coulomb field. A relativistic hydrogen atom is modeled by such Dirac equation. We are able to prove for the relativistic hydrogen atom both the fermionic and bosonic symmetries known from our papers in the case of a non-interacting spinor field. New symmetry operators are found on the basis of new gamma matrix representations of the Clifford and SO(8) algebras, which are known from our recent papers as well. Hidden symmetries were found both in the canonical Foldy–Wouthuysen and covariant Dirac representations. The found symmetry operators, which are pure matrix ones in the Foldy–Wouthuysen representation, become non-local in the Dirac model.

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25

Limpanuparb, Taweetham, Josh Milthorpe, Alistair P. Rendell, and Peter M. W. Gill. "Resolutions of the Coulomb Operator: VII. Evaluation of Long-Range Coulomb and Exchange Matrices." Journal of Chemical Theory and Computation 9, no. 2 (January 16, 2013): 863–67. http://dx.doi.org/10.1021/ct301110y.

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26

HALL, RICHARD L., WOLFGANG LUCHA, and FRANZ F. SCHÖBERL. "DISCRETE SPECTRA OF SEMIRELATIVISTIC HAMILTONIANS FROM ENVELOPE THEORY." International Journal of Modern Physics A 17, no. 14 (June 10, 2002): 1931–51. http://dx.doi.org/10.1142/s0217751x02010522.

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We analyze the (discrete) spectrum of the semirelativistic "spinless-Salpeter" Hamiltonian [Formula: see text] where V(r) is an attractive, spherically symmetric potential in three dimensions. In order to locate the eigenvalues of H, we extend the "envelope theory", originally formulated only for nonrelativistic Schrödinger operators, to the case of Hamiltonians involving the relativistic kinetic-energy operator. If V(r) is a convex transformation of the Coulomb potential -1/r and a concave transformation of the harmonic-oscillator potential r2, both upper and lower bounds on the discrete eigenvalues of H can be constructed, which may all be expressed in the form [Formula: see text] for suitable values of the numbers P here provided. At the critical point, the relative growth to the Coulomb potential h(r)=-1/r must be bounded by d V/ d h < 2β/π.

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27

Walter, Stefan. "Positivity of the two-dimensional Brown—Ravenhall operator." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 142, no. 5 (September 20, 2012): 1109–20. http://dx.doi.org/10.1017/s0308210510001708.

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We determine the critical coupling of the two-dimensional Brown–Ravenhall operator with Coulomb potential. Boundedness from below has essentially been proven by Bouzouina. However, that work contains a trivial error leading to an incorrect constant that is exactly half of the actual critical constant. Furthermore, we show that the operator is in fact positive. Our proof of that is, for the most part, analogous to Tix's proof of the corresponding result for the three-dimensional operator.

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28

SHIROKOV, M. I. "REGULARIZATION OF THE MULTIPOLAR FORM OF QUANTUM ELECTRODYNAMICS." International Journal of Modern Physics A 07, no. 28 (November 10, 1992): 7065–77. http://dx.doi.org/10.1142/s0217751x92003240.

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The multipolar form of quantum electrodynamics has been proposed by Power, Zienau et al. It is widely used in nonrelativistic calculations but has the deficiency: its Hamiltonian has a divergent operator term. It is shown that the divergency can be removed by a regularization of the unitary transformation which converts the Coulomb gauge into the multipolar form. The regularized multipolar form is proven to have the same ultraviolet radiative divergencies as the Coulomb gauge electrodynamics. It is also demonstrated that the interaction with soft photons is represented by the usual electric dipole term e qE and interatomic Coulomb interactions persist to be absent.

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29

Katsuki, Shinichi. "Model potential in spectral representation form. Its fidelity to the frozen-core operator and comparison with other model potentials." Canadian Journal of Chemistry 73, no. 5 (May 1, 1995): 696–702. http://dx.doi.org/10.1139/v95-088.

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The model potential, in which the Coulomb and exchange core operators are converted to the matrix elements by use of the spectral representation technique, should be equivalent to the frozen-core operator, if the basis set of the spectral representation is complete. Its fidelity to the frozen-core operator is examined in this paper through a thorough study of basis set convergence in both the spectral space and the atomic orbital space, along with comparison with the Sakai–Huzinaga and the Huzinaga–Seijo–Barandiaran–Klobukowski model potentials. The RHF molecular calculations on N2, P2, As2, Sb2, PN, and AsN show that the present model potential can approximate, with reliable accuracy, the results obtained from the frozen-core calculations. Keywords: model potential, spectral representation, molecular orbital calculation, electronic structure.

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30

HILKE, M., and M. RUIZ-ALTABA. "THE COULOMB GAS FOR EXCITED STATES IN THE FRACTIONAL QUANTUM HALL EFFECT." Modern Physics Letters B 05, no. 19 (August 20, 1991): 1307–11. http://dx.doi.org/10.1142/s021798499100160x.

