Energy Eigenvalues Research Articles

Transient simulation of the electrical hysteresis in a metal/polymer/metal nanostructure.

The time-dependent quantum transportation through a metal/polymer/metal system is theoretically investigated on the basis of a Su-Schrieffer-Heeger model combined with the hierarchical equations of motion formalism. Using a non-adiabatic dynamical method, the evolution of the electron subspace and lattice atoms with time can be obtained. It is found that the calculated transient currents vary with time and reach stable values after a response time under the bias voltages. However, the stable current as the system reaches its dynamical steady state exhibits a discrepancy between two sweep directions of the bias voltage, which results in pronounced electrical hysteresis loops in the current-voltage curve. By analyzing the evolution of instantaneous energy eigenstates, the occupation number of the instantaneous eigenstates, and the lattice of the polymer, we show that the formation of excitons and the delay of their annihilation are responsible for the hysteretic current-voltage characteristics, where electron-phonon interactions play the key factor. Furthermore, the hysteresis width and amplitude can also be modulated by the strength of the electron-phonon coupling, level-width broadening function, and temperature. We hope these results about past condition-dependent switching performance at a sweep voltage can provide further insight into some of the basic issues of interest in hysteresis processes in conducting polymers.

Information entropies with Varshni-Hellmann potential in higher dimensions

This work investigates the behavior of Shannon entropy and Fisher information for the Varshni-Hellmann potential (VHP) in one and three dimensions using the Nikiforov-Uvarov method. We employ the Greene-Aldrich approximation scheme to obtain the energy eigenvalues and normalized wavefunctions, which are then used to calculate these information-theoretic quantities. Our analysis revealed remarkably similar high-order features in both position and momentum spaces. Notably, our calculations showed enhanced accuracy in predicting particle localization within position space. Furthermore, the combined position and momentum entropies obeyed the lower and upper bounds established by the Berkner-Bialynicki-Birula-Mycieslki inequality. Additionally, for three-dimensional systems, the Stam-Cramer-Rao inequalities were fulfilled for different eigenstates with respect to the calculated Fisher information. It is observed that as the position Fisher entropy decreases, indicating a more precise measurement of position, the momentum Fisher entropy must increase. This implies that the Fisher information regarding momentum decreases, resulting in a decrease in the precision of momentum measurement. This demonstrates how position and momentum uncertainties complement each other in quantum mechanics. Exploring the balance between position and momentum Fisher entropy reveals a fundamental aspect of the uncertainty principle in quantum mechanics, highlighting the restrictions on measuring certain pairs of conjugate variables simultaneously with high precision.

Determination of the Energy Eigenvalues of the Varshni-Hellmann Potential

In this paper, we solve the bound state problem for the Varshni-Hellmann potential via a useful technique. In our technique, we obtain the bound state solution of the Schrödinger equation for the Varshni-Hellmann potential via ansatz method. We obtain the energy eigenvalues and the corresponding eigenfunctions. Also, the behavior of the energy spectra for both the ground and the excited state of the two body systems is illustrated graphically. The similarity of our results to the accurate numerical values is indicative of the efficiency of our technique.

Solutions of the Schrödinger equation with velocity-dependent potentials:a study on Kratzer, Mie and Hulthen potentials

The effect of isotropic velocity-dependent potentials on the bound state energy eigenvalues of the Kratzer, Mie and Hulthen potentials is obtained for any quantum states in the presence of constant form factor εr=γρ0. The corresponding energy eigenvalues and eigenfunctions are determined and tabulated for a set of finite quantum numbers n and l in the framework of the well-known Nikiforov-Uvarov method.

Predictive torque control of induction motor for rotor bar faults diagnosis

Unlike DC motors and synchronous motors, they are maintenance-free motors due to the absence of brushes, commutators and slip rings. Induction motors can be operated in polluted and explosive environments as they do not have brushes which can cause sparks. In this paper, the performance of two control techniques, namely direct torque control (DTC) and predictive torque control (PTC), are compared in transient and static states when applied to a faulty induction machine (IM). The current and torque ripples is evaluated in a healthy machine, as well as in the presence of faults, at various speed and load values. During the transient state, the objective is to assess the method that provides the optimal dynamic response, which is achieving the desired speed without any overshooting while during the static state, the objective is to minimize torque ripple and harmonics in the stator current. The Discrete Wavelet Transform (DWT) is used to analyze stator phase current. In addition, the energy eigen value (EEV) analysis has been used to determine the fault severity. The healthy and faulty systems are simulated using Matlab/Simulink for the two control methods. The results show the superiority of the PTC method compared to the DTC. A comparison of the proposed control method with other works reported in the literature is performed to verify the superiority of the proposed strategy.

