Wentzel Kramers Brillouin Research Articles

Effects of deformation on the cluster and the [formula omitted]-decay half-lives for isotopes of the Trans-lead and the undetected superheavy nuclei

In the present investigation, based on the Wentzel–Kramers–Brillouin (WKB) approximation, and by considering deformation of the cluster and the daughter nuclei, the cluster radioactivity half-lives of 22 Trans-lead isotopes ranging from 221Fr to 242Cm are calculated. Also, the α-decay half-lives of even–even isotopes for the superheavy nuclei with Z in the range 104≤Z≤118 are computed. For the cluster radioactivity, a preformation factor, Pc depending on the atomic numbers of the cluster and the daughter nuclei is used according to the Santhosh and Jose (2021). The α preformation factor, Pα is evaluated based on the cluster-formation model (CFM). A universal decay law (UDL) proposed by Qi et al. (2009), was used to obtain the decay half-lives of the cluster and the α-decay for checking the credibility of our approach. The effects of the deformation of decay products on the half-lives of the cluster and the α-decay have also been investigated by comparing the obtained half-lives considering deformation with ones of the spherical nuclei and the results of the UDL as well as the available experimental data. Comparison indicates that our calculated cluster and α-decay half-lives considering deformation reproduce the experimental data more accurately than the UDL and the spherical nuclei. Furthermore, the cluster radioactivity half-lives of some isotopes that whose cluster radioactivity is energetically allowed but not observed preciously yet, are predicted. Also, the cluster and the α-decay half-lives and the branching ratios between them for some not yet discovered superheavy isotopes with Z=122 and Z=124 are obtained.

Propagation of twisted laser carrying orbital angular momentum in magnetized plasma

The propagation of electromagnetic beams carrying orbital angular momentum l is investigated in a cold collisionless plasma where a static magnetic field is applied in the axial direction. The relativistic and ponderomotive nonlinearities are taken into consideration simultaneously. A stationary nonlinear Schrödinger equation is derived using the Wentzel–Kramers–Brillouin method and the slowly varying envelope approximation. The critical condition for the self-trapped mode is achieved as a function of orbital angular momentum (OAM), magnetic field, and initial laser intensity of the beam. The response of the medium to the two types of polarizations, i.e., left circular polarization (LCP) and right circular polarization (RCP), is compared, and it is observed that the RCP laser shows better focusing than the LCP laser and also requires a smaller beam radius for achieving the self-trapped mode. The effect of applied magnetic field and OAM of the laser is also studied on the beam width evolution. The laser is found to be focused earlier in the cases of a larger applied magnetic field. A Laguerre–Gaussian laser with higher OAM is observed to show efficient self-focusing. This study enables exploration in the fields of particle acceleration, electron bunch generation, x-ray sources, and more.

Quasinormal Spectrum of (2+1)$(2+1)$‐Dimensional Asymptotically Flat, dS and AdS Black Holes

AbstractWhile ‐dimensional black holes in the Einstein theory allow for only the anti‐de Sitter (AdS) asymptotic, when the higher curvature correction is tuned on, the asymptotically flat, de Sitter, and AdS cases are included. Here, a detailed study of the stability and quasinormal spectra of the scalar field perturbations around such black holes with all three asymptotics is proposed. Calculations of the frequencies are fulfilled with the help of the 6th order Wentzel–Kramers–Brillouin (WKB) method with Pade approximants, Bernstein polynomial method, and time‐domain integration. Results obtained by all three methods are in a very good agreement in their common range of applicability. When the multipole moment is equal to zero, the purely imaginary, i.e., non‐oscillatory, modes dominate in the spectrum for all types of the asymptotic behavior, while the spectrum at higher resembles that in four‐dimensional spacetime with the corresponding asymptotic.