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We follow Fubini's suggestion to use vertex operators for describing electrons and holes in the two-dimensional set-up appropriate for the description of the fractional quantum Hall effect, i.e., on the gauge-fixed magnetic plane. Laughlin's wave function is thus reproduced as the correlator of primary conformal fields, represented as exponentials of a free scalar field. We generalize an Ansatz by Halperin and present a new wave function describing the ground-state and the excited states of a system of unpolarized electrons. We realize these wave functions as correlators of normal-ordered exponentials of two free fields. We also give an explicit representation for the creation operator of an excitation.

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31

Ji, Jeong-Young, Min Uk Lee, Eric D. Held, and Gunsu S. Yun. "Moments of the Boltzmann collision operator for Coulomb interactions." Physics of Plasmas 28, no. 7 (July 2021): 072113. http://dx.doi.org/10.1063/5.0054457.

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32

Kelbert, E., A. Hyder, F. Demir, Z. T. Hlousek, and Z. Papp. "Green's operator for Hamiltonians with Coulomb plus polynomial potentials." Journal of Physics A: Mathematical and Theoretical 40, no. 27 (June 19, 2007): 7721–28. http://dx.doi.org/10.1088/1751-8113/40/27/020.

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33

Hogreve, H. "The one-dimensional Schrödinger–Coulomb operator with definite parity." Journal of Physics A: Mathematical and Theoretical 47, no. 12 (March 7, 2014): 125302. http://dx.doi.org/10.1088/1751-8113/47/12/125302.

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34

Lenters, Geoffrey T., James A. Miller, and James C. Sommer. "A Heuristic Coulomb Collision Operator for Cylindrical Velocity Coordinates." Astrophysical Journal 534, no. 2 (May 10, 2000): 997–1007. http://dx.doi.org/10.1086/308766.

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35

Gill, Peter M. W., and Andrew T. B. Gilbert. "Resolutions of the Coulomb operator: II. The Laguerre generator." Chemical Physics 356, no. 1-3 (February 2009): 86–90. http://dx.doi.org/10.1016/j.chemphys.2008.10.047.

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36

Ji, Jeong-Young, and Eric D. Held. "Exact linearized Coulomb collision operator in the moment expansion." Physics of Plasmas 13, no. 10 (October 2006): 102103. http://dx.doi.org/10.1063/1.2356320.

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37

Dimits, Andris M., Chiaming Wang, Russel Caflisch, Bruce I. Cohen, and Yanghong Huang. "Understanding the accuracy of Nanbu’s numerical Coulomb collision operator." Journal of Computational Physics 228, no. 13 (July 2009): 4881–92. http://dx.doi.org/10.1016/j.jcp.2009.03.041.

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38

Boldo, J. L., B. M. Pimentel, and J. L. Tomazelli. "Infrared dynamics in (2+1) dimensions." Canadian Journal of Physics 76, no. 1 (January 1, 1998): 69–76. http://dx.doi.org/10.1139/p97-046.

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In this work we study the asymptotic behavior of (2+1)-dimensional quantum electrodynamics in the infrared region. We show that an appropriate redefinition of the fermion current operator leads to an asymptotic evolution operator that contains a divergent Coulomb phase factor and a contribution from the electromagnetic field at large distances, factored from the evolution operator for free fields, and we conclude that the modified scattering operator maps two spaces of coherent states of the electromagnetic field, as in the KulishFaddeev model for QED (quantum electrodynamics) in four space-time dimensions. PACS No. 11.10Kk, 11.55m

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39

Yanagisawa, Takashi, Kunihiko Yamaji, and Mitake Miyazaki. "On the Kinetic Energy Driven Superconductivity in the Two-Dimensional Hubbard Model." Condensed Matter 6, no. 1 (February 26, 2021): 12. http://dx.doi.org/10.3390/condmat6010012.

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We investigate the role of kinetic energy for the stability of superconducting state in the two-dimensional Hubbard model on the basis of an optimization variational Monte Carlo method. The wave function is optimized by multiplying by correlation operators of site off-diagonal type. This wave function is written in an exponential-type form given as ψλ=exp(−λK)ψG for the Gutzwiller wave function ψG and a kinetic operator K. The kinetic correlation operator exp(−λK) plays an important role in the emergence of superconductivity in large-U region of the two-dimensional Hubbard model, where U is the on-site Coulomb repulsive interaction. We show that the superconducting condensation energy mainly originates from the kinetic energy in the strongly correlated region. This may indicate a possibility of high-temperature superconductivity due to the kinetic energy effect in correlated electron systems.

