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Автор: Grafiati

Опубліковано: 10 грудня 2022

Оновлено: 28 січня 2023

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1

Berry, Dominic W., Craig Gidney, Mario Motta, Jarrod R. McClean, and Ryan Babbush. "Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization." Quantum 3 (December 2, 2019): 208. http://dx.doi.org/10.22331/q-2019-12-02-208.

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Анотація:

Recent work has dramatically reduced the gate complexity required to quantum simulate chemistry by using linear combinations of unitaries based methods to exploit structure in the plane wave basis Coulomb operator. Here, we show that one can achieve similar scaling even for arbitrary basis sets (which can be hundreds of times more compact than plane waves) by using qubitized quantum walks in a fashion that takes advantage of structure in the Coulomb operator, either by directly exploiting sparseness, or via a low rank tensor factorization. We provide circuits for several variants of our algorithm (which all improve over the scaling of prior methods) including one with O~(N3/2λ) T complexity, where N is number of orbitals and λ is the 1-norm of the chemistry Hamiltonian. We deploy our algorithms to simulate the FeMoco molecule (relevant to Nitrogen fixation) and obtain circuits requiring about seven hundred times less surface code spacetime volume than prior quantum algorithms for this system, despite us using a larger and more accurate active space.

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2

Oleynichenko, Alexander V., Andréi Zaitsevskii, Nikolai S. Mosyagin, Alexander N. Petrov, Ephraim Eliav, and Anatoly V. Titov. "LIBGRPP: A Library for the Evaluation of Molecular Integrals of the Generalized Relativistic Pseudopotential Operator over Gaussian Functions." Symmetry 15, no. 1 (January 9, 2023): 197. http://dx.doi.org/10.3390/sym15010197.

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Generalized relativistic pseudopotentials (GRPP) of atomic cores implying the use of different potentials for atomic electronic shells with different principal quantum numbers give rise to accurate and reliable relativistic electronic structure models of atoms, molecules, clusters, and solids. These models readily incorporate the effects of Breit electron–electron interactions and one-loop quantum electrodynamics effects. Here, we report the computational procedure for evaluating one-electron integrals of GRPP over contracted Gaussian functions. This procedure was implemented in a library of routines named LIBGRPP, which can be integrated into existing quantum chemistry software, thus enabling the application of various methods to solve the many-electron problem with GRPPs. Pilot applications to electronic transitions in the ThO and UO2 molecules using the new library and intermediate-Hamiltonian Fock space relativistic coupled cluster method are presented. Deviations of excitation energies obtained within the GRPP approach from their all-electron Dirac–Coulomb–Gaunt counterparts do not exceed 50 cm−1 for the 31 lowest-energy states of ThO and 110 cm−1 for the 79 states of UO2. The results clearly demonstrate that rather economical tiny-core GRPP models can exceed in accuracy relativistic all-electron models defined by Dirac–Coulomb and Dirac–Coulomb–Gaunt Hamiltonians.

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3

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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4

Chi, Xuguang, Angbo Fang, Wuyi Hsiang, and Ping Sheng. "Kinetic energy operator approach to the quantum three-body problem with Coulomb interactions." Solid State Communications 141, no. 4 (January 2007): 173–77. http://dx.doi.org/10.1016/j.ssc.2006.10.031.

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5

Kay, Bernard S. "A product picture for quantum electrodynamics." AVS Quantum Science 4, no. 3 (September 2022): 031401. http://dx.doi.org/10.1116/5.0085813.

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We present a short account of our work to provide quantum electrodynamics (QED) with a product picture. We aim to complement the longer exposition in a recent paper in Foundations of Physics and to help to make that work more accessible. The product picture is a formulation of QED, equivalent to standard Coulomb gauge QED, in which the Hilbert space arises as (a certain physical subspace of) a product of a Hilbert space for the electromagnetic field and a Hilbert space for charged matter (i.e., the Dirac field) and the Hamiltonian arises as the sum of an electromagnetic Hamiltonian, a charged matter Hamiltonian, and an interaction term. (The Coulomb gauge formulation of QED is not a product picture because, in it, the longitudinal part of the electromagnetic field is made out of charged matter operators.) We also recall a “Contradictory Commutator Theorem” for QED, which exposes flaws in previous attempts at temporal gauge quantization of QED, and we explain how our product picture appears to offer a way to overcome those flaws. Additionally, we discuss the extent to which that theorem may be generalized to Yang–Mills fields. We also develop a product picture for nonrelativistic charged particles in interaction with the electromagnetic field and point out how this leads to a novel way of thinking about the theory of many nonrelativistic electrically charged particles with Coulomb interactions. In an afterword, we explain how the provision of a product picture for QED gives hope that one will be able likewise to have a product picture for (Yang Mills and for) quantum gravity—the latter being needed to make sense of the author's matter-gravity entanglement hypothesis. Also, we briefly discuss some similarities and differences between that hypothesis and its predictions and ideas of Roger Penrose related to a possible role of gravity in quantum state reduction and related to cosmological entropy.