Analysis of Deep-Water Low-Frequency Sound Multipath Arrivals and Interference Striation Patterns

The deep-water sound multipath arrivals and interference striation patterns not only vary with range and depth but also with frequency. The first two cases can be solved using a ray-mode method in the high-frequency limit. However, this method may cause unsatisfactory results in treating low-frequency sounds (as low as tens of Hertz) because of the Wentzel-Kramers-Brillouin (WKB) high-frequency approximation assumption. To overcome this problem, the authors exploited phase information to modify the ray parameters, such as the propagation range, the time delay, and the group velocity. Following that, a waveguide invariant (WI) expression was derived to address low-frequency sound interference problems. Numerical investigations demonstrated that the physical mechanism of the frequency dependence of the multipath arrivals and interference striation patterns could be better understood using this modified ray-mode method. In addition, the influence of bottom sound speed on multipath interference structures is also considered.

Effect of mutual interaction of two cosh-Gaussian laser beams on upper hybrid wave excitation and subsequent electron acceleration

This paper presents the excitation of an upper hybrid wave by resonant excitation of two intense cosh-Gaussian laser beams of frequencies ω 1 and ω 2 in a collisionless plasma. The excited upper hybrid wave is used for electron acceleration which accelerates the electrons towards higher energy. The acceleration of electrons through an excited upper hybrid wave has also been studied. This study has been analysed using the Wentzel Kramers Brillouin (WKB) and paraxial-ray approximation, where relativistic and ponderomotive nonlinearities are employed together. Analytical expressions for the beam width/intensity of the cosh-Gaussian laser beams, the electric field/power of the excited upper hybrid wave and the electron acceleration have been derived, which have been solved numerically for an established set of laser and plasma parameters. The results are also compared to relativistic nonlinearity. It has been observed that the mutual interaction of two cosh-Gaussian laser beams at a difference frequency significantly affects the self-focusing of each beam, leading to an increase in the amplitude/power of the upper hybrid wave as well as energy gain by the electrons. The effect of the magnetic field (ωc) and decentered parameter (b) on the power of the excited upper hybrid wave and the energy gain by the electrons are also explored. The results show that the power of upper hybrid wave and the energy gain by the electrons increase at higher values ​​of b and ω c.

Functional Formulation of Quantum Theory of a Scalar Field in a Metric with Lorentzian and Euclidean Signatures.

We study the Schrödinger equation in quantum field theory (QFT) in its functional formulation. In this approach, quantum correlation functions can be expressed as classical expectation values over (complex) stochastic processes. We obtain a stochastic representation of the Schrödinger time evolution on Wentzel-Kramers-Brillouin (WKB) states by means of the Wiener integral. We discuss QFT in a flat expanding metric and in de Sitter space-time. We calculate the evolution kernel in an expanding flat metric in the real-time formulation. We discuss a field interaction in pseudoRiemannian and Riemannian metrics showing that an inversion of the signature leads to some substantial simplifications of the singularity problems in QFT.

Heavy mesons mass spectroscopy under a spin-dependent Cornell potential within the framework of the spinless Salpeter equation

Abstract The energy bound-state solutions of the spinless Salpeter equation (SSE) have been obtained under a spin-dependent Cornell potential function via the Wentzel–Kramers–Brillouin approximation. The energy levels were applied to predict the mass spectra for the charmonium, bottomonium, and bottom-charmed mesons. The relativistic corrections for the angular momentum quantum number l > 0 l\gt 0 , total angular momentum quantum numbers j = l , j = l ± 1 j=l,\hspace{.3em}j=l\pm 1 , and the radial quantum numbers n = 1–4 improve the mass spectra. The results agree fairly with experimental data and theoretic results reported in existing works, where the authors utilized different forms of the inter-quark potentials and methods. The deviation of the obtained masses for the charmonium and bottomonium from the observed data yields a total percentage error of 3.32 and 1.11%, respectively. The results indicate that the accuracy of the masses is correlated with the magnitude of masses for the charm and bottom quarks. The SSE together with the phenomenological spin-dependent Cornell potential provides an adequate account of the mass spectroscopy for the heavy mesons and may be used to predict other spectroscopic parameters.

