Wentzel Kramers Brillouin Research Articles

STM/STS Study of the Density of States and Contrast Behavior at the Boundary between (7 × 7)N and (8 × 8) Structures in the SiN/Si(111) System

The origin of the contrast appearing in STM images at the boundary between diverse ordered structures is studied using the example of two structures, (7 × 7)N and (8 × 8), formed in the system of a two-dimensional silicon nitride layer on the Si(111) surface during ammonia nitridation. A significant dependence of the contrast between these structures on the voltage applied to the tunnel gap was found and studied both experimentally and theoretically. Variations in the contrast were quantitatively studied in the range from −3 V to +3 V, and they were studied in more detail for the positive biases on the sample from +1 V to +2.5 V, where the contrast was changed more than 2 times. Within the one-dimensional Wentzel–Kramers–Brillouin (WKB) model for the tunnel current, a comparatively simple procedure is proposed for the correction of the experimental STS-spectra of differential conductivity to identify the adequate (feasible) density of electron states (DOS). It is shown that the (8 × 8) structure DOS corresponds to a graphene-like layer of silicon nitride structure. The proposed correction procedure of the empirical differential conductivity spectra measured by STS will be useful for the quantitative determination of the DOS of new two-dimensional materials and surface structures.

Electron density variability in the day-side ionosphere of Mars: The role of gravity waves

ABSTRACTMars Atmosphere and Volatile EvolutioN (MAVEN) has observed oscillations in the density, velocity, and temperature of ionospheric plasma on Mars. Atmospheric gravity waves can be an underlying mechanism. We propose a linearized wave–electron interaction model adopting a Wentzel–Kramers–Brillouin approximation to explore the electron density variations in the Martian day-side ionosphere for two regions, which are dominated by crustal magnetic fields and horizontal draped interplanetary magnetic fields. Our model results reveal that the electron density fluctuations associated with the crustal magnetic fields and the draped magnetic fields range from ∼ 40 per cent to ∼ 83 per cent and ∼ 29 per cent to ∼ 125 per cent, respectively. The wave-induced vertical electron flux peaks occur in a region ranging from ∼ 115 km to ∼ 179 km altitude. These results are comparable to the satellite observations. We further investigate the effect of the Martian magnetic topology on the wave-induced electron fluxes and demonstrate that the electron motions associated with the propagating gravity waves can be significantly influenced by the magnetic field orientations. The wave-induced variations in the electron temperature, ion density, and magnetic field combined with a comprehensive gravity wave model will be studied in further work.

Scattering from the weakly absorbing cylindrical capsule in the WKB approximation

In this work, the Wentzel-Kramers-Brillouin (WKB) approximation is used to determine the form factor of a particle having a refractive index close to the outer medium. The analytical expression of the light scattering amplitude by a cylinder with conical ends and a cylinder with ellipsoidal ends in a WKB approximation are calculated for a special case, where the direction of incident light is parallel to the axis of revolution of the particle. For illustration, the numerical results are compared with those computed for the cylinder and ellipsoid.

Light scattering by particles of a polygonal-based in the WKB approximation

Using the Wentzel-Kramers-Brillouin (WKB) approximation, we obtain a general analytical expression of the form factor for a particle with polygonal bases in the case where the wave vector of the incident light is parallel to this base. This expression allows a rapid calculation of the form factor for any shape regular particle. After a brief description of the WKB approximation, we present the new calculation of form factor which is based on the geometric decomposition of the particle has simple regions. Finally, for the validation of this expression, we applied it to some special cases.

