Coulomb-like Interaction Research Articles

KG- oscillators in Som-Raychaudhuri rotating cosmic string spacetime in a mixed magnetic field

We investigate Klein-Gordon (KG) oscillators in a Gödel-type Som-Raychaudhuri spacetime in a mixed magnetic field (given by the vector potential Aμ=(0,0,Aφ,0), with Aφ=B1r2/2+B2r). The resulting KG equation takes a Schrödinger-like form (with an oscillator plus a linear plus a Coulomb-like interactions potential) that admits a solution in the form of biconfluent Heun functions/series HB(α,β,γ,δ,z). The usual power series expansion of which is truncated to a polynomial of order nr+1=n≥1 through the usual condition γ=2(nr+1)+α. However, we use the very recent recipe suggested by Mustafa [42] as an alternative parametric condition/correlation. i.e., δ=−β(2nr+α+3), to facilitate conditional exact solvability of the problem. We discuss and report the effects of the mixed magnetic field as well as the effects of the Gödel-type SR-spacetime background on the KG-oscillators' spectroscopic structure.

Arbitrary (k, l) States-Solutions of the Dirac and Schrödinger Equations Interacting with Improved Spatially-Dependent Mass Coulomb Potential with an improved Coulomb-like tensor interaction Model for H-atoms from 3D-RNCS and 3D-NRNCS symmetries

The improved spatially dependent mass Coulomb potential with an improved Coulomb-like tensor interaction (ISDM(CP-CLTI)) model has been used to investigate the new bound state solutions of the deformed Dirac equation under the condition of spin symmetry and pseudospin symmetry in the 3D-relativistic noncommutative space (3D-RNCS) symmetries. The combination of spatially dependent mass Coulomb potential with Coulomb-like tensor interaction (ISDM(CP-CLTI)) and the terms (1/r^3 and 1/r^4 ) which are connected with the induced couplings (LΘ and L ̃Θ) produced from the topological defects of space-space gives ISDM(CP-CLTI) model. The new relativistic and non-relativistic energy eigenvalues for the hydrogen atoms (H-atoms) such as He+, Li+2, and Be3+ under the ISDM(CP-CLTI) model have been derived within the parameters of the parametric Bopp shift method and standard perturbation theory. The new values E_nc^sp(n,C,m_0,m_1,H,Θ,τ,χ,j,l,s,m) and E_nc^ps(n,C,m_0,m_1,H,Θ,τ,χ,j,l,l ̃,s ̃,m ̃) that we obtained appeared to be sensitive to the quantum atomic discrete quantum numbers (j,k,l,s,m,l ̃,s ̃,m ̃), the mixed potential depths (C/q,m_0,m_1,H), and noncommutativity parameters (NP) (Θ,σ,χ). Within the context of relativistic extended quantum mechanics, we have obtained certain significant special cases that, in our view, will be interesting to the specialized researcher. When we applied the three simultaneous limitations (Θ,σ,χ)→(0,0,0), NP we were able to retrieve the typical results of relativistic and non-relativistic cases in the literature. Our new model presented new physical features compared to other models known in the literature.

Arbitrary (k, l) States-Solutions of the Dirac and Schrödinger Equations Interacting with Improved Spatially-Dependent Mass Coulomb Potential with an improved Coulomb-like tensor interaction Model for H-atoms from 3D-RNCS and 3D-NRNCS symmetries

The deformed Dirac equation has been investigated, in the context of 3D-relativistic noncommutative space (3D-RNCS) symmetries, using the improved spatially dependent mass Coulomb potential with an improved Coulomb-like tensor interaction (ISDM(CP-CLTI)) model under the conditions of spin symmetry and pseudospin symmetry. The ISDM(CP-CLTI) model is the combining the spatially dependent mass Coulomb potential with the Coulomb-like tensor interaction (CP-CLTI) and the two central terms that are generated to the topological defects of spacespace. Within the confines of the parametric Bopp shift method and conventional perturbation theory, the new relativistic and non-relativistic energy eigenvalues for the hydrogen atoms ( H-atoms), such as He+,Li+2, and Be3+ under the ISDM(CP-CLTI) model have been derived. The novel values Encsp(n,C,m0,m1,H,Θ,τ,χ,j,l,s,m) and Encps(n,C,m0,m1,H,Θ,τ,χ,j,l,l̃,s̃,m̃) that we discovered examined to be dependent on the noncommutativity parameters (NP) (Θ,σ,χ), mixed potential depths C/q,m0,m1,H), and quantum atomic discrete quantum numbers (j,k,l,s,m,l̃,s̃,m̃). We have obtained several interesting special examples within the framework of relativistic extended quantum mechanics, which we believe will be of interest to the expert researcher. We were able to retrieve the typical results of relativistic and non-relativistic examples in the literature when we applied the three simultaneous constraints (Θ,σ,χ)→(0,0,0). Compared to previous models that are known from the literature, our new model had novel physical characteristics.