Arbitrary Amplification of Quantum Coherence in Asymptotic and Catalytic Transformation.

Quantum coherence is one of the fundamental aspects distinguishing classical and quantum theories. Coherence between different energy eigenstates is particularly important, as it serves as a valuable resource under the law of energy conservation. A fundamental question in this setting is how well one can prepare good coherent states from low coherent states and whether a given coherent state is convertible to another one. Here, we show that any low coherent state is convertible to any high coherent state arbitrarily well in two operational settings: asymptotic and catalytic transformations. For a variant of asymptotic coherence manipulation where one aims to prepare desired states in local subsystems, the rate of transformation becomes unbounded regardless of how weak the initial coherence is. In a non-asymptotic transformation with a catalyst, a helper state that locally remains in the original form after the transformation, we show that an arbitrary state can be obtained from any low coherent state. Applying this to the standard asymptotic setting, we find that a catalyst can increase the coherence distillation rate significantly-from zero to infinite rate. We also prove that such anomalous transformation requires small but nonzero coherence in relevant modes, establishing the condition under which a sharp transition of the operational capability occurs. Our results provide a general characterization of the coherence transformability in these operational settings and showcase their peculiar properties compared to other common resource theories such as entanglement and quantum thermodynamics.

The spectra masses for heavy pentaquark using generalized fractional of the extended Nikiforov-Uvaro method

The Nikiforov-Uvarov method is an efficient technique for solving of heavy diquark systems. It has been used to derive analytic-exact energy eigenvalues and eigenfunctions in fractional forms, which are useful in describing such systems. The potentials employed include the Cornell potential, harmonic potential, and spin-spin interaction; have been updated with respect to previous studies. Mass spectra of heavy pentaquarks were also calculated using this method. Compared to previous studies, the present results exhibit good experimental data agreement and are improved. We deduce that the fractional models contribute greatly to the heavy pentaquark masses.

Spherical quantum dot described by a scalar exponential potential under the influence of a linear scalar potential and a global monopole

Based on the power-exponential potential, we study the confinement of a particle to a spherical quantum dot under the influence of a linear scalar potential. We show that the energy eigenvalues s-waves can be obtained from approximate solutions to the Schrödinger equation. Further, we consider the global monopole spacetime and study the topological effects of this spacetime background on the confinement of a particle to a spherical quantum dot under the influence of a linear scalar potential.

Investigation of bound state energy spectra for fermionic particles in the presence of ultra generalized exponential hyperbolic potential model

By considering the ultra generalized exponential hyperbolic potential, which covers many potential types, the solutions of the Dirac equation with spin/pseudo-spin symmetric limits are achieved. In both approaches, the relation giving the bound state energy eigenvalues is obtained in a closed form. By using these relations, the energy values are calculated numerically for both symmetry cases via the software program. In addition, it has been identified how the bound state energy eigenvalues depend on the parameters. Besides, the energy equations for the Schrödinger and Klein–Gordon particles in the limit states are derived.

Approximate solutions of the spin and pseudospin symmetries under coshine Yukawa tensor interaction

The approximate solutions of the Dirac equation for spin symmetry and pseudospin symmetry are studied with a coshine Yukawa potential model via the traditional supersymmetric approach (SUSY). To remove the degeneracies in both the spin and pseudospin symmetries, a coshine Yukawa tensor potential is proposed and applied to both the spin symmetry and the pseudospin symmetry. The proposed coshine tensor potential removes the energy degenerate doublets in both the spin symmetry and pseudospin symmetry for a very small value of the tensor strength (H = 0.05). This shows that the coshine Yukawa tensor is more effective than the real Yukawa tensor. The non-relativistic limit of the spin symmetry is obtained by using certain transformations. The results obtained showed that the coshine Yukawa potential and the real Yukawa potential has the same variation with the angular momentum number but the variation of the screening parameter with the energy for the two potential models differs. However, the energy eigenvalues of the coshine Yukawa potential model, are more bounded compared to the energies of the real Yukawa potential model.

