Position-dependent Mass Research Articles

Quasi-exact l-states of Klein–Gordon equation with position-dependent effective mass for exponential scalar and vector fields

Quasi-exact l-states of Klein–Gordon equation with position-dependent effective mass for exponential scalar and vector fields

Effective particles in a multishell nanostructure with hardcore

In-medium effective carriers with position-dependent mass in a multishell heterostructure are analytically studied. We obtain the exact spectrum of three-dimensional bound eigenstates and the scattering wave-functions for several von Roos ordering classes. Ascribing a continuously varying mass to the carriers in a multilayer type spherical system we use our solutions to compute optical properties such as the absorption coefficients and refraction indices of a nanometric heterostructure. We analyze in detail the case of a GaAs/AℓGaAs alloy and show how these results depend on the ordering class of the kinetic Hamiltonian.

Effects of doping concentrations and position-dependent mass on the nonlinear optical properties of asymmetric double delta-doped GaAs quantum wells

Effects of doping concentrations and position-dependent mass on the nonlinear optical properties of asymmetric double delta-doped GaAs quantum wells

Effect of position-dependent mass formalism on expectation values and thermodynamic properties of some molecules with Kratzer potential

Effect of position-dependent mass formalism on expectation values and thermodynamic properties of some molecules with Kratzer potential

PDM-Coulombic effects of non-inertial cosmic string on a Klein-Gordon oscillator

This paper addresses the problem of a three-dimensional Klein-Gordon oscillator with position-dependent mass in a non-inertial cosmic string background. We provide solutions to this problem and analyze the eigensolutions, considering the influence of non-inertial effects and the presence of position-dependent mass (PDM) on the eigenvalues. Expressions are obtained for the bound state energies and wave functions.

Position dependent mass dissipative scalar field at finite temperature

Position dependent mass dissipative scalar field is a theoretical framework that combines the concepts of position-dependent mass and dissipative systems in the context of scalar field theory. In this framework, the mass of the scalar field is allowed to vary with position, leading to interesting physical phenomena such as non-locality and non-Hermiticity. We consider a generalized classical Lagrangian for the system and by developing a theoretical formulation, quantized system canonically. In follow, two-point correlation functions of the system is obtained at finite temperature and Free energy of the system is calculated in terms of Matsubara frequencies. This research can provide insights into the behavior of particles and fields in non-uniform environments, and has potential applications in various fields of physics.

Effects of hydrostatic pressure, temperature, and position-dependent mass on the nonlinear optical properties of triple delta-doped GaAs quantum well

In this study, we thoroughly investigate the impacts of hydrostatic pressure, temperature, and position-dependent mass (PDM) on the nonlinear optical properties of asymmetric triple δ-doped GaAs quantum wells. Our analysis covers total optical absorption coefficients, relative refractive index changes, nonlinear optical rectification, second harmonic generation, and third harmonic generation. Initially, we employ PDM to solve the time-independent Schrödinger equation using the diagonalization method under effective mass and parabolic band approaches, considering pressure and temperature dependencies. Utilizing the first four energy eigenvalues and eigenfunctions, we apply the compact density matrix method to compute the system’s nonlinear optical properties numerically. The results indicate a shift in optical property peak positions toward lower (higher) energy spectra with increasing hydrostatic pressure (temperature). Furthermore, the influence of PDM shifts the system’s optical properties toward the higher energy spectrum, resembling the effect of temperature. From an experimental and theoretical perspective, one of the topics that researchers work on most is GaAs-based δ-doped systems (δ-doped heterojunction bipolar transistors, δ-doped field effect transistors, δ-multiple independent gate field effect transistors, etc.). We believe these findings will provide valuable insights for the researchers involved in GaAs-based δ-doped optoelectronic device design.

PDM relativistic quantum oscillator in Einstein–Maxwell–Lambda space-time

In this paper, we study the relativistic dynamics of quantum oscillator fields within the context of a position-dependent mass (PDM) system in the background of a curved space-time. The chosen curved space-time is generated by a magnetic field incorporating a non-zero cosmological constant called Einstein–Maxwell–Lambda solution. To analyze PDM quantum oscillator fields, we introduce a modification into the Klein–Gordon equation by substituting the four-momentum vector [Formula: see text], where various four-vectors are defined by [Formula: see text], [Formula: see text] with [Formula: see text], and [Formula: see text] is the mass oscillator frequency. The radial wave equation for the modified Klein–Gordon equation is derived and subsequently solve for two distinct scalar multipliers: (i) [Formula: see text] and (ii) [Formula: see text], where [Formula: see text] and [Formula: see text]. The resultant approximate energy levels and wave function for quantum oscillator fields are demonstrated to be influenced by the cosmological constant and the geometrical topology parameter which breaks the degeneracy of the energy spectrum. Furthermore, we observed noteworthy modifications in the approximate energy levels and wave function when compared to the results derived in the flat space.

