Duffin–Kemmer–Petiau Oscillator Research Articles

The [formula omitted]-deformation of the generalized DKP oscillator

We consider the Duffin–Kemmer–Petiau (DKP) oscillator for spin-zero bosons, coupled to a pseudoscalar Coulomb potential, in a (3+1)-dimensional noncommutative space–time characterized by κ-deformation. We use the method of Dirac derivatives to build the κ-deformed DKP equation. We work out the solutions of the generalized oscillator so obtained using a perturbation method: This allowed to examine first-order effects of the non-commutativity on its eigenenergies and eigenfunctions. Notably, we find that, due to the deformation, the energy levels of s-states become discontinuous at a certain critical value of the coupling constant of the Coulomb term. We also note an asymmetry between particle and antiparticle energies revealing the breaking of the charge-conjugation symmetry for deformed DKP equation. In addition, we discuss the κ-deformed DKP oscillator as a particular case of the considered model.

The vector DKP oscillator in the plane within the context of the extended uncertainty principle

The Extended Uncertainty Principle (EUP) is a gravitational correction to quantum mechanics that extends and modifies Heisenberg’s uncertainty principle. Particularly, it suggests the existence of a minimum measurable momentum scale, often referred to as the Minimal Momentum (MM), a quantity which is expected to influence the properties of all quantum mechanical systems. In this paper we investigate the effects of the EUP on the quantum features of the Two-Dimensional (2D) Duffin-Kemmer-Petiau Oscillator (DKPO) for spin-one particles subject to an external Homogeneous Magnetic Field (HMF). Using the position representation, we solve the corresponding problem and we obtain the exact wave functions and eigenenergies of the system, then we analyze how they are affected by the MM. We also examine the special case of a spin-one particle moving in a plane under a perpendicular HMF.

Topological effects on generalized Duffin-Kemmer-Petiau oscillator under Aharonov–Bohm flux field and Coulomb potential

In this paper, we study the relativistic quantum motions of the oscillator field of the wave equation under the influence of the Aharonov–Bohm (AB) flux field with a Coulomb vector potential in the background of the topological defects produced by a cosmic string and global monopole space-time. We derive the radial equation of the generalized Duffin-Kemmer-Petiau (DKP) oscillator in a static cosmic string space-time and solve it through the Heun function equation. Afterwards, we derive the radial equation of the same generalized DKP oscillator in a point-like global monopole background and obtain the eigenvalue solutions using the same procedure. The generalized oscillator field is studied by substituting the radial momentum operator ∂ r → (∂ r + i M ω η 0 f(r)), where f(r) is an arbitrary function other than linear and introduces a vector potential of Coulomb-types through a minimal substitution via ∂ μ → (∂ μ − i q A μ ) in the relativistic wave equation. It is shown that the eigenvalue solutions of the oscillator field are influenced by the topological defects of the cosmic string and point-like global monopole space-times and get them modified. Furthermore, we see that the eigenvalue solutions depend on the geometric quantum phase, and hence, shifted them more in addition to the topological defects that show the gravitational analogue to the Aharonov–Bohm effect for the bound-states.

The spin-one DKP oscillator with an extra spin–orbit coupling

We consider a generalization of the Duffin–Kemmer–Petiau oscillator (DKPO) for spin-1 bosons, built by implementing an extra spin–orbit coupling (SOC) into the standard DKPO equation. This model meets the requirements of Lorentz covariance as well as the existence of a conserved four-current, and is found to be exactly solvable for both natural and unnatural parity states and for an arbitrary total angular momentum number. The obtained energy eigenvalues show that the additional SOC brings about radical modifications in the spectroscopy of the DKPO. Notably, the spin–orbit splitting of the energy levels becomes controllably independent from oscillator shells. Moreover, interesting particular cases of the model as well as its non-relativistic limit are discussed.

The spin-one DKP oscillator in the plane with an external magnetic field

We successfully obtained the complete exact solution of the Duffin–Kemmer–Petiau oscillator (DKPO) for spin-1 bosons in (1+2)-dimensional space time using a 10×10 representation of the beta-matrices. We show that the problem can be decoupled into three independent subproblems, each of which is assigned with one of the spin-projection numbers ms=0 and ms=±1. Moreover, the solutions such that ms=0 and those for which ms=±1 are found to be respectively associated with (−1)J and (−1)J+1 parities. In addition, we investigate the effect of the presence of an external transverse homogeneous magnetic field on the dynamics of the oscillator: different settings, as well as interesting particular cases, are considered and the non-relativistic limit of the model is also discussed.

