Solving Dirac Equation with New Ring-Shaped Non-Spherical Harmonic Oscillator Potential

A new ring-shaped non-harmonic oscillator potential is proposed. The precise bound solution of Dirac equation with the potential is gained when the scalar potential is equal to the vector potential. The angular equation and radial equation are obtained through the variable separation method. The results indicate that the normalized angle wave function can be expressed with the generalized associated-Legendre polynomial, and the normalized radial wave function can be expressed with confluent hypergeometric function. And then the precise energy spectrum equations are obtained. The ground state and several low excited states of the system are solved. And those results are compared with the non-relativistic effect energy level in Phys. Lett. A 340 （2005） 94. The positive energy states of system are discussed and the conclusions are made properly.

Potential Power of the Pyramidal Structure VIII: Exploration of Periodic Diurnal Oscillation of Pyramid Power and Bio-Entanglement

To date, numerous books have been published on so-called “pyramid power” but there have been few academic papers on this subject other than our own. Since 2007, to demonstrate the pyramid power, we have undertaken strictly scientific experiments using a pyramidal structure (PS) that we have carefully constructed. In previous reports, we used the edible cucumber, Cucumis sativus as an effective and practical biosensor. Through measurement and analysis of volatile components (gas concentrations) emitted from the biosensor, we were able to demonstrate the existence of the pyramid power and revealed some of its characteristics. In a paper published in 2022, we showed that gas concentration release from this biosensor displayed a circadian rhythm and that this rhythm changed with the season. Based on the result that the biosensor had a periodic diurnal oscillation called a circadian rhythm, we questioned whether or not pyramid power and Bio-Entanglement also had periodic diurnal oscillations. In this paper, we investigated that possibility. Our results have shown that pyramid power and Bio-Entanglement do not exhibit significant periodic diurnal oscillations. Thus we have revealed for the first time that the field associated with pyramid power is a type of static field that always exerts a constant influence. We expect that our research results will be widely accepted in the future and will become the foundation for a new research field in science, with a wide range of applications.

Supersymmetry and Shape Invariance of Hartmann Potential and Ring-Shaped Oscillator Potential in the γ and θ Dimensions of Spherical Polar Coordinates

This article shows that in spherical polar coordinates, some noncentral separable potentials have super-symmetry and shape invariance in the r and θ dimensions, we choose Hartmann potential and ring-shaped oscillator astwo important examples, thus in principle the energy eigenvalues and energy eigenfunctions of such the potentials in ther and θ dimensions can be obtained by the method of supersymmetric quantum mechanics. Here we use an alternativemethod to get the required results.

The nonrelativistic oscillator strength of a hyperbolic-type potential

We consider the D-dimensional SchrSdinger equation under the hyperbolic potential V0（1 -coth（ar））＋ 171 （1 - coth（ar））2. Using a Pekeris-type approximation, the approximate analytical solutions of the problem are obtained via the supersymmetric quantum mechanics. The behaviors of energy eigenvalues versus dimension are discussed for various quantum numbers. Useful expectation values as well as the oscillator strength are obtained.

Splitting of Spectra in Anharmonic Oscillators Described by Kratzer Potential Function

A perturbation theory model that describes splitting of the spectra in highly symmetrical molecular species in electrostatic field is proposed. An anahrmonie model of a two-dimensional oscillator having Kratzer potential energy function is used to model the molecular species and to represent the unperturbed system. A selection rule for the radial quantum number of the oscillator is derived. The eigenfunctions of a two-dimensional anharmonic oscillator in cylindrical coordinates are used for the matrix elements representing the probability for energy transitions in dipole approximation to be calculated. Several forms of perturbation operators are proposed to model the interaction between the polyatomic molecular species and an electrostatic field. It is found that the degeneracy is removed in the presence of the electric field and spectral splitting occurs. Anharmonic approximation for the unperturbed system is more accurate and reliable representation of a reaJ polyatomic molecular species.

The Quantum Oscillatory Modulated Potential Ⅰ- The Hydrogen Atom

In this work we are presenting a modified Coulomb potential function to describe the interaction between two micro-scopic electric charges. In particular, concerning the interaction between the proton and the electron in the hydrogen atom. The modified potential function is the product of the classical Coulomb potential and an oscillatory function dependent on a quantized phase factor. The oscillatory function picks up only selected points along the Coulomb potential, creating potential wells and barriers around the nucleus of the atom. The new potential reveals us new features of the hydrogen atom. Searching for a manner to determine the phase factor, we are using the concept of the de Broglie particle wavelike behavior and the quantum analogue of the virial theorem for describing the bound motion of a particle in a central force field. This procedure is a kind of feedback action, where we are making use of well established concepts of the quantum mechanics aiming to determine the phase factor of the new interaction potential.