Resonant detectors of gravitational wave in the linear and quadratic generalized uncertainty principle framework

In this work, we consider a resonant bar detector of gravitational waves in the generalized uncertainty principle (GUP) framework with linear and quadratic momentum uncertainties. The phonon modes in these detectors vibrate due to the interaction with the incoming gravitational wave. In this uncertainty principle framework, we calculate the resonant frequencies and transition rates induced by the incoming gravitational waves on these detectors. We observe that the energy eigenstates and the eigenvalues get modified by the GUP parameters. We also observe non-vanishing transition probabilities between two adjacent energy levels due to the existence of the linear order momentum correction in the generalized uncertainty relation which was not present in the quadratic GUP analysis (Class Quantum Gravity 37:195006, 2020). We finally obtain bounds on the dimensionless GUP parameters using the form of the transition rates obtained during this analysis.

Path integral formulation for Dunkl-Dirac oscillator in (1+1)-dimensional space-time coordinates

In this paper, we extend the path integral formalism for the Dirac oscillator in (1+1) dimension by replacing the spatial derivative with the Dunkl derivative. Utilizing representations in position space-time coordinates, we precisely calculate the propagator, expressed in terms of generalized Hermite polynomials. The energy eigenvalues of the electron, along with their corresponding wave functions, are determined. In special cases, we can precisely evaluate the non-relativistic energy eigenvalues and wave functions, even in the absence of Dunkl parameters.

Second harmonic generation in Harmonic-Gaussian asymmetric double quantum well: effect of magnetic and intense laser fields

We have theoretically analyzed the effects of externally applied fields (magnetic and intense laser) as well as various structural parameters such as well width, barrier width, barrier height, and structural asymmetry on the second harmonic generation (SHG) coefficients of GaAs/Al0.3Ga0.7As Harmonic-Gaussian asymmetric double quantum wells (QW). The time-independent Schrödinger equation was solved using the diagonalization method and effective mass approximation to obtain the energy eigenvalues and eigenfunctions of the structure. An expression derived within the compact density matrix approach has been used to evaluate the second harmonic generation (SHG) coefficient. Our numerical results indicate that increasing the magnitude of the magnetic (intense laser) field causes the peak positions of SHG to shift towards higher energy regions/blue (lower energy regions/red). On the other hand, as the structural parameters A1 and A2 ( k and z0 ) increase, the peak positions of the SHG coefficients exhibit a shift towards higher energy regions/blue (lower energy regions/red). We expect that the results of our study will contribute to the development of new optoelectronic devices based on the Harmonic-Gaussian asymmetric double quantum well structure.

Remarks on the global monopole topological effects on spherical symmetric potentials

In this paper, we study the topological effects of the global monopole spacetime on the energy eigenvalues of spherical symmetric potentials in the nonrelativistic regime. We deal with the radial equation by using the Wentzel, Kramers and Brillouim (WKB) approximation. In the cases where the energy levels of the [Formula: see text]-waves can be achieved, the WKB approximation is used based on the Langer transformation.

Thermodynamics of harmonic oscillator with minimal length

The generalized uncertainty principle has been applied to the Schrödinger wave equation for a one-dimensional harmonic oscillator to generate a sixth-order generalized Schrödinger equation in the position representation. The energy eigenvalues and the eigenfunctions of the sixth-order equation have been obtained. The results show the approximate correction terms of the energies due to the modified uncertainty principle. The quantum partition functions derived from the energy eigenvalue have also been used to study the thermodynamic properties of the system. The results suggest a lower bound for the minimal length equivalent to the thermal wavelength of the oscillator at very high temperature.