SPRAY: A smoothed particle radiation hydrodynamics code for modeling high intensity laser-plasma interactions

Here we report the development of SPRAY, a massively parallel GPU accelerated, smoothed particle hydrodynamics (SPH)-based, radiation hydrodynamics (RHD) code designed specifically for simulating high intensity laser-plasma interactions. When a target is irradiated by an intense laser, highly complex fluid deformation occurs due to instabilities, which is challenging to study numerically. SPRAY is particle-based, mesh-free, and Lagrangian, which addresses numerical issues that posed difficulties to existing methods. Its SPH formulations for RHD governing equations are tailored toward accurate and reliable simulations of laser-target irradiation phenomena, and are solved via a time-dependent, flux-limited diffusion method. A new laser energy coupling module, which is based on the Wentzel-Kramers-Brillouin (WKB) approximation, is implemented with a totally mesh-free ray-tracing scheme that is applicable for arbitrary geometry and dimensions. The accuracy and reliability of the code are demonstrated with a series of benchmark problems. To the authors' knowledge, this is the first attempt to employ SPH method for simulations of laser-plasma interactions in high energy density physics research. Possible expansions to the code, such as laser beam-beam interaction modeling and more sophisticated multi-group radiation transport are left for future development.

Surface wrinkling of a film coated to a graded substrate

We study the surface wrinkling of a stiff thin elastic film bonded to a compliant graded elastic substrate subject to compressive stress generated either by compression or growth of the bilayer. Our aim is to clarify the influence of the modulus gradient on the onset and surface pattern in this bilayer. Within the framework of finite elasticity, an exact bifurcation condition is obtained using the Stroh formulation and the surface impedance matrix method. Further analytical progress is made by focusing on the case of short wavelength limit for which the Wentzel–Kramers–Brillouin method can be used to resolve the eigenvalue problem of ordinary differential equations with variable coefficients. An explicit bifurcation condition is obtained from which the critical buckling load and the critical wavelength are derived asymptotically. In particular, we consider two distinct situations depending on the ratio β of the shear modulus at the substrate surface to that at infinity. If β is of O(1) or small, the parameters related to modulus gradient all appear in the higher-order terms and play an insignificant role in the bifurcation. In that case, it is the modulus ratio between the film and substrate surface that governs the onset of surface wrinkling. If, however, β≫1, the modulus gradient affects the critical condition through leading-order terms. Through our analysis we unravel the influence of different material and geometric parameters, including the modulus gradient, on the bifurcation threshold and the associated wavelength which can be of importance in many biological and technological settings.

Terminator effect in the model Schumann resonance signals

We model Schumann resonance (SR) amplitude variations driven by the diurnal and seasonal motion of the day–night interface in the Earth – ionosphere cavity that is regarded as the terminator effect. The current moment of the equatorial source is a constant. The observer occupies the middle, the high latitudes, or the South Pole. Vertical electric field is calculated at the frequencies 8, 14, and 20 Hz. The following results were obtained. Amplitude modulations relevant to the day-night interface acquire ubiquitous patterns in the local time of the observer. The date–time changes have a convex lens-like structure at the mid-latitude observatory. The simultaneous displacement of the source and observer along the longitude causes an appropriate shift of the date–time pattern plotted in the universal time (UT). Relocation of the observer from the Northern to the Southern Hemisphere shifts the pattern by 6 months. These changes might totally alter the outline of the observed “12 months - 24 h” pattern. The shape of date–time variation alters from the convex lens-like to the cross-like when the observer is located in the high latitudes owing to the polar day and the polar night periods. When the observatory occupies a geographic pole, the season-diurnal variations resemble a ‘chessboard’. The Wentzel – Kramers – Brillouin (WKB) approximation allows obtaining the general outline of the date–time variations. The data obtained might be interpreted as a combination of two effects. The first one forms the general outline of temporal changes; and it is linked to the height of the Earth-ionosphere cavity above the source and the observer. The second one is related to "reflections" of ELF radio waves from the day–night interface, and it drives oscillations with the period equivalent to the wavelength at the particular frequency. All effects are related to the position of the day–night interface and occur in the observer's local time. The range of amplitude modulations in a non-uniform cavity is of ± (10–15)% relative to the average amplitude.