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6

Zhang, Xin, Wei Zhang, Xin-Jun Ma, Pei-Fang Li, Yong Sun, and Jing-Lin Xiao. "The Impurity and Decay-Magnetic Polaron Effects in III–V Compound Gaussian Quantum Wells." Coatings 12, no. 8 (July 29, 2022): 1072. http://dx.doi.org/10.3390/coatings12081072.

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The effects of a decay magnetic field and hydrogen-like impurities on the ground-state binding energy (GSBE) and ground-state energy (GSE) of weak-coupling bound polarons in asymmetrical Gaussian potential (AGP) III–V compound quantum wells (QWs) were studied based on unitary transformation methods and linear combination operators. By numerical calculation, we found that the polarons were affected by the AGP, the decay magnetic field, Coulomb impurities, and the type of crystal, which led to a series of interesting phenomena, such as changes in the ground-state energy and the ground-state binding energy. The results obtained provide good theoretical guidance for optoelectronic devices and quantum information.

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7

Mathieu, J., L. Marchildon, and D. Rochon. "The bicomplex quantum Coulomb potential problem." Canadian Journal of Physics 91, no. 12 (December 2013): 1093–100. http://dx.doi.org/10.1139/cjp-2013-0261.

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Анотація:

Generalizations of the complex number system underlying the mathematical formulation of quantum mechanics have been known for some time, but the use of the commutative ring of bicomplex numbers for that purpose is relatively new. This paper provides an analytical solution of the quantum Coulomb potential problem formulated in terms of bicomplex numbers. We define the problem by introducing a bicomplex hamiltonian operator and extending the canonical commutation relations to the form [Formula: see text], where ξ is a bicomplex number. Following Pauli’s algebraic method, we find the eigenvalues of the bicomplex hamiltonian. These eigenvalues are also obtained, along with appropriate eigenfunctions, by solving the extension of Schrödinger’s time-independent differential equation. Examples of solutions are displayed. There is an orthonormal system of solutions that belongs to a bicomplex Hilbert space.

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8

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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9

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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10

Bai, Shuming, Peng Zhang, Panayiotis Antoniou, Spiros S. Skourtis, and David N. Beratan. "Quantum interferences among Dexter energy transfer pathways." Faraday Discussions 216 (2019): 301–18. http://dx.doi.org/10.1039/c9fd00007k.

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Анотація:

We explore Dexter coupling pathway interferences in non-covalent assemblies, employing a method that enables the assessment of Dexter coupling pathway strengths, interferences, and their physical origins in the context of one-particle and two-particle (i.e., coulombic) operators.

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11

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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12

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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13

XIAO, WEI, and JING-LIN XIAO. "VIBRATIONAL FREQUENCY OF IMPURITY BOUND MAGNETOPOLARON IN AN ANISOTROPIC QUANTUM DOT." Modern Physics Letters B 23, no. 20n21 (August 20, 2009): 2449–56. http://dx.doi.org/10.1142/s0217984909020618.

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Анотація:

We study the vibrational frequency and the interaction energy of the weak-coupling impurity bound magnetopolaron in an anisotropic quantum dot. The effects of the transverse and longitudinal effective confinement lengths, the electron–phonon coupling strength, the cyclotron frequency of a magnetic field and the Coulomb bound potential are taken into consideration by using an improved linear combination operator method. It is found that the vibrational frequency and the interaction energy will increase rapidly with decreasing confinement lengths and increasing the cyclotron frequency. The vibrational frequency is an increasing function of the Coulomb bound potential, whereas the interaction energy is an decreasing one of the potential and the electron–phonon coupling strength.

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14

XIAO, WEI, and JING-LIN XIAO. "PROPERTIES OF IMPURITY BOUND MAGNETOPOLARON IN QUANTUM RODS." Modern Physics Letters B 25, no. 01 (January 10, 2011): 21–30. http://dx.doi.org/10.1142/s0217984911025468.