Correction to: The Dunkl–Duffin–Kemmer–Petiau Oscillator

Correction to: The Dunkl–Duffin–Kemmer–Petiau Oscillator

Interaction of the generalized Duffin–Kemmer–Petiau equation with a non-minimal coupling under the cosmic rainbow gravity

In this study, we survey the generalized Duffin–Kemmer–Petiau oscillator containing a non-minimal coupling interaction in the context of rainbow gravity in the presence of the cosmic topological defects in space-time. In this regard, we intend to investigate relativistic quantum dynamics of a spin-0 particle under the modification of the dispersion relation according to the Katanaev–Volovich geometric approach. Thus, based on the geometric model, we study the aforementioned bosonic system under the modified background by a few rainbow functions. In this way, by using an analytical method, we acquire energy eigenvalues and corresponding wave functions to each scenario. Regardless of rainbow gravity function selection, the energy eigenvalue can present symmetric, anti-symmetric, and symmetry breaking characteristics. Besides, one can see that the deficit angular parameter plays an important role in the solutions.

DKP oscillator in the presence of a spinning cosmic string

In this paper, we investigate the modification of gravitational fields generated by topological defects on a generalized Duffin–Kemmer–Petiau (DKP) oscillator for spin-0 particle under spinning cosmic string background. The generalized DKP oscillator equation under spinning cosmic string background is established, and the impact of the Cornell potential on the generalized DKP oscillator is presented. We give the influence of space-time and potential parameters on energy levels.

An extended version of the spin-one Duffin–Kemmer–Petiau oscillator

We study a covariant extension of the spin-one DuffinKemmerPetiau (DKP) oscillator constructed by combining a Lorentz tensor spin–orbit coupling with the basic DKP oscillator one. We show that this model has a spin-orbit splitting controllably independent from oscillator shells and admits exact analytical solutions for both natural and unnatural parity states. The corresponding energy spectrum is then obtained for any value of the total angular momentum number and a drastic change in its structure is observed due to the additional spin–orbit coupling. In particular energy bounds and, in some cases, forbidden energy ranges are noted.

Aharonov–Bohm effect on the generalized Duffin–Kemmer–Petiau oscillator in the Som–Raychaudhuri spacetime

The generalized Duffin–Kemmer–Petiau (DKP) oscillator with electromagnetic interactions in the curved spacetimes is investigated. We introduce firstly the generalized DKP oscillator in Som–Raychaudhuri spacetime with Cornell potential. Then, we consider the electromagnetic interactions into the generalized DKP oscillator. The energy eigenvalues and eigenfunction of our problem are obtained. The effects from the parameters of spacetime, the frequency of oscillator, the Cornell potential and the magnetic flux on the energy eigenvalues have been analyzed. We find an analog effect for the bound states from the Aharonov–Bohm effect in our considered system.

Duffin–Kemmer–Petiau oscillator in the presence of a cosmic screw dislocation

We examine the behavior of spin-zero bosons in an elastic medium which possesses a screw dislocation, which is a type of topological defect. Therefore, we solve analytically the Duffin–Kemmer–Petiau (DKP) oscillator for bosons in the presence of a screw dislocation with two types of potential functions: Cornell and linear-plus-cubic potential functions. For each of these functions, we analyze the impact of screw dislocations by determining the wave functions and the energy eigenvalues with the help of the Nikiforov–Uvarov method and Heun function.

Thermal properties of a two-dimensional Duffin–Kemmer–Petiau oscillator under an external magnetic field in the presence of a minimal length

Generalized uncertainty principle puts forward the existence of the shortest distances and/or maximum momentum at the Planck scale for consideration. In this article, we investigate the solutions of a two-dimensional Duffin–Kemmer–Petiau (DKP) oscillator within an external magnetic field in a minimal length (ML) scale. First, we obtain the eigensolutions in ordinary quantum mechanics. Then, we examine the DKP oscillator in the presence of an ML for the spin-zero and spin-one sectors. We determine an energy eigenvalue equation in both cases with the corresponding eigenfunctions in the non-relativistic limit. We show that in the ordinary quantum mechanic limit, where the ML correction vanishes, the energy eigenvalue equations become identical with the habitual quantum mechanical ones. Finally, we employ the Euler–Mclaurin summation formula and obtain the thermodynamic functions of the DKP oscillator in the high-temperature scale.