Analysis of tunneling probability in heavily doped 4H-SiC Schottky barrier diodes based on complex band structure considering barrier potential

The tunneling probability in heavily doped 4H-SiC Schottky barrier diodes (SBDs) is analyzed based on the empirical pseudopotential method (EPM). A method of calculating the tunneling probability within the WKB approximation using the EPM electronic states of bulk 4H-SiC has been reported. In the present study, to investigate the validity of this method, the tunneling probability is calculated by connecting the incident, transmitted, and reflected wavefunctions considering the barrier potential of a SBD instead of using the WKB approximation. Comparing the calculated results with and without the WKB approximation, the difference is found to be rather small. This suggests that we can safely use the WKB approximation with the bulk electronic states, which are obtained without considering the barrier potential, when calculating the tunneling current in the heavily doped 4H-SiC SBDs.

Self-focusing/defocusing of skew-cosh-Gaussian laser beam for collisional plasma

The inverse relationship between the linear increase in skewness parameter s and the domain’s width of the order of skewness n plays a vital role in both critical beam radius and propagation dynamics of skew-cosh-Gaussian (skew-chG) laser beams. The interplay between the skewness parameter s and the order of skewness n is explored analytically and graphically in the current study to unveil the complexity of the propagation dynamics of the skew-chG laser beam. Naturally, the intensity’s complexity considerably affects the dielectric constant of the medium. Basically, the nonlinearity in the dielectric function of collisional plasma is attributed to the non-uniform heating of energy carriers along the wavefront of the laser beam, which becomes important and is used in the current study. By following Akhmanov’s parabolic wave equation approach under Wentzel–Kramers–Brillouin and paraxial approximations, the nonlinear differential equations are set up for the beam width parameters f 1 and f 2 and solved numerically. The present work analytically investigates the domains of the order n of skew-chG laser beams for a given set of skewness parameter s to investigate their effects on the self-focusing and defocusing of skew-chG laser beams. The critical curve also gets affected significantly due to the choice of domains for n. Finally, the numerical results are presented in the form of graphs and discussed in this study.

Non‐Thermal Oxygen Escape on Mars in the Presence of Gravity Waves

AbstractExtensive measurements made over the past two decades have indicated the widespread and frequent occurrence of gravity waves in the atmosphere of Mars. Gravity waves are able to significantly modify the atmospheric structure and potentially affect atmospheric escape. This study is devoted to examining the hot O escape variability on Mars in the presence of gravity waves with the aid of the Wentzel–Kramers–Brillouin approximation and the multi collision model as well as the multi‐instrument MAVEN data set. Our calculations suggest that the hot O escape probability tends to be enhanced or suppressed in the presence of gravity waves near the Martian exobase and the impacts vary substantially with the ejection angle and nascent energy of hot O, and gravity wave characteristics. Further study indicates that although gravity waves play a negligible role in the averaged hot O escape probability, they are able to enhance hot O escape flux by 20% via altering the hot O production rate rather. Since gravity waves are omnipresent on any planetary body with a permanent atmosphere, they are expected to affect the non‐thermal escape on solar system and extrasolar bodies.