Matrix-decomposed two-electron integrals in the infinite-order two-component Hamiltonian

The Cholesky decomposition (CD) and lower–upper decomposition (LUD) of two-electron integral (TEI) matrices were applied to a spin-free infinite-order two-component (IOTC) relativistic Hamiltonian. In the Hamiltonian, the evaluation of three types of TEIs of primitive basis functions and the unitary transformation of TEIs are required. CD was used to calculate the symmetric TEI matrices: Coulomb-like and specific spin-free interaction terms. LUD was used for the asymmetric TEI matrix: Darwin-like term. Unitary transformation was performed on the decomposed matrices. Numerical assessments suggest that the proposed method can reduce the computational cost without loss of accuracy.

Freeze-in dark matter in EDGES 21-cm signal* *Supported in part by the National Natural Science Foundation of China (11775039), the High-level Talents Research and Startup Foundation Projects for Doctors of Zhoukou Normal University (ZKNUC2021006), and the Natural Science Foundation of Henan Province, China(232300421358)

The first measurement of the temperature of the hydrogen 21-cm signal reported by EDGES strongly favors the Coulomb-like interaction between freeze-in dark matter and baryon fluid. We investigate such dark matter in both the one- and two-component context with the light force carrier(s) essential for the Coulomb-like interaction being other than photons. Using a conversion of cross sections used by relevant experiments and Boltzmann equations to encode the effects of the dark matter-baryon interaction, we show that both cases are robustly excluded by the stringent stellar cooling bounds in the sub-GeV dark matter mass range. The exclusion of the one-component case applies to simplified freeze-in dark matter with the light force carrier as dark photons, gauged , ,, or axion-like particles, whereas the exclusion of the two-component case applies to simplified freeze-in dark matter with the two light force carriers as two axion-like particles coupled to standard model quarks and leptons.

Study of energies spectra and thermodynamic properties of the relativistic Dirac equation using Feynman path integral method

In the current paper, the contribution of a Coulomb-like potential tensor interaction on the solution of the Dirac equation with a new generalized Morse-like potential is investigated using the Feynman path integral method. Relativistic and non-relativistic energy spectra were obtained. It has been established that the Coulomb-like potential eliminates the degeneracy of all pairs of spin doublets. Using the resulting non-relativistic energy eigenvalues equation, three diatomic molecules (H2, LiH, and HCl) were investigated and their thermodynamic properties, including mean energy, free energy, entropy, and specific heat capacity were shown. A comparison with the available literature shows that the thermodynamic plots obtained are consistent with previous work.

Noncommutative Dirac and Schrödinger equations in the background of the new generalized Morse potential and a class of Yukawa potential with the improved Coulomb-like tensor potential as a tensor in 3D-ERQM and 3D-ENRQM symmetries

Relativistic and nonrelativistic quantum mechanics formulated in a noncommutative space–space have recently become the object of renewed interest. In the context of three-dimensional extended relativistic quantum mechanics (3D-ERQM) symmetries with arbitrary spin-orbit coupling quantum number [Formula: see text], we approximate to solve the deformed Dirac equation for a new suggested new generalized Morse potential and a class of Yukawa potential including improved Coulomb-like tensor interaction (N(GMP-CYP) plus ICLTI). In the framework of the spin and pseudospin (p-spin) symmetry, we obtain the global new energy eigenvalue which equals the energy eigenvalue in the usual relativistic QM as the main part plus three corrected parts produced from the effect of the spin-orbit interaction, the new modified Zeeman, and the rotational Fermi term, by using the parametric of the well-known Bopp’s shift method and standard perturbation theory using Greene–Aldrich approximation to nonlinear and exponential terms in the effective potential. The new values that we got appeared sensitive to the quantum numbers ([Formula: see text]), the mixed potential depths ([Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text]), the range of the potential [Formula: see text] and noncommutativity parameters ([Formula: see text],[Formula: see text],[Formula: see text]). We have studied the nonrelativistic limit of new spin symmetry under the N(GMP-ICYP) model, we will also treat some important special cases such as the new generalized Morse potential, the new class of Yukawa potential, the new Hellmann potential, the new inversely quadratic Yukawa potential, the new Hulthén potential and new Coulomb potential. Finally, we studied a case of composite systems.