Lorentzian vacuum transitions with a generalized uncertainty principle

The vacuum transition probabilities between to minima of a scalar field potential in the presence of gravity are studied using the Wentzel–Kramers–Brillouin approximation. First we propose a method to compute these transition probabilities by solving the Wheeler–DeWitt equation in a semi-classical approach for any model of superspace that contains terms of squared as well as linear momenta in the Hamiltonian constraint generalizing in this way previous results. Then we apply this method to compute the transition probabilities for a Friedmann–Lemaitre–Robertson–Walker (FLRW) metric with positive and null curvature and for the Bianchi III metric when the coordinates of minisuperspace obey a Standard Uncertainty Principle and when a Generalized Uncertainty Principle (GUP) is taken into account. In all cases we compare the results and found that the effect of considering a GUP is that the probability is enhanced at first but it decays faster so when the corresponding scale factor is big enough the probability is reduced. We also consider the effect of anisotropy and compare the result of the Bianchi III metric with the flat FLRW metric which corresponds to its isotropy limit and comment the differences with previous works.

Inflation and Fractional Quantum Cosmology

The Wheeler–DeWitt equation for a flat and compact Friedmann–Lemaître–Robertson–Walker cosmology at the pre-inflation epoch is studied in the contexts of the standard and fractional quantum cosmology. Working within the semiclassical regime and applying the Wentzel-Kramers-Brillouin (WKB) approximation, we show that some fascinating consequences are obtained for our simple fractional scenario that are completely different from their corresponding standard counterparts: (i) The conventional de Sitter behavior of the inflationary universe for constant potential is replaced by a power-law inflation. (ii) The non-locality of the Riesz’s fractional derivative produces a power-law inflation that depends on the fractal dimension of the compact spatial section of space-time, independent of the energy scale of the inflaton.

Theoretical Study of Carrier Transport in Metal–Ferroelectric–Insulator–Semiconductor Ferroelectric Tunnel Junction Memristor

Ferroelectric tunnel junction (FTJ) based on the metal–ferroelectric–insulator–semiconductor (MFIS) stacks shows great potential in neuromorphic and in-memory computing. Tunneling current in the MFIS-FTJ can be calculated by the Wentzel–Kramers–Brillouin (WKB) method with the band profile solved from Poisson’s equation or by self-consistently solving Poisson’s equation and the drift-diffusion transport equations with a tunneling-induced carrier generation rate. The carrier redistribution in the semiconductor is neglected in the former method, which reduces the complexity and saves the computational cost but may or may not lead to significant errors. In this article, a comprehensive study of the two simulation methods mentioned above is performed to investigate their applicable conditions and balance the accuracy and computational cost. The current densities of the MFIS-FTJs with different material parameters, including the barrier width, barrier height, carrier mobility, and polarization charge density simulated by the two methods, are compared and analyzed. As the voltage drop across the semiconductor cannot be neglected, method II is required to take the carrier transport in the semiconductor into account and method I is not accurate; otherwise, method I is more suitable due to its low computational cost without loss of accuracy.

Impact of Interface Traps in Floating-Gate Memory Based on Monolayer MoS

Two-dimensional materials (2DMs) have found potential applications in many areas of electronics, such as sensing, memory systems, optoelectronics, and power. Despite an intense experimental work, the literature is lacking of accurate modeling of nonvolatile memories (NVMs) based on 2DMs. In this work, using technology CAD simulations and model calibration with experiments, we show that the experimental program/erase characteristics of floating-gate (FG) memory devices based on monolayer molybdenum disulphide can be explained by considering bandgap trap states at the dielectric–semiconductor interface. The simulation model includes a classical approach based on drift-diffusion longitudinal channel transport and on nonlocal Wentzel–Kramers–Brillouin (WKB) tunneling for transversal transport (responsible of FG charging/discharging) and for tunneling at contacts. From hysteresis and pulse programming simulations on scaled devices, we find that the long-channel programming window is still maintained at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim 100$ </tex-math></inline-formula> nm and that process improvements aimed at reducing the concentration of interface traps in the semiconducting bandgap could significantly optimize memory operation.