Integrable and superintegrable quantum mechanical systems with position dependent masses invariant with respect to one parametric Lie groups. 1. Systems with cylindric symmetry

Cylindrically symmetric quantum mechanical systems with position dependent masses admitting at least one second order integral of motion are classified. It is proved that there exist 68 such systems which are inequivalent. Among them there are thirty superintegrable and twelve maximally superintegrable ones. The arbitrary elements of the corresponding Hamiltonians (i.e.,masses and potentials) are presented explicitly.

Duality in spontaneous broken time translation symmetry: Sisyphus dynamics and the Liénard equation

In this paper, we establish a connection between Sisyphus dynamics and the Liénard-II equation through branched Hamiltonians. Sisyphus dynamics stem from a higher-order Lagrangian. Surprisingly, when expressed in terms of velocity, the Sisyphus dynamical equations align closely with the Liénard-II equation. Sisyphus dynamics introduces velocity-dependent “mass functions”, a departure from conventional position-dependent mass, potentially linked to cosmological time crystals. Additionally, we demonstrate that spontaneously broken time translational symmetry results in a deformed symplectic structure, resembling the classical counterpart of the Generalized Uncertainty Principle (GUP).

Relativistic energy spectra of diatomic molecules through the solutions of general conformable fractional (GCF) Klein-Gordon equation for Hulthen potential with position-dependent mass (PDM) and the thermodynamic properties

In this study, we investigate the thermodynamic properties of some diatomic molecules modelled by Hulthen potential with PDM. The GCF Klein-Gordon equation in the GCF cylindrical coordinate for the Hulthen potential and the PDM function is solved by using the GCF Laplace method to obtain the GCF energy equation and GCF wave function. The effect of the fractional order, quantum number, potential parameter, and PDM parameter on the energy eigenvalue of the H2, LiH, and HF diatomic molecules is discussed through the corresponding graphs computed using MATLAB software. The results show that the fractional order, quantum number, and potential parameter cause the energy spectrum to increase. In addition, the thermodynamic properties are examined by calculating the partition function. Based on the results, internal energy tends to be constant at lower temperatures, and the specific heat capacity decreases with increasing β . Whereas free energy and entropy increase monotonically with increasing β . To validate our findings, we compare our results with those obtained in the literature.

The Klein-Gordon equation in the cosmic string and rainbow gravity spacetime under the influence of an external magnetic field and Coulomb potential for PDM particles

Abstract The Klein-Gordon equation in the cosmic string and rainbow gravity spacetime under the influence of an external magnetic field and Coulomb potential for PDM particles is investigated using the NU method. From solution of the Klein-Gordon system with PDM particles, the energy levels are obtained. The energy levels are numerically calculated as a function of rainbow gravity parameters, as a function of magnetic field parameters, as a function of position-dependent mass parameters. We apply some rainbow functions and the results show that the negative and positive energy levels for rainbow function 1 are symmetrical compared to rainbow function 2.

Exact solutions of Pauli–Schrödinger equation for a particle with position dependent mass and magnetic momentum in a generalized Morse potential and magnetic field

Abstract The Pauli–Schrodinger equation for a non-relativistic position dependent mass with spin 1/2 and magnetic momentum μ 0 in a generalized Morse potential and permanent magnetic field is solved using the Nikiforov–Uvarov method. The energy eigenvalues and the corresponding eigenfunctions are obtained analytically. It is also shown that the results established in a previous work appear to be a special case.

Darboux transformations for Dunkl–Schrödinger equations with energy-dependent potential and position-dependent mass

We construct arbitrary-order Darboux transformations for Schrödinger equations with energy-dependent potential and position-dependent mass within the Dunkl formalism. Our construction is based on a point transformation that interrelates our equations with the standard Schrödinger case. We apply our method to generate several solvable Dunkl–Schrödinger equations.