Electromagnetically induced transparency in a quantum ring: Interband transition

In this paper, we study the electromagnetically induced transparency (EIT) of a quantum ring by considering both interband and intraband transitions, under the influence of external electric and magnetic fields, as well as Rashba spin–orbit interaction (RSOI). Four band k⋅p model along with effective mass one band approximation were respectively employed to compute valence and conduction bands energy eigenvalues. We investigate the effects of applied electric and magnetic fields, as well as RSOI and the ring dimensions, on EIT. Our results reveal that the external magnetic field and the ring dimensions have a great influence on the EIT phenomenon. Ultimately, our numerical results will be used to develop devices with controllable nonlinear optical absorption and refraction.

Analyzing the Time Evolution of a Particle by Decomposes the Initial State Confinement in 1D Well into the Lowest Eigenstates Energy

In this work, we obtained the time evolution of the wave function of a limited quantum system (1D Box), hence getting a mathematical model to describe the system. By using programming computes, it performs a time evolution that decomposes the initial state into the 2,10, and 20 lowest energy eigenstates. Finally, by comparing numerical de-composition coefficients for the wave function to the analytical values, it found the number of knots increases directly versus the energy of the particle's quantum state. As a result, the mean bending given by the second derivative which is proportional to the kinetic energy operator should increase. We found there is a negligible mean and standard deviation of the energy in units of the ground state energy.

Dissociation of J/ψ and Y Using Dissociation Energy Criteria in N-Dimensional Space

The analytical exact iteration method (AEIM) has been widely used to calculate N-dimensional radial Schrodinger equation with medium-modified form of Cornell potential and is generalized to the finite value of magnetic field (eB) with quasiparticle approach in hot quantum chromodynamics (QCD) medium. In N-dimensional space, the energy eigenvalues have been calculated for any states (n, l). These results have been used to study the properties of quarkonium states (i.e, the binding energy and mass spectra, dissociation temperature, and thermodynamical properties in the N-dimensional space). We have determined the binding energy of the ground states of quarkonium with magnetic field and dimensionality number. We have also determined the effects of magnetic field and dimensionality number on mass spectra for ground states of quarkonia. But the main result is quite noticeable for the values of dissociation temperature in terms of magnetic field and dimensionality number for ground states of quarkonia after using the criteria of dissociation energy. At last, we have also calculated the thermodynamical properties of QGP (i.e., pressure, energy density, and speed of sound) using the parameter eB with ideal equation of states (EoS). A preprint has previously been published (Solanki et al., 2023).

Berry phase and the Mandel parameter of the non-degenerate parametric amplifier

We study the non-degenerate parametric amplifier problem from an algebraic approach of the SU(1,1) group. We write the Hamiltonian of this problem in terms of the boson generators of the SU(1,1) group and the difference operator. We apply the tilting transformation to our results to exactly solve this Hamiltonian and obtain its energy spectrum and eigenfunctions. Then, by assuming that our Hamiltonian is an explicit function of time, we calculate its Berry phase. Finally we obtain the Mandel Q-parameter of the photon numbers n a and n b .

Exploring the microscopic effects of surrounding matrices (HfO2 and SiO2) on CdSe/ZnS and ZnS/CdSe cylindrical core/shell quantum dot for microelectronic transport applications

The primary goal of this study is to comprehensively describe the physical impact of surrounding dielectrix oxides on the electronic and optical properties of a confined electron within CdSe/ZnS and ZnS/CdSe cylindrical core/shell quantum dot (CCSQD). The effective mass approximation and the compact density matrix approach have been employed to compute the energy eigenvalues as well as the optical absorption coefficients (OACs) and the refractive index changes (RICs). Our calculations revealed that the presence of enveloping oxides acts as an additional confinement tool altering the electron energy spectrum. The ZnS/CdSe CCSQD exhibited more pronounced response and the exploitation of the local electric factor can effectively enhance the optical nonlinearity of OACs and RICs. We demonstrated that confined electrons within the ZnS/CdSe CCSQD are subjected to an intense interaction at the microscopic scale with the host medium. In addition, saturation effects in the nonlinear computed coefficients have been meticulously analyzed in terms of size and dielectric surroundings. Our findings demonstrated that electronic band edge states are heavily impacted by the sharp dielectric mismatch occurring at QD/matrix interface which could be exploited for the creation of novel optoelectronic devices in the future.