Structure formation and the global 21-cm signal in the presence of Coulomb-like dark matter-baryon interactions

Many compelling dark matter (DM) scenarios feature Coulomb-like interactions between DM particles and baryons, in which the cross section for elastic scattering scales with relative particle velocity as ${v}^{\ensuremath{-}4}$. Previous studies have invoked such interactions to produce heat exchange between cold DM and baryons and alter the temperature evolution of hydrogen. Here, we present a comprehensive study of the effects of Coulomb-like scattering on structure formation, in addition to the known effects on the thermal history of hydrogen. We find that interactions which significantly alter the temperature of hydrogen at Cosmic Dawn also dramatically suppress the formation of galaxies that source the Lyman-$\ensuremath{\alpha}$ background, further affecting the global 21-cm signal. In particular, an interaction cross section at the current observational upper limit leads to a decrease in the abundance of star-forming halos by a factor of $\ensuremath{\sim}2$ at $z\ensuremath{\sim}20$, relative to cold, collisionless DM. We also find that DM that is 100% millicharged cannot reproduce the depth and the timing of the reported EDGES anomaly in any part of the parameter space. These results critically inform modeling of the global 21-cm signal and structure formation in cosmologies with DM--baryon scattering, with repercussions for future and upcoming cosmological data analysis.

Deformed Dirac and Shrödinger Equations with Improved Mie-Type Potential for Diatomic Molecules and Fermionic Particles in the Framework of Extended Quantum Mechanics Symmetries

In this study, the bound-state solutions of the deformed Dirac equation (DDE) have been determined with the improved Mie-type potential including an improved Coulomb-like tensor potential (IMTPICLP) under the condition of the spin or pseudospin symmetry in the extended relativistic quantum mechanics (ERQM) symmetries. The IMTPICLP model includes a combination of the terms 1/r3 and 1/r4 which coupled with the couplings (LΘ and L̃︀Θ) between the physical properties of the system with the topological deformations of space-space. In the framework of the parametric Bopp’s shift method and standard perturbation theory, the new relativistic and nonrelativistic energy eigenvalues for the improved Mietype potential have been found. The new obtained values appeared sensitive to the quantum numbers (j, k, l,̃︀ l, s, s,̃︀ m, m̃︀ ), the mixed potential depths (A, B, C, α), and noncommutativity parameters (Θ, σ, χ). The new energy spectra of the improved Kratzer–Fues potential within an improved Coulomb-like tensor interaction and the improved modified Kratzer potential within the Coulomb-like tensor interaction have been derived as particular cases of IMTPICLP. We recovered the usual relativistic and nonrelativistic results from the literature by applying the three simultaneous limits (Θ, σ, χ) → (0, 0, 0). One can notice that our results are in close agreement with the recent studies.

Approximate arbitrary (k,l) states solutions of deformed Dirac and Schrödinger equations with new generalized Schiöberg and Manning–Rosen potentials within the generalized tensor interactionsin 3D-EQM symmetries

Relativistic and nonrelativistic quantum mechanics formulated in a noncommutative space-space have recently become the object of renewed interest. In the context of extended relativistic quantum mechanics (ERQM) symmetries with arbitrary spin-orbit coupling quantum number [Formula: see text], we approximate to solve the deformed Dirac equation (DDE) for a new suggested new generalized Schiöberg and Manning–Rosen potentials within the generalized (Coulomb and Yukawa)-like tensor interactions (NGSM-GLTs). In the framework of the spin and pseudospin (p-spin) symmetry, we obtain the global new energy eigenvalue which equals the energy eigenvalue in usual relativistic quantum mechanics (RQM) as the main part plus three corrected parts produced from the effect of the spin-orbit interaction, the new modified Zeeman, and the rotational Fermi term, by using the parametric of the well-known Bopp’s shift method and standard perturbation theory using Greene–Aldrich approximation to handle [Formula: see text], [Formula: see text] and other terms in the effective potential. The new values that we got appeared sensitive to the quantum numbers ([Formula: see text]), the mixed potential depths ([Formula: see text],[Formula: see text],[Formula: see text],[Formula: see text],[Formula: see text]), the range of the potential [Formula: see text], and noncommutativity parameters ([Formula: see text],[Formula: see text],[Formula: see text]). We recovered several potentials, including the improved Schiöberg and Manning–Rosen potentials within the improved Yukawa-like tensor interaction, the new Schiöberg and Manning–Rosen potentials within the improved Coulomb-like tensor interaction, the new Schiöberg potential within the improved Yukawa-like tensor interaction, the new Manning–Rosen potential within the improved Yukawa-like tensor interaction, and the new Schiöberg and Manning–Rosen potentials potential problems in the context of nonrelativistic extended quantum mechanics symmetries.