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40

Nag, Nivedita, and Rajkumar Roychoudhury. "Algebraic Approach to the Fixed Point Structure of the Quantum Mechanical Dirac -Coulomb System." Zeitschrift für Naturforschung A 50, no. 11 (November 1, 1995): 995–97. http://dx.doi.org/10.1515/zna-1995-1104.

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Abstract It is shown that a non-perturbative ß like function can be obtained for a Dirac-Coulomb system with both vector and scalar couplings using the properties of 0(2,1) algebra and the tilting operator mechanism.

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41

Güldü, Yalçın, and Merve Arslantaş. "Direct and Inverse Problems for Sturm-Liouville Operator Which Has Discontinuity Conditions and Coulomb Potential." Chinese Journal of Mathematics 2014 (February 18, 2014): 1–10. http://dx.doi.org/10.1155/2014/804383.

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We give a derivation of the main equation for Sturm-Liouville operator with Coulomb potential and prove its unique solvability. Using the solution of the main equation, we get an algorithm for the solution of the inverse problem.

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42

DZYUBENKO, ALEXANDER. "MANY-BODY EFFECTS IN LANDAU LEVELS: NON-COMMUTATIVE GEOMETRY AND SQUEEZED CORRELATED STATES." International Journal of Modern Physics B 21, no. 08n09 (April 10, 2007): 1476–80. http://dx.doi.org/10.1142/s021797920704304x.

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We discuss symmetry-driven squeezing and coherent states of few-particle systems in magnetic fields. An operator approach using canonical transformations and the SU(1, 1) algebras is developed for considering Coulomb correlations in the lowest Landau levels.

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43

Vaskivskyi, V. I. "Third-Order Correlation Functions for a Coulomb Pair." Ukrainian Journal of Physics 64, no. 6 (August 2, 2019): 477. http://dx.doi.org/10.15407/ujpe64.6.477.

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Third-order correlation functions for two particles with the electrostatic interaction have been obtained for the first time using the direct algebraic method. The main relations for the correlation functions that do not depend on the explicit form of the interaction potential between particles, as well as the relations that appear for four specific forms of the interaction operator, are considered.

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44

PEYRAUD-CUENCA, N., and P. FAUCHER. "The role of collective effects in the kinetics of a molecular plasma generated by a particle beam. Application to nitrogen." Journal of Plasma Physics 60, no. 2 (September 1998): 393–411. http://dx.doi.org/10.1017/s0022377898006898.

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A molecular plasma generated by a particle beam generally departs strongly from a Maxwellian distribution and exhibits a pronounced depletion of electrons as soon as cold electrons cross the first vibrational barrier. We show that this situation produces screened Coulomb interactions that enlarge the Coulomb cross-section in the neighbourhood of this first vibrational threshold. Including these screened interactions through the Balescu–Lenard operator with all excitation transitions leads to a modification of the distribution at the first vibrational barrier. An application is given to the case of low-pressure nitrogen lasers.

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Dimits, A. M., I. Joseph, J. W. Banks, R. L. Berger, S. Brunner, T. Chapman, D. Copeland, D. Ghosh, W. J. Arrighi, and J. Hittinger. "Linearized Coulomb Collision Operator for Simulation of Interpenetrating Plasma Streams." IEEE Transactions on Plasma Science 47, no. 5 (May 2019): 2074–80. http://dx.doi.org/10.1109/tps.2019.2897790.

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Goncharov, P. R. "A note on the Coulomb collision operator in curvilinear coordinates." Plasma Physics and Controlled Fusion 52, no. 10 (September 7, 2010): 102001. http://dx.doi.org/10.1088/0741-3335/52/10/102001.

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Fan, Hong-Yi, and Liang Fu. "Normally ordered expansion of 3-dimensional bipartite Coulomb potential operator." Physics Letters A 329, no. 3 (August 2004): 173–80. http://dx.doi.org/10.1016/j.physleta.2004.06.082.

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Coti Zelati, Vittorio, and Margherita Nolasco. "Pohozaev identity and Virial Theorem for the Dirac–Coulomb operator." Journal of Fixed Point Theory and Applications 19, no. 1 (November 8, 2016): 601–15. http://dx.doi.org/10.1007/s11784-016-0367-z.

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Limpanuparb, Taweetham, Joshua W. Hollett, and Peter M. W. Gill. "Resolutions of the Coulomb operator. VI. Computation of auxiliary integrals." Journal of Chemical Physics 136, no. 10 (March 14, 2012): 104102. http://dx.doi.org/10.1063/1.3691829.

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Ozarslan, Ramazan, Ahu Ercan, and Erdal Bas. "β −type fractional Sturm‐Liouville Coulomb operator and applied results." Mathematical Methods in the Applied Sciences 42, no. 18 (July 17, 2019): 6648–59. http://dx.doi.org/10.1002/mma.5769.

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