How fabricated semiconductor heterostructures enable quantum particles to resist curved space

We show how fabricated semiconductor heterostructures enable quantum particles to exhibit resilience to curved space, achieved through a suitable position-dependent mass distribution within the semiconductor. Following the proposed approach, we show that the first-order approximation of curved space requires a position-dependent mass distribution that is common for semiconductor heterostructures. For more complex structures of curved space, one has to consider a more exotic fabricated semiconductor.

Position-dependent mass from noncommutativity and its statistical descriptions

A set of position-dependent noncommutative algebra in two dimension (2D) that describes the space near the Planck scale had been introduced [J. Phys. A: Math. Theor. 53 (2020) 115303]. This algebra predicted the existence of maximal length of graviton measurable at low energy. From this algebra, we deduce in the present paper, a new noncommutative algebra that is compatible with the deformed algebra proposed by Costa Filho et al. [Phys. Rev. A 84 (2011) 050102] to describe the Position-Dependent Mass (PDM) system in 1D. To this aim, we derive from the momentum operators, the Schrödinger-like equation which describes PDM system in null quantum well potential. The spectrum of this system is asymetrically deformed and exhibits different behaviours from the one obtained by Costa Filho et al. Thus, we observe that by increasing the PDM, the energy decreases and this decrease is more pronounced as the quantum number increases. Finally, we evaluate the thermodynamic quantities within the canonical ensemble and we show that these results are consistent with the ones recently obtained by Bensalem and Bouaziz [Phys. A Stat. Mech. Appl. 523 (2019) 583–592].

Simultaneous effects of the position dependent mass and magnetic field on quantum well with the improved Tietz potential

In this study, we explored the synergistic impact of position-dependent mass and magnetic field on the electronic and optical properties of quantum wells, featuring an enhanced Tietz potential confinement incorporating both standard Morse and improved Rosen–Morse potentials, as influenced by variations in the structural parameter. Calculations were conducted within the framework of effective mass and parabolic band approximations. The diagonalization method was employed, selecting a wave function basis of trigonometric orthonormal functions to determine the eigenvalues and eigenfunctions of the confined electron potential. Our findings reveal that alterations in the sizes and shapes of the quantum wells, magnetic field strength, geometric asymmetry, and confinement parameters lead to significant variations in electron energies, transition between electron states, and the absorption spectrum. These outcomes offer valuable insights for investigating the electronic and structural properties of materials and devising novel materials with tailored optical characteristics.

Demonstrating Shrodenger equation involving harmonic oscillator potential with a position dependent mass in an external electric field

An external electric field is provided to the familiar one-dimensional quantum harmonic oscillator model with a various position mass m(x)=(a m_0)/(a+x). The Nikiforov-Uvarov approach is involved to investigate a particular solution to the exact Schrödinger equation. The exactly solvable confined model of the quantum harmonic oscillator in an external electric field was proposed. Starting with the BenDanial-Duke kinetic energy operator approximations, the construction of the position-dependent mass Schrödinger equation is studied. The analytic representation of the wave functions of the stationary states is expressed analytically and graphically using modified Laguerre polynomials as well as the energy spectrum. In contrast with the absence of an external electric field, when the energy spectrum totally overlaps with that of the harmonic oscillator potential in an external electric field: the energy spectrum becomes non-equidistant and varies depending on some factors. The Nikiforov-Uvarov approach succeeds broadly in demonstrating the wave function and energy spectrum and showing good sense.

Closed-form bound states for two Dunkl–Liénard oscillator systems

In this paper, we construct the general Hamiltonian for position-dependent mass systems within the Dunkl formalism. The associated Schrödinger equation is shown to admit closed-form solutions of bound state type for two particular Dunkl–Liénard systems, given by the Dunkl–Higgs oscillator, and a spiked mass Dunkl oscillator. Differences to the conventional scenario are discussed.

On Klein–Gordon Gürses oscillators and pseudo-Gürses oscillators: Vorticity–energy correlations and spacetime-associated degeneracies

In this paper, we discuss Klein–Gordon (KG) oscillators in the [Formula: see text]-dimensional Gürses spacetime and under position-dependent mass (PDM) settings. We observe that the KG Gürses oscillators are introduced as a byproduct of the very nature of the Gürses spacetime structure. We report that the energy levels of such KG Gürses oscillators admit vorticity–energy correlations as well as spacetime-associated degeneracies (STADs). Moreover, we introduce a new set of KG pseudo-Gürses oscillators that admits isospectrality and invariance with the KG Gürses oscillators and inherits the same vorticity–energy correlations as well as STADs.