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Анотація:

The Hamiltonian of a quantum rod with an ellipsoidal boundary is given after a coordinate transformation, which changes the ellipsoidal boundary into a spherical one. We then study the vibrational frequency and the ground state binding energy of the weak-coupling impurity bound magnetopolaron in it. The effects of the aspect ratio of the ellipsoid, the transverse effective confinement lengths, the electron-phonon coupling strength, the magnetic field cyclotron frequency and the Coulomb bound potential are taken into consideration by using linear combination operator method. It is found that the vibrational frequency and the ground state binding energy will increase with increasing Coulomb bound potential and the cyclotron frequency. They are decreasing functions of the aspect ratio of the ellipsoid and the transverse effective confinement lengths, whereas the ground state binding energy is an increasing function of the electron-phonon coupling strength.

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15

Benzair, H., M. Merad, and T. Boudjedaa. "Path integral for quantum dynamics with position-dependent mass within the displacement operator approach." Modern Physics Letters A 35, no. 30 (July 29, 2020): 2050246. http://dx.doi.org/10.1142/s0217732320502466.

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In the context of quantum mechanics reformulated in a modified Hilbert space, we can formulate the Feynman’s path integral approach for the quantum systems with position-dependent mass particle using the formulation of position-dependent infinitesimal translation operator. Which is similar a deformed quantum mechanics based on modified commutation relations. An illustration of calculation is given in the case of the harmonic oscillator, the infinite square well and the inverse square plus Coulomb potentials.

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16

Staruszkiewicz, A. "Probability Distribution for the First Casimir Operator \(C_1\) in the Quantum Coulomb Field." Acta Physica Polonica B 51, no. 5 (2020): 1185. http://dx.doi.org/10.5506/aphyspolb.51.1185.

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17

Arda, Altuğ, and Ramazan Sever. "Effective Mass Quantum Systems with Displacement Operator: Inverse Square Plus Coulomb-Like Potential." Few-Body Systems 56, no. 10 (June 9, 2015): 697–702. http://dx.doi.org/10.1007/s00601-015-1008-6.

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18

Kröger, Helmut. "On the wave operator in few‐body quantum scattering with Coulomb‐like interactions." Journal of Mathematical Physics 26, no. 1 (January 1985): 139–42. http://dx.doi.org/10.1063/1.526973.

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19

Husain, V. "Singularity avoidance, lattices, and quantum gravity." Canadian Journal of Physics 86, no. 4 (April 1, 2008): 583–86. http://dx.doi.org/10.1139/p07-201.

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An ingredient in recent discussions of curvature singularity avoidance in quantum gravity is the “inverse scale factor” operator in quantum cosmology, and its generalizations to field theoretic models such as scalar-field collapse in spherical symmetry. I describe a general lattice origin of this idea, and show how it applies to the Coulomb singularity in quantum mechanics. The example demonstrates that a discretized Schrodinger equation is computationally equivalent to the so-called polymer quantization derived loop quantum gravity. This applies also to lattice discretized forms of the Wheeler–deWitt equation.PACS Nos.: 04.60.–m, 04.60.Ds, 04.70.Dy

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20

de Prunelé, E. "Some Aspects of o(2,1) and Some Applications of o(4) and o(4,2) to Atomic Physics." International Journal of Modern Physics A 12, no. 01 (January 10, 1997): 89–97. http://dx.doi.org/10.1142/s0217751x97000116.

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Анотація:

Relations between o(2,1) and o(3) and the application of o(4) = o(3) × o(3) coherent states to the description of elliptical hydrogenic states are presented. The method of o(4,2) operator replacements with its application to the quantum mechanical three-body-Coulomb problem is introduced.

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21

CRISTOFANO, G., G. MAIELLA, R. MUSTO, and F. NICODEMI. "HALL CONDUCTANCE AND EDGE STATES IN THE COULOMB GAS VERTEX OPERATOR FORMALISM." Modern Physics Letters A 06, no. 32 (October 20, 1991): 2985–93. http://dx.doi.org/10.1142/s0217732391003493.

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The fractional quantum Hall effect is discussed in terms of a c = 1 conformal field theory and the associated U(1) Kac–Moody current algebra, using the Coulomb gas vertex operators. A geometrical derivation of the Hall conductance is given and the possible topological order is considered. The consistency requires that only at filling ν = 1/m one of the "particles" described by the vertices can be associated with the electron.

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22

WANG, CHENG-SHUN, and JING-LIN XIAO. "TRANSITION FREQUENCY OF WEAK-COUPLING IMPURITY BOUND MAGNETOPOLARON IN AN ANISOTROPIC QUANTUM DOT." Modern Physics Letters B 26, no. 01 (January 10, 2012): 1150003. http://dx.doi.org/10.1142/s0217984911500035.