Favored one proton radioactivity within a one-parameter model* *Supported by National Natural Science Foundation of China (Grant No.12175100 and No. 11705055), the construct program of the key discipline in Hunan province, the Research Foundation of Education Bureau of Hunan Province, China (Grant No. 18A237), the Innovation Group of Nuclear and Particle Physics in USC, the Shandong Province Natural Science Foundation,

In the present work, a phenomenological one-parameter model (OPM) based on the Wentzel-Kramers-Brillouin (WKB) theory is applied to study the favored one proton radioactivity (the orbital angular momentum l taken away by the emitted proton is equal to zero) half-lives. The calculated results can reproduce the experimental data well within a factor of ∼3. In addition, we extend the OPM to predict the half-lives of possible favored one proton radioactivity nuclei whose decay is energetically allowed or observed but not quantified in NUBASE2020. For comparison, a universal decay law of one proton radioactivity (UDLP) is also used. It is obviously found that our predicted results are close to the ones using UDLP. The predictions are helpful for searching for the new nuclides with favored one proton radioactivity.

Quasinormal modes and thermodynamic properties of GUP-corrected Schwarzschild black hole surrounded by quintessence

We study the Quasinormal Modes (QNMs) of the Schwarzschild black hole surrounded by a quintessence field after implementing the quantum corrections to its solution as required by the Generalized Uncertainty Principle (GUP). We analyze the dependence of the QNMs on the deformation parameters of GUP as well as on the quintessence parameter. In most cases the QNMs show the appreciable dependency on these parameters. For a better idea of the accuracy of calculations of QNMs, we compare the results of the QNMs obtained via Mashhoon method with the sixth-order Wentzel–Kramers–Brillouin method. A good agreement between these two methods of QNM calculations is seen depending on the different factors. Further, we study the thermodynamic properties of the GUP-corrected Schwarzschild black hole and check for any dependence with the deformation parameters and the quintessence parameter. In particular, we compute the Hawking temperature, heat capacity and entropy for the black hole and analyze the results graphically to show the dependency of the thermodynamic properties on the said parameters. We have seen that the thermodynamic properties of black holes also depend noticeably on the model parameters in most cases. Black hole remnants have been studied and it is shown that the possible existence of remnant radius as well as remnant temperature depends on the deformations introduced. However, it is observed that the GUP-corrected black hole constructed here cannot become a remnant.

Novel Wentzel–Kramers–Brillouin Solutions to the Nonisentropic Helmholtz Equation in a Nonuniform Duct With Mean Temperature Gradient and Mean Flow

Abstract We derive the generalized Helmholtz equation (GHE) governing nonisentropic acoustic fluctuations in a quasi 1D duct with nonuniform cross section, mean temperature gradient, and nonuniform mean flow. Nonisentropic effects are included via heat conduction terms in the mean and fluctuating energy equations. To derive the Helmholtz equation exclusively in terms of the fluctuating pressure field, a relationship between density and pressure fluctuations is needed, which is shown to be a second-order differential equation for nonisentropic motions. Novel analytical solutions that are accurate for both low/high frequencies and small/large mean gradients are presented for the GHE based on the Wentzel–Kramers–Brillouin (WKB) method. WKB solutions are developed using the ansatz that the pressure fluctuation field has a travelling wave form, p^(x)=exp[∫0x(a+ib)dx], where x is the axial coordinate. Substituting this form into the Helmholtz equation yields coupled, nonlinear ordinary differential equations (ODEs) for a and b. Analytical solutions to the ODEs are obtained using the approximations of high frequency and slowly varying mean properties. This simplification allows us to obtain the lower order solutions b0 and a0. We then enhance solution accuracy by using a0 to solve for b1 without any approximations. Finally, b1 is employed to get a1, giving us the higher order solution. The p^ calculated from (a1, b1) is in good to excellent agreement with numerical solution of the GHE for both low and high frequencies and for a range of mean Mach numbers, including M¯≳1.