Nonequilibrium phenomena in driven and active Coulomb field theories

The classical Coulomb gas model has served as one of the most versatile frameworks in statistical physics, connecting a vast range of phenomena across many different areas. Nonequilibrium generalisations of this model have so far been studied much more scarcely. With the abundance of contemporary research into active and driven systems, one would naturally expect that such generalisations of systems with long-ranged Coulomb-like interactions will form a fertile playground for interesting developments. Here, we present two examples of novel macroscopic behaviour that arise from nonequilibrium fluctuations in long-range interacting systems, namely (1) unscreened long-ranged correlations in strong electrolytes driven by an external electric field and the associated fluctuation-induced forces in the confined Casimir geometry, and (2) out-of-equilibrium critical behaviour in self-chemotactic models that incorporate the particle polarity in the chemotactic response of the cells. Both of these systems have nonlocal Coulomb-like interactions among their constituent particles, namely, the electrostatic interactions in the case of the driven electrolyte, and the chemotactic forces mediated by fast-diffusing signals in the case of self-chemotactic systems. The results presented here hint to the rich phenomenology of nonequilibrium effects that can arise from strong fluctuations in Coulomb interacting systems, and a rich variety of potential future directions, which are discussed.

Solutions of the Dirac equation with position-dependent mass for q-deformed Pöschl–Teller and Coulomb-like tensor potentials

We consider the Dirac equation with position-dependent mass for a q-deformed Pöschl–Teller potential plus a Coulomb-like tensor interaction in the limits of spin and pseudospin symmetries. Under the condition of spin symmetry, the bound state energy eigenvalue equation and the two radial components of the Dirac wave function in terms of the Jacobi polynomials are obtained approximately for an arbitrary shifted spin-orbit quantum number λκ = κ + H and for any value of the deformation parameter q ≥ 1. In the case of the pseudospin symmetry limit, there are no bound states. The Dirac equation describes a free physical system and the two components of the wave function are expressed in terms of the spherical Bessel functions.

Relativistic symmetries of the deformed Dirac equation through the improved Hulthén plus a class of Yukawa potential including a Coulomb-like tensor interaction in deformation quantum mechanics

Relativistic symmetries of the deformed Dirac equation through the improved Hulthén plus a class of Yukawa potential including a Coulomb-like tensor interaction in deformation quantum mechanics

Mattertronics for programmable manipulation and multiplex storage of pseudo-diamagnetic holes and label-free cells

Manipulating and separating single label-free cells without biomarker conjugation have attracted significant interest in the field of single-cell research, but digital circuitry control and multiplexed individual storage of single label-free cells remain a challenge. Herein, by analogy with the electrical circuitry elements and electronical holes, we develop a pseudo-diamagnetophoresis (PsD) mattertronic approach in the presence of biocompatible ferrofluids for programmable manipulation and local storage of single PsD holes and label-free cells. The PsD holes conduct along linear negative micro-magnetic patterns. Further, eclipse diode patterns similar to the electrical diode can implement directional and selective switching of different PsD holes and label-free cells based on the diode geometry. Different eclipse heights and junction gaps influence the switching efficiency of PsD holes for mattertronic circuitry manipulation and separation. Moreover, single PsD holes are stored at each potential well as in an electrical storage capacitor, preventing multiple occupancies of PsD holes in the array of individual compartments due to magnetic Coulomb-like interaction. This approach may enable the development of large programmable arrays of label-free matters with high throughput, efficiency, and reliability as multiplex cell research platforms.

Analytical bound state solutions of the Dirac equation with the Hulthén plus a class of Yukawa potential including a Coulomb-like tensor interaction

We examine the bound state solutions of the Dirac equation under the spin and pseudospin symmetries for a new suggested combined potential, Hulthén plus a class of Yukawa potential including a Coulomb-like tensor interaction. An improved scheme is employed to deal with the centrifugal (pseudocentrifugal) term. Using the Nikiforov–Uvarov and SUSYQM methods, we analytically develop the relativistic energy eigenvalues and associated Dirac spinor components of wave functions. We find that both methods give entirely the same results. Modification of our results to fit some particular potentials, which are useful in some other systems, is also discussed. We obtain complete agreement with the findings of previous works. The spin and pseudospin bound state energy spectra for various levels are presented in the absence as well as the presence of tensor coupling. Both energy spectrums are sensitive with regard to the quantum numbers $$\kappa $$ and n, as well as the parameter $$\delta $$ . We also notice that the degeneracies between Dirac spin and pseudospin-doublet eigenstate partners are completely removed by the tensor interaction. Finally, we present the parameter space of allowable bound state regions of potential strength $$V_0$$ with constants $$C_{S}$$ and $$C_{PS}$$ for both symmetry limits.