Study on the oscillating phenomena of electrical potential across a liquid membrane

The electrical oscillations across a liquid membrane in water/oil/water system was studied with octanol as oil phase by introducing two opposite charged surfactants in oil and aqueous phase, respectively. The sustained and rhythmic oscillation was observed. To a certain extent, the features of the oscillation （e.g. induction time, frequency, life time and orientation of the pulse pikes） strongly depend on the property of surfactant, dissolved in octanol. The mechanism may be explained by the formation and destruction of dual-ion surfactant membrane accompanying with emulsification at the interface and considering the coupling effect of diffusion and associated reaction in the vicinity of the interface.

Two Types of Potential Oscillation During the Reduction of Dichromate on Gold Electrode in H2SO4 Solution

Two different types of potential oscillations have been identified for the first time during dichromate reduction on a gold electrode in a solution of dilute sulfuric acid. One occurs before hydrogen evolution due to the formation and dissolution of passivating films of low-valence chromium oxides, and the other generates, accompanying periodic hydrogen evolution, from the coupling of electrochemical reactions with diffusive and convective mass transport. More interestingly, these two types of oscillations correspond to two crossing loops in the cyclic voltammogram （CV）. Such a relation of oscillations with crossed CVs will provide a new way to find electrochemical oscillatory systems systematically and rapidly.

Photodetachment dynamics of H^- ion in a harmonic potential plus a time-dependent oscillating electric field

The photodetachment dynamics of H^- ion in a harmonic potential plus an oscillating electric field is studied using the time-dependent closed orbit theory. An analytical formula for calculating the photodetachment cross section of this system is put forward. It is found that the photodetachment cross section of this system is nearly unaffected for the weak oscillating electric field strength, but oscillates complicatedly when the oscillating electric field strength turns strong. In addition, the frequency of the harmonic potential and the oscillating electric field （the frequency of the harmonic potential and the frequency of the oscillating electric field are the same in the paper, unless otherwise stated.） can also affect the photodetachment dynamics of this system. With the increase of the frequency in the harmonic potential and the oscillating electric field, the number of the closed orbits for the detached electrons increased, which makes the oscillatory structure in the photodetachment cross section much more complex. Our study presents an intuitive understanding of the photodetachment dynamics driven by a harmonic potential plus an oscillating electric field from a space and time dependent viewpoint. This study is very useful in guiding the future experimental research for the photodetachment dynamics in the electric field both changing with space and time.

Cortico-striatal gamma oscillations are modulated by dopamine D3 receptors in dyskinetic rats

Long-term levodopa administration can lead to the development of levodopa-induced dyskinesia.Gamma oscillations are a widely recognized hallmark of abnormal neural electrical activity in levodopa-induced dyskinesia.Currently,studies have reported increased oscillation power in cases of levodopa-induced dyskinesia.However,little is known about how the other electrophysiological parameters of gamma oscillations are altered in levodopa-induced dyskinesia.Furthermore,the role of the dopamine D3 receptor,which is implicated in levodopa-induced dyskinesia,in movement disorder-related changes in neural oscillations is unclear.We found that the cortico-striatal functional connectivity of beta oscillations was enhanced in a model of Parkinson’s disease.Furthermore,levodopa application enhanced cortical gamma oscillations in cortico-striatal projections and cortical gamma aperiodic components,as well as bidirectional primary motor cortex(M1)↔dorsolateral striatum gamma flow.Administration of PD128907(a selective dopamine D3 receptor agonist)induced dyskinesia and excessive gamma oscillations with a bidirectional M1↔dorsolateral striatum flow.However,administration of PG01037(a selective dopamine D3 receptor antagonist)attenuated dyskinesia,suppressed gamma oscillations and cortical gamma aperiodic components,and decreased gamma causality in the M1→dorsolateral striatum direction.These findings suggest that the dopamine D3 receptor plays a role in dyskinesia-related oscillatory activity,and that it has potential as a therapeutic target for levodopa-induced dyskinesia.

Oscillation properties of matter–wave bright solitons in harmonic potentials

We investigate the oscillation periods of bright soliton pair or vector bright soliton pair in harmonic potentials. We demonstrate that periods of low-speed solitons are greatly affected by the position shift during their collisions. The modified oscillation periods are described by defining a characterized speed, with the aid of asymptotic analysis on related exact analytic soliton solutions in integrable cases. The oscillation period can be used to distinguish the inter-and intra-species interactions between solitons. However, a bright soliton cannot oscillate in a harmonic trap, when it is coupled with a dark soliton(without any trapping potentials). Interestingly, it can oscillate in an anti-harmonic potential, and the oscillation behavior is explained by a quasi-particle theory. The modified period of two dark-bright solitons can be also described well by the characterized speed. These results address well the effects of position shift during soliton collision, which provides an important supplement for previous studies without considering phase shift effects.