Systematic calculations of cluster radioactivity half-lives in trans-lead nuclei* *This work is supported in part by the National Natura Science Foundation of China (12175100 and 11975132), the Construct Program of the Key Discipline in Hunan Province, the Research Foundation of Education Bureau of Hunan Province (18A237), the Natural Science Foundation of Hunan Province (2018JJ3324), the Innovation Group of Nuclear and

In the present work, based on the Wentzel-Kramers-Brillouin (WKB) theory, considering the cluster preformation probability (), we systematically investigate the cluster radioactivity half-lives of 22 trans-lead nuclei ranging from 221Fr to 242Cm. When the mass number of the emitted cluster 28, is obtained by the exponential relationship of to the α decay preformation probability () proposed by R. Blendowskeis [Phys. Rev. Lett. 61, 1930 (1988)], while is calculated through the cluster-formation model (CFM). When 28, is calculated through the charge-number dependence of on the decay products proposed by Ren [Phys. Rev. C 70, 034304 (2004)]. The half-lives of cluster radioactivity have been calculated by the density-dependent cluster model [Phys. Rev. C 70, 034304 (2004)] and by the unified formula of half-lives for alpha decay and cluster radioactivity [Phys. Rev. C 78, 044310 (2008)]. For comparison, a universal decay law (UDL) proposed by Qi [Phys. Rev. C 80, 044326 (2009)], a semi-empirical model for both α decay and cluster radioactivity proposed by Santhosh [J. Phys. G: Nucl. Part. Phys. 35, 085102 (2008)], and a unified formula of half-lives for alpha decay and cluster radioactivity [Phys. Rev. C 78, 044310 (2008)] are also used. The calculated results of our work, Ni's formula , and the UDL can well reproduce the experimental data and are better than those of Santhosh's model. In addition, we extend this model to predict the half-lives for 51 nuclei, whose cluster radioactivity is energetically allowed or observed but not yet quantified in NUBASE2020.

Asymptotic Green’s function solutions of the general relativistic thin disc equations

ABSTRACT The leading order Green’s function solutions of the general relativistic thin disc equations are computed, using a pseudo-Newtonian potential and asymptotic Laplace mode matching techniques. This solution, valid for a vanishing innermost stable circular orbit (ISCO) stress, is constructed by ensuring that it reproduces the leading order asymptotic behaviour of the near-ISCO, Newtonian, and global Wentzel–Kramers–Brillouin limits. Despite the simplifications used in constructing this solution, it is typically accurate, for all values of the Kerr spin parameter a and at all radii, to less than a per cent of the full numerically calculated solutions of the general relativistic disc equations. These solutions will be of use in studying time-dependent accretion discs surrounding Kerr black holes.

Regulation of stem cell dynamics through volume exclusion

The maintenance and regeneration of adult tissues rely on the self-renewal of stem cells. Regeneration without over-proliferation requires precise regulation of the stem cell proliferation and differentiation rates. The nature of such regulatory mechanisms in different tissues, and how to incorporate them in models of stem cell population dynamics, is incompletely understood. The critical birth-death (CBD) process is widely used to model stem cell populations, capturing key phenomena, such as scaling laws in clone size distributions. However, the CBD process neglects regulatory mechanisms. Here, we propose the birth-death process with volume exclusion (vBD), a variation of the birth-death process that considers crowding effects, such as may arise due to limited space in a stem cell niche. While the deterministic rate equations predict a single non-trivial attracting steady state, the master equation predicts extinction and transient distributions of stem cell numbers with three possible behaviours: long-lived quasi-steady state (QSS), and short-lived bimodal or unimodal distributions. In all cases, we approximate solutions to the vBD master equation using a renormalized system-size expansion, QSS approximation and the Wentzel–Kramers–Brillouin method. Our study suggests that the size distribution of a stem cell population bears signatures that are useful to detect negative feedback mediated via volume exclusion.