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Анотація:

We study the first excited-state energy, the excitation energy and the transition frequency between the first excited- and the ground-state of weak-coupling magnetopolaron in an anisotropic quantum dot. The effects of the Coulomb bound potential, the cyclotron frequency of the magnetic field, the electron–phonon interaction and the transverse and the longitudinal effective confinement lengths are taken into account by using the linear combination operator method. It is found that studied quantities will increase with increasing Coulomb bound potential and the cyclotron frequency of the magnetic field. They are decreasing functions of the effective confinement lengths, which can be attributed to the interesting quantum size confining effect. The first excited-state energy is a decreasing function of the electron–phonon coupling strength.

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23

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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24

WANG, CHENG-SHUN, YU-FANG CHEN, and JING-JIN XIAO. "TRANSITION FREQUENCY OF STRONG-COUPLING IMPURITY BOUND POLARON IN AN ASYMMETRIC QUANTUM DOT." International Journal of Nanoscience 11, no. 03 (June 2012): 1250026. http://dx.doi.org/10.1142/s0219581x12500263.

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Анотація:

Properties of the excited state of strong-coupling impurity bound polaron in an asymmetric quantum dot are studied by using linear combination operator and unitary transformation methods. The first internal excited state energy, the excitation energy and the transition frequency between the first internal excited and the ground states of the impurity bound polaron as functions of the transverse and the longitudinal effective confinement lengths of the dot, the electron–phonon coupling strength and the Coulomb bound potential were derived. Our numerical results show that they will increase with decreasing the effective confinement lengths, due to interesting quantum size confining effects. But they are an increasing functions of the Coulomb bound potential. The first internal excited state energy is a decreasing function of the electron–phonon coupling strength whereas the transition frequency and the excitation energy are an increasing one of the electron–phonon coupling strength.

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25

TANATAR, B., and V. MOLDOVEANU. "RPA APPROACH TO NON-LINEAR TRANSPORT IN QUANTUM DOTS." International Journal of Modern Physics B 23, no. 20n21 (August 20, 2009): 4414–21. http://dx.doi.org/10.1142/s0217979209063560.

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An accurate theoretical treatment of electron-electron interactions in mesoscopic systems is available in very few cases and approximation schemes are developed in most of the applications, especially for many-level quantum dots. Here we present transport calculations within the random-phase approximation for the Coulomb interaction using the Keldysh Green's functions formalism. We describe the quantum dot systems by a tight-binding Hamiltonian. Our method is similar to the one used by Faleev and Stockman [Phys. Rev. B 66 085318 (2002)] in their study of the equilibrium properties of a homogeneous 2D electron gas. The important extension at the formal level is that we combine the RPA and the Keldysh formalism for studying non-linear transport properties of open quantum dots. Within the Keldysh formalism the polarization operator becomes a contour-ordered quantity that should be computed either from the non-interacting Green functions of the coupled quantum dot (the so-called G0W approximation) either self-consistently (GW approximation). We performed both non-selfconsistent and self-consistent calculations and compare the results. In particular we recover the Coulomb diamonds for interacting quantum dots and we discuss the charge sensing effects in parallel quantum dots.

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26

XIAO, WEI, and JING-LIN XIAO. "THE PROPERTIES OF STRONG-COUPLING IMPURITY BOUND MAGNETOPOLARON IN AN ANISOTROPIC QUANTUM DOT." International Journal of Modern Physics B 25, no. 26 (October 20, 2011): 3485–94. http://dx.doi.org/10.1142/s0217979211101259.

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Анотація:

We study the vibrational frequency, the ground-state energy and the ground-state binding energy of the strong-coupling impurity bound magnetopolaron in an anisotropic quantum dot. The effects of the transverse and longitudinal effective confinement lengths, the electron–phonon coupling strength, the cyclotron frequency of a magnetic field and the Coulomb bound potential are taken into consideration by using an linear combination operator and unitary transformation methods. It is found that the vibrational frequency, the ground-state energy and the ground-state binding energy will increase rapidly with decreasing confinement lengths. The vibrational frequency is an increasing function of the Coulomb bound potential, the electron–phonon coupling strength and cyclotron frequency, whereas the ground-state energy is a decreasing function of the potential and coupling strength, and the ground-state binding energy is an increasing function of the potential and coupling strength. The ground-state energy and the ground-state binding energy increases with increasing cyclotron frequency.