Functional near-infrared spectroscopy can detect low-frequency hemodynamic oscillations in the prefrontal cortex during steady-state visual evoked potentialinducing periodic facial expression stimuli presentation

Brain oscillations are vital to cognitive functions,while disrupted oscillatory activity is linked to various brain disorders.Although high-frequency neural oscillations(>1 Hz)have been extensively studied in cognition,the neural mechanisms underlying low-frequency hemodynamic oscillations(LFHO)<1 Hz have not yet been fully explored.One way to examine oscillatory neural dynamics is to use a facial expression(FE)paradigm to induce steady-state visual evoked potentials(SSVEPs),which has been used in electroencephalography studies of high-frequency brain oscillation activity.In this study,LFHO during SSVEP-inducing periodic flickering stimuli presentation were inspected using functional near-infrared spectroscopy(fNIRS),in which hemodynamic responses in the prefrontal cortex were recorded while participants were passively viewing dynamic FEs flickering at 0.2 Hz.The fast Fourier analysis results demonstrated that the power exhibited monochronic peaks at 0.2 Hz across all channels,indicating that the periodic events successfully elicited LFHO in the prefrontal cortex.More importantly,measurement of LFHO can effectively distinguish the brain activation difference between different cognitive conditions,with happy FE presentation showing greater LFHO power than neutral FE presentation.These results demonstrate that stimuli flashing at a given frequency can induce LFHO in the prefrontal cortex,which provides new insights into the cognitive mechanisms involved in slow oscillation.

The Dynamic Role of Breathing and Cellular Membrane Potentials in the Experience of Consciousness

Understanding the mechanics of consciousness remains one of the most important challenges in modern cognitive science. One key step toward understanding consciousness is to associate unconscious physiological processes with subjective experiences of sensory, motor, and emotional contents. This article explores the role of various cellular membrane potential differences and how they give rise to the dynamic infrastructure of conscious experience. This article explains that consciousness is a body-wide, biological process not limited to individual organs because the mind and body are unified as one entity;therefore, no single location of consciousness can be pinpointed. Consciousness exists throughout the entire body, and unified consciousness is experienced and maintained through dynamic repolarization during inhalation and expiration. Extant knowledge is reviewed to provide insight into how differences in cellular membrane potential play a vital role in the triggering of neural and non-neural oscillations. The role of dynamic cellular membrane potentials in the activity of the central nervous system, peripheral nervous system, cardiorespiratory system, and various other tissues (such as muscles and sensory organs) in the physiology of consciousness is also explored. Inspiration and expiration are accompanied by oscillating membrane potentials throughout all cells and play a vital role in subconscious human perception of feelings and states of mind. In addition, the role of the brainstem, hypothalamus, and complete nervous system (central, peripheral, and autonomic) within the mind-body space combine to allow consciousness to emerge and to come alive. This concept departs from the notion that the brain is the only organ that gives rise to consciousness.

Effects of external fields on a two-dimensional Klein-Gordon particle under pseudo-harmonic oscillator interaction

We study the effects of the perpendicular magnetic and Aharonov-Bohm （AB） flux fields on the energy levels of a two-dimensional （2D） Klein Gordon （KG） particle subjected to an equal scalar and vector pseudo-harmonic oscillator （PHO）. We calculate the exact energy eigenvalues and normalized wave functions in terms of chemical potential param- eter, magnetic field strength, AB flux field, and magnetic quantum number by means of the Nikiforov Uvarov （NU） method. The non-relativistic limit, PHO, and harmonic oscillator solutions in the existence and absence of external fields are also obtained.

Potential vorticity analysis of quasi-biweekly rainfall events over the Yangtze Basin in summer 2014

A series of heavy rainfall events occurred over the Yangtze River Valley(YRV)in summer 2014,which were modulated by the 10-20-day quasi-biweekly oscillation(QBWO).Thus,the strongest QBWO cycle for the period 10-24 July was used as a representative case to reveal the dynamical mechanism for the QBWO of the YRV rainfall from the potential vorticity(PV)perspective and based on MERRA-2 reanalysis data.The quasi-biweekly YRV rainfall was found to depend closely on the QBWO of the upper-tropospheric South Asian high(SAH),with the SAH configuration modified by the southward-intruding midlatitude high PV stream along with southwestward-advected high PV,altering the divergent condition over the YRV.Quantitative diagnoses for the anomalous vertical motion demonstrated that,in the wet phase of the QBWO cycle,the upper-tropospheric southward-intruding high PV stream acted as a positive PV advection,while negative PV advection was generated due to the lower-tropospheric southerlies,thereby forming a positive vertical gradient of horizontal PV advection to induce evident isentropic-displacement ascending motion.On the other hand,the southward-intruding high PV stream extended downward to the middle troposphere,causing the isentropic surfaces to become more sloping,thus producing a strong isentropic-gliding ascending component.Subsequently,the stronger diabatic heating-related ascending motion was induced to generate positive rainfall anomalies over the YRV.The opposite situation arose in the dry phase,with weak descending motion in magnitude.