Implementation and validation of a three-dimensional semi-coherent energy flux model for underwater acoustic propagation

The energy flux method uses a continuum of adiabatic Wentzel–Kramers–Brillouin modes to integrate intensity directly as a function of propagation angle. Work published a decade ago extended the energy flux method to include semi-coherent interference between neighboring modes to capture convergence zones. This study seeks to generalize the energy flux method to three-dimensional inhomogeneous underwater environments by converting a cross-product of double mode-sums to a double integration over solid angle. Theoretical derivations for a proof of concept model were presented previously, and current work has been focused on the numerical implementation of the model. Model validation will be discussed with comparisons to analytical solutions and other three-dimensional underwater acoustic propagation models.

Asymptotics of eigenvalue sums when some turning points are complex

Recent work has shown a deep connection between semilocal approximations in density functional theory and the asymptotics of the sum of the Wentzel–Kramers–Brillouin (WKB) semiclassical expansion for the eigenvalues. However, all examples studied to date have potentials with only real classical turning points. But systems with complex turning points generate subdominant (SD) terms beyond those in the WKB series. The simplest case is a pure quartic oscillator. We show how to generalize the asymptotics of eigenvalue sums to include SD contributions to the sums, if they are known for the eigenvalues. These corrections to WKB greatly improve accuracy for eigenvalue sums, especially for many levels. We obtain further improvements to the sums through hyperasymptotics. For the lowest level, our summation method has error below 2 × 10−4. For the sum of the lowest ten levels, our error is less than 10−22. We report all results to many digits and include copious details of the asymptotic expansions and their derivation.

WKB approximation with conformable operator

In this paper, the Wentzel–Kramers–Brillouin (WKB) method is extended to be applicable for conformable Hamiltonian systems, where the concept of conformable operator with fractional order [Formula: see text] is involved. The WKB approximation for the [Formula: see text]-wave function is derived for potentials which slowly vary in space. Some illustrative examples to demonstrate the method are presented. The quantities of the conformable form are found to be in exact agreement with the corresponding traditional quantities when [Formula: see text].

A simple estimation of OLED light extraction enhancement due to refractive modulation lattice diffraction

To estimate the light extraction enhancement of an organic light emitting diode due to a periodic refractive modulation lattice simulating a photonic or plasmonic lattice, a noniterative scheme was proposed based on the Wentzel–Kramers–Brillouin solution used to calculate the input/output efficiency of a refractive index grating coupler for optical circuits, treating the lattice as a two-dimensional Bravais lattice.

Sampling rare trajectories using stochastic bridges.

The numerical quantification of the statistics of rare events in stochastic processes is a challenging computational problem. We present a sampling method that constructs an ensemble of stochastic trajectories that are constrained to have fixed start and end points (so-called stochastic bridges). We then show that by carefully choosing a set of such bridges and assigning an appropriate statistical weight to each bridge, one can focus more processing power on the rare events of a target stochastic process while faithfully preserving the statistics of these rare trajectories. Further, we also compare the stochastic bridges we produce to the Wentzel-Kramers-Brillouin (WKB) optimal paths of the target process, derived in the limit of low noise. We see that the generated paths, encoding the full statistics of the process, collapse onto the WKB optimal path as the level of noise is reduced. We propose that the method can also be used to judge the accuracy of the WKB approximation at finite levels of noise.

Effect of Asymmetry in the Modulation Parameters on Self-Focusing of Asymmetric Finite Airy-Gaussian Laser Beam in Collisionless Plasma

The self-focusing/defocusing of asymmetric finite Airy-Gaussian (AiG) laser beam has been investigated by employing standard Wentzel–Kramers–Brillouin (WKB) and paraxial-ray approximations in a nonrelativistic regime for underdense plasma. The second-order non-linear coupled differential equations have been solved numerically by using the fourth-order Range-Kutta method. The effect of asymmetry in the modulation parameters on the self-focusing/defocusing of the asymmetric finite AiG laser beam in collisionless plasma has been studied. It is observed that the self-focusing/ defocusing of asymmetric finite AiG laser beam is strongly connected with the initial values of the laser and plasma parameters such as modulation parameters and plasma frequency.