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27

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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28

Ahmad El-Nabulsi, Rami, and Waranont Anukool. "Acceleration in quantum mechanics and electric charge quantization." Modern Physics Letters A 36, no. 26 (August 30, 2021): 2150185. http://dx.doi.org/10.1142/s0217732321501856.

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Анотація:

In this study, we have discussed the implications of acceleration in quantum mechanics by means of a generalized derivative operator (GDO). A new Schrödinger equation is obtained which depends on the reduced Compton wavelength of the particle. We have discussed its implications in quantum mechanics for different types of potentials mainly the infinite wall potential, the gravitational linear field potential, the Cornell potential and the Coulomb repulsive potential. The corresponding wave functions and discrete energies are modified and differ from the results obtained in the conventional formalism. The major results obtained concerned the large improvement of the ground energy of the electron subject to the gravitational acceleration in addition to Cornell potential and the emergence of quantized electric charge in the theory without including Dirac monopoles or using gauge theories.

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29

FLORES, J. C. "MESOSCOPIC ELECTRICAL TRANSMISSION LINE IN THE CHARGE–ANTICHARGE FRAMEWORK: SPECTRAL PROPERTIES AND CASIMIR FORCES." Modern Physics Letters B 25, no. 06 (March 10, 2011): 403–12. http://dx.doi.org/10.1142/s0217984911025778.

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In the charge–anticharge framework, we solve explicitly the nonlinear quantum evolution equation for the charge operator of the direct transmission line with discrete charge. The associated spectrum is completely consistent with the well-known limit of continuous charge. In the zero point charge fluctuations state, the attraction between plates is compared with the corresponding Casimir force (related to field fluctuations) which, now, could be interpreted in terms of virtual charge fluctuations. The spectrum of the dual transmission line (left-handed) is also found. Some aspects related to quantum dots (coulomb blockade), structure fine constant and thermodynamics properties are also touched upon.

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30

Shubov, M. A. "Stark quantum defect for high Rydberg states of three-dimensional Schrödinger operator with screened Coulomb potential." Il Nuovo Cimento B Series 11 110, no. 9 (September 1995): 1057–92. http://dx.doi.org/10.1007/bf02726154.

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31

CHOI, JEONG RYEOL, and KYU HWANG YEON. "QUANTUM PROPERTIES OF LIGHT IN LINEAR MEDIA WITH TIME-DEPENDENT PARAMETERS BY LEWIS–RIESENFELD INVARIANT OPERATOR METHOD." International Journal of Modern Physics B 19, no. 14 (June 10, 2005): 2213–24. http://dx.doi.org/10.1142/s0217979205029845.

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Анотація:

We investigated exact quantum states of the light confined in cubes filled with conductive media whose parameters are explicitly dependent on time and the light propagating under periodic boundary condition by making use of the LR (Lewis–Riesenfeld) invariant operator method. The choice of Coulomb gauge in the charge free space allowed us to evaluate quantized electric and magnetic fields by expanding only the vector potential, since the scalar potential is zero. We also described the fields with a spectrum of continuous mode, which can be obtained by setting the side L to infinity.

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32

Lebed, A. G. "Does the Equivalence between Gravitational Mass and Energy Survive for a Composite Quantum Body?" Advances in High Energy Physics 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/678087.

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We define passive and active gravitational mass operators of the simplest composite quantum body—a hydrogen atom. Although they do not commute with its energy operator, the equivalence between the expectation values of passive and active gravitational masses and energy is shown to survive for stationary quantum states. In our calculations of passive gravitational mass operator, we take into account not only kinetic and Coulomb potential energies but also the so-called relativistic corrections to electron motion in a hydrogen atom. Inequivalence between passive and active gravitational masses and energy at a macroscopic level is demonstrated to reveal itself as time-dependent oscillations of the expectation values of the gravitational masses for superpositions of stationary quantum states. Breakdown of the equivalence between passive gravitational mass and energy at a microscopic level reveals itself as unusual electromagnetic radiation, emitted by macroscopic ensemble of hydrogen atoms, moved by small spacecraft with constant velocity in the Earth’s gravitational field. We suggest the corresponding experiment on the Earth’s orbit to detect this radiation, which would be the first direct experiment where quantum effects in general relativity are observed.

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33

Leonau, Aliaksandr U., and Ilya D. Feranchuk. "Analytical diagonalisation of the Hamiltonian of the quantum Rabi model in the Coulomb gauge." Journal of the Belarusian State University. Physics, no. 1 (January 27, 2022): 44–51. http://dx.doi.org/10.33581/2520-2243-2022-1-44-51.