Exact Quantized Momentum Eigenvalues and Eigenstates of a General Potential Model

We obtain the quantized momentum eigenvalues, Pn, and the momentum eigenstates for the space-like Schrödinger equation, the Feinberg-Horodecki equation, with the general potential which is constructed by the temporal counterpart of the spatial form of these potentials. The present work is illustrated with two special cases of the general form: time-dependent Wei-Hua Oscillator and time-dependent Manning-Rosen potential. We also plot the variations of the general molecular potential with its two special cases and their momentum states for few quantized states against the screening parameter.

An improved potential field method for mobile robot navigation

In order to overcome the inherent oscillation problem of potential field methods(PFMs) for autonomous mobile robots in the presence of obstacles and in narrow passages,an enhanced potential field method that integrates Levenberg-Marquardt(L-M) algorithm and k-trajectory algorithm into the basic PFMs is proposed and simulated.At first,the mobile robot navigation function based on the basic PFMs is established by choosing Gaussian model.Then,the oscillation problem of the navigation function is investigated when a mobile robot nears obstacles and passes through a long and narrow passage,which can cause large computation cost and system instability.At last,the L-M algorithm is adopted to modify the search direction of the navigation function for alleviating the oscillation,while the k-trajectory algorithm is applied to further smooth trajectories.By a series of comparative experiments,the use of the L-M algorithm and k-trajectory algorithm can greatly improve the system performance with the advantages of reducing task completion time and achieving smooth trajectories.

Steady and oscillatory plasma properties in the near-field plume of a hollow cathode

Hollow cathodes serve as electron sources in Hall thrusters,ion thrusters and other electric propulsion systems.One of the vital problems in their application is the cathode erosion.However,the basic erosion mechanism and the source of high-energy ions cause of erosion are not fully understood.In this paper,both potential measurements and simulation analyses were performed to explain the formation of high-energy ions.A high-speed camera,a single Langmuir probe and a floating emissive probe were used to determine the steady and oscillatory plasma properties in the near-field plume of a hollow cathode.The temporal structure,electron temperature,electron density,and both static and oscillation of plasma potentials of the plume have been obtained by the diagnostics mentioned above.The experimental results show that there exists a potential hill（about 30 V） and also severe potential oscillations in the near-plume region.Moreover,a simple 2 D particle-in-cell model was used to analyze the energy transition between the potential hill and/or its oscillations and the ions.The simulation results show that the energy of ions gained from the static potential background is about 20 e V,but it could reach to 60 e V when the plasma oscillates.

Spin Supercurrent in Phenomena of Quantum Non-Locality (Quantum Correlations, Magnetic Vector Potential) and in Near-Field Antenna Effect

It is shown that such phenomena as quantum correlations (interaction of space-separated quantum entities), the action of magnetic vector potential on quantum entities in the absence of magnetic field, and near-field antenna effect (the existence of superluminally propagating electromagnetic fields) may be explained by action of spin supercurrents. In case of quantum correlations between quantum entities, spin supercurrent emerges between virtual particles pairs (virtual photons) created by those quantum entities. The explanation of magnetic vector potential and near-field antenna effect is based on contemporary principle of quantum mechanics: the physical vacuum is not an empty space but the ground state of the field consisting of quantum harmonic oscillators (QHOs) characterized by zero-point energy. Using the properties of the oscillators and spin supercurrent, it is proved that magnetic vector potential is proportional to the moment causing the orientation of spin of QHO along the direction of magnetic field. The near-field antenna effect is supposed to take place as a result of action of spin supercurrent causing secondary electromagnetic oscillations. In this way, the electromagnetic field may spread at the speed of spin supercurrent. As spin supercurrent is an inertia free process, its speed may be greater than that of light, which does not contradict postulates of special relativity that sets limits to the speed of inertial systems only.

Quantum and semiclassical studies on photodetachment cross sections of H^- in a harmonic potential

The photodetachment cross section of H- in a linear harmonic oscillator potential is investigated. This system pro- vides a rare example that can be studied analytically by both quantum and semiclassical methods with some approxi- mations. The formulas of the cross section for different laser polarization directions are explicitly derived by both the traditional quantum approach and closed-orbit theory. In the traditional quantum approach, we calculate the cross sections in coordinate representation and momentum representation, and get the same formulas. We compare the quantum formulas with closed-orbit theory formulas, and find that when the detachment electron energy is larger than hco, where co is the frequency of the oscillator potential, the quantum results are shown to be in good agreement with the semiclassical results.