The study of the generalized boson oscillator in a chiral conical space–time

Our work mainly study the relativistic generalized boson oscillator namely generalized Duffin–Kemmer–Petiau (DKP) oscillator with the function [Formula: see text] considered as the Cornell potential under the chiral conical space–time background. We obtain the wave function and energy spectrum of radial equation by using commonly used the Nikiforov–Uvarov method. It is shows that the energy spectrum of the generalized DKP oscillator depend explicitly on the angular deficit [Formula: see text], related rotation parameter [Formula: see text] and torsion parameter [Formula: see text], which characterize the global structure of the metric in the chiral conical space–time. In addition, the Cornell potential parameters [Formula: see text] have non-negligible influence on the energy spectrum of the studied systems.

The Duffin-Kemmer-Petiau equation in a κ-Minkowski space-time

We study a Duffin-Kemmer-Petiau (DKP) equation built in a κ-Minkowski space-time using Dirac derivatives, and analyse its consequences. We show that the κ-deformation preserves parity and time reversal symmetries while it breaks that of the charge conjugation. Then, we investigate effects of this deformation on the energy spectrum of the spin-one DKP oscillator using a perturbation method. These effects are calculated for any value of the total angular momentum number in the case of natural-parity states and for vanishing angular momentum in the case of unnatural-parity states.

Effects of Generalized Uncertainty Principle on the $$\mathbf (1+1) $$ Dimensional DKP Oscillator with Linear Potential

Based on $$ 3\times 3$$ irreducible representation of Duffin–Kemmer–Petiau (DKP) algebras, we obtain the bound-states energy spectrum, the wave function and the probability density of DKP oscillator with linear potential under the effect of Generalized Uncertainty Principle in the momentum space representation. In addition, the numerical results of the bound-states energy spectrum are discussed. It shows that the deformation parameter $$\beta $$ and the linear potential parameter $$\lambda $$ have non-negligible effect on the $$(1 + 1)$$ dimensional DKP oscillator system.

Relativistic quantum motion of the scalar bosons in the background space–time around a chiral cosmic string

In this paper, a relativistic behavior of spin-zero bosons is studied in a chiral cosmic string space–time. The Duffin–Kemmer–Petiau (DKP) equation and DKP oscillator are written in this curved space–time and are solved by using an appropriate ansatz and the Nikiforov–Uvarov method, respectively. The influences of the topology of this space–time on the DKP spinor and energy levels and current density are also discussed in detail.

The DKP Oscillator in Spinning Cosmic String Background

In this article, we investigate the behaviour of relativistic spin-zero bosons in the space-time generated by a spinning cosmic string. We obtain the generalized beta-matrices in terms of the flat space-time ones and rewrite the covariant form of Duffin-Kemmer-Petiau (DKP) equation in spinning cosmic string space-time. We find the solution of DKP oscillator and determine the energy levels. We also discuss the influence of the topology of the cosmic string on the energy levels and the DKP spinors.

Solution of the spin-one DKP oscillator under an external magnetic field in noncommutative space with minimal length**Project supported by the National Natural Science Foundation of China (Grant Nos. 11465006 and 11565009) and the Project of Research Foundation for Graduate Students in Guizhou Province, China (Grant No. (2017)11108).

The spin-one Duffin–Kemmer–Petiau (DKP) oscillator under a magnetic field in the presence of the minimal length in the noncommutative coordinate space is studied by using the momentum space representation. The explicit form of energy eigenvalues is found, and the eigenfunctions are obtained in terms of the Jacobi polynomials. It shows that for the same azimuthal quantum number, the energy E increases monotonically with respect to the noncommutative parameter and the minimal length parameter. Additionally, we also report some special cases aiming to discuss the effect of the noncommutative coordinate space and the minimal length in the energy spectrum.

Exact solutions of a two-dimensional Duffin–Kemmer–Petiau oscillator subject to a Coulomb potential in the gravitational field of cosmic string

In this paper, the problem of a two-dimensional Duffin–Kemmer–Petiau (DKP) oscillator in the presence of a Coulomb potential in the cosmic string background is solved. The eigensolutions of the problem in question have been found, and the influence of the Coulomb potential in the presence of the gravitational field of cosmic string has been analyzed.

Effects of generalized uncertainty principle on the two-dimensional DKP oscillator

Using the momentum space representation, we study the quantum features of the two-dimensional Duffin-Kemmer-Petiau (DKP) oscillator under the condition that the position and the momentum operator obey the generalized commutation relation that leads to the appearance of minimal length with the order of the Planck length. In this context, the energy spectrum, the wave function, the probability densities and the corresponding thermodynamic functions of the DKP oscillator for spin-0 and spin-1 are obtained, respectively. They depend explicitly on the deformed parameter a which characterizes the structure of the considered system and its finite size.