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In the present paper we investigate the approximate analytical diagonalisation of the Hamiltonian of the quantum Rabi model written in the Coulomb gauge and taking into account the gauge invariance of the system. It is shown that the Hamiltonian of the model can be diagonalised with high accuracy on the basis of a unitary operator of the gauge transformation utilising a simple basis set of state vectors. It is essential that the obtained approximate expressions do not depend on the variational parameters and are valid within the whole range of the parameter values. The zeroth-order approximation and uniformly available approximation are derived for the eigenstates of the system, and their comparison with the results of the numerical simulation is elaborated. The second-order correction to the zeroth-order approximation is deduced and its contribution to the energy of the system is estimated. The obtained results could be useful for description of the evolution of the quantum Rabi model as well as for investigation of systems of two-level atoms in the resonant quantum field.

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34

RIAZUDDIN. "DIRAC EQUATION FOR QUASI-PARTICLES IN GRAPHENE AND QUANTUM FIELD THEORY OF THEIR COULOMB INTERACTION." International Journal of Modern Physics B 26, no. 21 (July 18, 2012): 1242005. http://dx.doi.org/10.1142/s0217979212420052.

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There is evidence for existence of massless Dirac quasiparticles in graphene, which satisfy Dirac equation in (1+2) dimensions near the so called Dirac points which lie at the corners at the graphene's brilluoin zone. We revisit the derivation of Dirac equation in (1+2) dimensions obeyed by quasiparticles in graphene near the Dirac points. It is shown that parity operator in (1+2) dimensions play an interesting role and can be used for defining "conserved" currents resulting from the underlying Lagrangian for Dirac quasiparticles in graphene which is shown to have UA(1) × UB(1) symmetry. Further the quantum field theory (QFT) of Coulomb interaction of 2D graphene is developed and applied to vacuum polarization and electron self-energy and the renormalization of the effective coupling g of this interaction and Fermi velocity vf which has important implications in the renormalization group analysis of g and vf.

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35

Limpanuparb, Taweetham, Andrew T. B. Gilbert, and Peter M. W. Gill. "Resolutions of the Coulomb Operator: IV. The Spherical Bessel Quasi-Resolution." Journal of Chemical Theory and Computation 7, no. 4 (March 16, 2011): 830–33. http://dx.doi.org/10.1021/ct200115t.

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36

Weniger, Ernst Joachim. "The Spherical Tensor Gradient Operator." Collection of Czechoslovak Chemical Communications 70, no. 8 (2005): 1225–71. http://dx.doi.org/10.1135/cccc20051225.

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The spherical tensor gradient operator Ylm(∇), which is obtained by replacing the Cartesian components of r by the Cartesian components of ∇ in the regular solid harmonic Ylm(r), is an irreducible spherical tensor of rank l. Accordingly, its application to a scalar function produces an irreducible spherical tensor of rank l. Thus, it is in principle sufficient to consider only multicenter integrals of scalar functions: Higher angular momentum states can be generated by differentiation with respect to the nuclear coordinates. Many of the properties of Ylm(∇) can be understood easily with the help of an old theorem on differentiation by Hobson [Proc. Math. London Soc. 24, 54 (1892)]. It follows from Hobson's theorem that some scalar functions of considerable relevance as for example the Coulomb potential, Gaussian functions, or reduced Bessel functions produce particularly compact results if Ylm(∇) is applied to them. Fourier transformation is very helpful in understanding the properties of Ylm(∇) since it produces Ylm(-ip). It is also possible to apply Ylm(∇) to generalized functions, yielding for instance the spherical delta function δlm(r). The differential operator Ylm(∇) can also be used for the derivation of pointwise convergent addition theorems. The feasibility of this approach is demonstrated by deriving the addition theorem of rvYlm(r) with v ∈ πR.

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37

Limpanuparb, Taweetham, and Peter M. W. Gill. "Resolutions of the Coulomb operator : Part III. Reduced-rank Schrödinger equations." Physical Chemistry Chemical Physics 11, no. 40 (2009): 9176. http://dx.doi.org/10.1039/b910613h.

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38

LAHIRI, ANURADHA, PRODYOT KUMAR ROY, and BIJAN BAGCHI. "SUPERSYMMETRY IN QUANTUM MECHANICS." International Journal of Modern Physics A 05, no. 08 (April 20, 1990): 1383–456. http://dx.doi.org/10.1142/s0217751x90000647.