Computation of effective front form Hamiltonians for massive Abelian gauge theory

Renormalization group procedure for effective particles (RGPEP) is applied in terms of a second-order perturbative computation to an Abelian gauge theory, as an example of application worth studying on the way toward derivation of a dynamical connection between the spectroscopy of bound states and their parton-model picture in the front form of Hamiltonian dynamics. In addition to the ultraviolet transverse divergences that are handled using the RGPEP in previously known ways, the small-x divergences are handled by introducing a mass parameter and a third polarization state for gauge bosons using a mechanism analogous to spontaneous breaking of global gauge symmetry, in a special limit that simplifies the theory to Soper's front form of massive QED. The resulting orders of magnitude of scales involved in the dynamics of effective constituents or partons in the simplified theory are identified for the fermion and boson mass counter terms, effective masses and self-interactions, as well as for the Coulomb-like effective interactions in bound states of fermions. Computations in orders higher than second are mentioned but not described in this article.

Ground state and peculiarity of particle interactions in liquid crystal colloids.

This research proposes a general approach to determine the peculiarity of the interaction between colloidal particles in different liquid crystals. The main idea of this approach is in the definition of the colloidal particle as a source of the possible deformation of the ground state of the director field distribution. The ground state imposes restrictions on possible deformations and determines the peculiarity of the interaction between colloidal particles. Based on this approach, the Coulomb-like interaction between dipole particles in a cholesteric liquid crystal and a crucial change in the character of the interaction in a smectic liquid crystal are predicted.

Times of Execution of the CCNOT and CCCNOT Quantum Gates in a Quantum Computer based on a Quantum Dots Technology

It is considered a quantum computer consisting of a system of quantum dots (electrons) which are described by a Hamiltonian having rotation, inversion, and exchange symmetries. We consider exclusively the cases of both n = 3 and n = 4 quantum dots. In order to neglect their mutual Coulomb-like interactions, the electron dots are allocated very far way one of each other. In quantum dot technologies the figure of merit is the structure of the confinement potential. Thus, a realistic confinement potential of an electron dot which is composed of a very high rectangular potential well of width approximately equal to three orders of magnitude of the electron dot Compton wavelength (one nanometer) is proposed here. In order to verify the consistence of the present approach, the times of execution of the CCNOT and CCCNOT gates are calculated. It is found that in the case of a soft tunneling through the walls of the potential, the times of execution of such a gates are drastically small.

Comment on “Solutions of the Dirac equation with an improved expression of the Rosen–Morse potential energy model including Coulomb-like tensor interaction”

The Nikiforov–Uvarov polynomial method employed by Aguda (Can. J. Phys. 2013, 91: 689. doi: 10.1139/cjp-2013-0109 ) to solve the Dirac equation with an improved Rosen–Morse potential plus a Coulomb-like tensor potential is shown to be inappropriate because the conditions of its application are not fulfilled. We clarify the problem and construct the correct solutions in the spin and pseudospin symmetric regimes via the standard method of solving differential equations. For the bound states, we obtain the spinor wave functions in terms of the generalized hypergeometric functions 2F1(a, b, c; z) and in each regime we show that the energy levels are determined by the solutions of a transcendental equation that can be solved numerically.

Entropy of Negative Temperature States for a Point Vortex Gas

We study the dynamics and statistical mechanical equilibria of a neutral two-dimensional point vortex gas with Coulomb-like interactions confined in a squared and a rectangular domain. Using a punctuated Hamiltonian model in which we model the process of vortex–antivortex annihilation in superfluids by removing vortex dipoles, we show that this leads to evaporative heating of the system. Consequently, the vortex gas enters the negative temperature regime and subsequently relaxes to a maximum entropy configuration. We demonstrate that the large scale flows that emerge in this regime can be explained by using an equilibrium statistical mechanical mean field theory of point vortices based on a Poisson–Boltzmann equation. In particular, we observe that the emergent large scale flows in our point vortex simulations in the squared domain give rise to a spontaneous acquisition of angular momentum whereas the flows in the rectangular domain prefers a state with zero angular momentum. In addition to the observed qualitative agreement between the dynamical simulations and the theory that we demonstrate for the two geometries, we also present an approach that allows us to accurately compute a coarse-grained vorticity field, and henceforth recover the entropy from our dynamical runs. This allows us to perform a quantitative comparison between the dynamical point vortex simulations and the statistical mechanical predictions of the mean field theory thereby allowing us to clearly assert the validity of the assumptions of the statistical approaches as applied to this system with long-range interactions.