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A pedagogical review on supersymmetry in quantum mechanis is presented which provides a comprehensive coverage of the subject. First, the key ingredients on the quantization of the systems with anticommuting variables are discussed. The supersymmetric Hamiltotian in quantum mechanics is then constructed by emphasizing the role of partner potentials and the superpotentials. We also make explicit the mathematical formulation of the Hamiltonian by considering in detail the N=1 and N=2 supersymmetric (quantum) mechanics. Supersymmetry is then discussed in the context of one-dimensional problems and the importance of the factorization method is highlighted. We treat in detail the technique of constructing a hierarchy of Hamiltonians employing the so-called ‘shape-invariance’ of potentials. To make transparent the relationship between supersymmetry and solvable potentials, we also solve several examples. We then go over to the formulation of supersymmetry in radial problems, paying a special attention to the Coulomb and isotropic oscillator potentials. We show that the ladder operator technique may be suitably modified in higher dimensions for generating isospectral Hamiltonians. Next, the criteria for the breaking of supersymmetry is considered and their range of applicability is examined by suitably modifying the definition of Witten’s index. Finally, we perform some numerical calculations for a class of potentials to show how a modified WKB approximation works in supersymmetric cases.

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39

Maireche, A. "A New Approach to the Approximate Analytic Solution of the Three-Dimensional Schrӧdinger Equation for Hydrogenic and Neutral Atoms in the Generalized Hellmann Potential Model". Ukrainian Journal of Physics 65, № 11 (12 листопада 2020): 987. http://dx.doi.org/10.15407/ujpe65.11.987.

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Within the framework of nonrelativistic noncommutative quantum mechanics using the improved approximation scheme to the centrifugal term for any l-states via the generalized Bopp’s shift method and standard perturbation theory, we have obtained the energy eigenvalues of a newly proposed generalized Hellmann potential model (the GHP model) for the hydrogenic atoms and neutral atoms. The potential is a superposition of the attractive Coulomb potential plus Yukawa one, and new central terms appear as a result of the effects of noncommutativity properties of space and phase in the Hellmann potential model. The obtained energy eigen-values appear as a function of the generalized gamma function, the discrete atomic quantum numbers (j, n, l, s and m), infinitesimal parameters (a, b, б) which are induced by the position-position and phase-phase noncommutativity, and, the dimensional parameters (Θ, 0) of the GHP model, in the nonrelativistic noncommutative three-dimensional real space phase (NC: 3D-RSP). Furthermore, we have shown that the corresponding Hamiltonian operator with (NC: 3D-RSP) symmetries is the sum of the Hamiltonian operator of the Hellmann potential model and two operators, the first one is the modified spin-orbit interaction, while the second is the modified Zeeman operator for the hydrogenic and neutral atoms.

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40

Yang, Ciann-Dong. "Solving quantum trajectories in Coulomb potential by quantum Hamilton–Jacobi theory." International Journal of Quantum Chemistry 106, no. 7 (2006): 1620–39. http://dx.doi.org/10.1002/qua.20878.

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41

Aste, Andreas. "Coulomb Solutions from Improper Pseudo-Unitary Free Gauge Field Operator Translations." Symmetry 6, no. 4 (December 15, 2014): 1037–57. http://dx.doi.org/10.3390/sym6041037.

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42

Niemann, T., P. Stange, A. Strate, and R. Ludwig. "When hydrogen bonding overcomes Coulomb repulsion: from kinetic to thermodynamic stability of cationic dimers." Physical Chemistry Chemical Physics 21, no. 16 (2019): 8215–20. http://dx.doi.org/10.1039/c8cp06417b.

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“Coulomb explosion” prevented! Quantum chemical calculations of dimers of like-charged molecular ions show that Coulomb repulsion can be overcome by hydrogen bonding and dispersion forces. Quantum-type short-range attraction wins over classical long-range electrostatic repulsion providing the first thermodynamically stable cationic dimer.

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43

Zhao, Weidong, V. Rexma Rexma Sherine, T. G. Gerly, G. Britto Antony Britto Antony Xavier, K. Julietraja, and P. Chellamani. "Symmetric Difference Operator in Quantum Calculus." Symmetry 14, no. 7 (June 25, 2022): 1317. http://dx.doi.org/10.3390/sym14071317.

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The main focus of this paper is to develop certain types of fundamental theorems using q, q(α), and h difference operators. For several higher order difference equations, we get two forms of solutions: one is closed form and another is summation form. However, most authors concentrate only on the summation part. This motivates us to develop closed-form solutions, and we succeed. The key benefit of this research is finding the closed-form solutions for getting better results when compared to the summation form. The symmetric difference operator is the combination of forward and backward difference symmetric operators. Using this concept, we employ the closed and summation form for q, q(α), and h difference symmetric operators on polynomials, polynomial factorials, logarithmic functions, and products of two functions that act as a solution for symmetric difference equations. The higher order fundamental theorems of q and q(α) are difficult to find when the order becomes high. Hence, by inducing the h difference symmetric operator in q and q(α) symmetric operators, we find the solution easily and quickly. Suitable examples are given to validate our findings. In addition, we plot the figures to examine the value stability of q and q(α) difference equations.

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44

Dulieu, O., and S. Willitsch. "Ion Coulomb crystals: from quantum technology to chemistry close to the absolute zero point." Europhysics News 48, no. 2 (March 2017): 17–20. http://dx.doi.org/10.1051/epn/2017203.

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Ion Coulomb crystals are ordered structures of atomic or molecular ions stored in ion traps at temperatures close to the absolute zero point. These unusual “crystals” form the basis of extremely accurate clocks, provide an environment for precise studies of chemical reactions and enable advanced implementations of the technology for a quantum computer. In this article, we discuss the techniques for generating atomic and molecular Coulomb crystals and highlight some of their applications.

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45

Zhang, X. G., and T. Xiang. "Tunable coulomb blockade and giant coulomb blockade magnetoresistance in a double quantum dot system." International Journal of Quantum Chemistry 112, no. 1 (July 11, 2011): 28–32. http://dx.doi.org/10.1002/qua.23196.

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46

Cao, Xian-Sheng, Xing-Yi Tan, and Bin Chen. "Shot noise in a quantum dot with the coulomb interaction." Solid State Communications 151, no. 7 (April 2011): 514–17. http://dx.doi.org/10.1016/j.ssc.2011.01.027.

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47

Abbas, Mohammed A. A., Lafy F. Al-Badry, and Amin H. Al-Khursan. "Coulomb Effect in a Double Quantum Dot System." Journal of Electronic Materials 51, no. 3 (January 3, 2022): 1202–14. http://dx.doi.org/10.1007/s11664-021-09344-2.

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48

Sasakura, H., S. Adachi, S. Muto, T. Usuki, and M. Takatsu. "Coulomb interaction in asymmetric triple-coupled quantum dots." Semiconductor Science and Technology 19, no. 4 (March 12, 2004): S409—S411. http://dx.doi.org/10.1088/0268-1242/19/4/134.

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49

Palii, Andrew, Sergey Aldoshin, and Boris Tsukerblat. "Functional Properties of Tetrameric Molecular Cells for Quantum Cellular Automata: A Quantum-Mechanical Treatment Extended to the Range of Arbitrary Coulomb Repulsion." Magnetochemistry 8, no. 8 (August 16, 2022): 92. http://dx.doi.org/10.3390/magnetochemistry8080092.

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We discuss the problem of electron transfer (ET) in mixed valence (MV) molecules that is at the core of molecular Quantum Cellular Automata (QCA) functioning. Theoretical modelling of tetrameric bi-electronic MV molecular square (prototype of basic QCA cell) is reported. The model involves interelectronic Coulomb repulsion, vibronic coupling and ET between the neighboring redox sites. Unlike the majority of previous studies in which molecular QCA have been analyzed only for particular case when the Coulomb repulsion energy significantly exceeds the ET energy, here we do not imply assumptions on the relative strength of these two interactions. Moreover, in the present work we go beyond the adiabatic semiclassical approximation often used in theoretical analysis of such systems in spite of the fact that this approximation ignores such an important phenomenon as quantum tunneling. By analyzing the electronic density distributions in the cells and the ell-cell response functions obtained from a quantum-mechanical solution of a complex multimode vibronic problem we have concluded that such key features of QCA cell as bistability and switchability can be achieved even under failure of the condition of strong Coulomb repulsion provided that the vibronic coupling is strong enough. We also show that the semiclassical description of the cell-cell response functions loses its accuracy in the region of strong non-linearity, while the quantum-mechanical approach provides correct results for this critically important region.

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50

Ghosh, Dibyajyoti, Parbati Senapati, Prakash Parida, and Swapan K. Pati. "A small heterocyclic molecule as a multistate transistor: a quantum many-body approach." Journal of Materials Chemistry C 9, no. 33 (2021): 10927–34. http://dx.doi.org/10.1039/d1tc01092a.

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Using the quantum master equation for many-body Hamiltonian, this study computationally investigates highly non-linear current–voltage characteristics such as negative differential conductance, and Coulomb blockade in a small molecular bridge.

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