Gravitational traces of bumblebee gravity in metric–affine formalism

This work explores various manifestations of bumblebee gravity within the metric–affine formalism. We investigate the impact of the Lorentz violation parameter, denoted as X, on the modification of the Hawking temperature. Our calculations reveal that as X increases, the values of the Hawking temperature attenuate. To examine the behavior of massless scalar perturbations, specifically the quasinormal modes, we employ the Wentzel–Kramers–Brillouin method. The transmission and reflection coefficients are determined through our calculations. The outcomes indicate that a stronger Lorentz–violating parameter results in slower damping oscillations of gravitational waves. To comprehend the influence of the quasinormal spectrum on time–dependent scattering phenomena, we present a detailed analysis of scalar perturbations in the time–domain solution. Additionally, we conduct an investigation on shadows, revealing that larger values of X correspond to larger shadow radii. Furthermore, we constrain the magnitude of the shadow radii using the EHT horizon–scale image of SgrA∗ . Finally, we calculate both the time delay and the deflection angle.

The waveguide invariant close to the deep-water bottom

Waveguide invariant, denoted by β, describes the dispersive nature of the underwater acoustic waveguide. In most range-independent shallow-water waveguides β≈1, whereas β is no longer constant in deep water and is more appropriately described by a distribution. This paper investigates the characteristic of β close to the deep-water bottom. The adiabatic normal mode theory is used to analyze β resulting from the bottom-bounce dominated acoustic field qualitatively. Then, the Wentzel–Kramers–Brillouin approximation with bottom reflection phase shift and the dominance of the acoustic field by groups of modes are employed to amend the original waveguide invariant theory. The interference between the phase-compensated dominant modal groups is calculated to obtain the value of β and analyze the distribution in the two-dimensional spectrum of the interference pattern. For a typical deep-water waveguide, both qualitative and quantitative analyses indicate that β≈1 when close to the bottom instead of a distribution. Simulation and experiment data demonstrate that the interference between phase-compensated dominant modal groups produces particular structure in the two-dimensional spectrum resulting from β being approximately equal to 1. The characteristic of β proposed in this paper has potential application in remote ranging the underwater acoustic source in deep water, which is verified using experimental data.

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New collision integrals and transport cross sections for O(3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{3}$$\\end{document}P)–O(3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{3}$$\\end{document}P) interaction are reported in the 300–30000 K range. Those values are based on a new set of potential energy curves (PECs) calculated with the multireference configuration interaction method. The results of the classical and semiclassical WKB (Wentzel–Kramers–Brillouin) methods are compared, excellent performance of the classical approach is shown (discrepancy much lower than 1% even at room temperature). In particular, the classical and WKB methods agree very well for the repulsive potentials effectively reducing overall uncertainty.

Floquet-based analysis on three-dimensional non-axisymmetric instabilities in oscillatory-driven Taylor–Couette flows and their low-frequency asymptotic behavior using Wentzel–Kramers–Brillouin method

This paper revisits the linear stability analysis of oscillatory-driven flows between two oscillating cylinders against non-axisymmetric disturbances. This study is motivated by the lack of a sufficiently reliable theoretical analysis giving insight into the experimentally observed spiral-like non-axisymmetric patterns when the cylinders are counter-oscillating. A new generalized time-dependent algebraic eigenvalue problem is constructed from the linearized set of the three-dimensional Navier–Stokes equations around the purely azimuthal basic state. Numerical evaluation of the critical eigenvalues combining both Floquet theory and spectral method reveals the existence of frequency ranges where this basic state becomes unstable against three-dimensional non-axisymmetric disturbances before it does so for two-dimensional axisymmetric ones. Indeed, as the oscillation frequency of the cylinders increases, the azimuthal wave number of the critical eigensolution is found to change from 0 to 2 to 1 and then back to 0. The primary bifurcation exchange between two instability modes with different azimuthal wave numbers occurs via different types of codimension-2 bifurcation points giving rise to discontinuities in the critical axial wave number where reversing and non-reversing non-axisymmetric Taylor vortex flows are identified. In addition, by extending our numerical calculations to the co-oscillating case, we show that the axisymmetric disturbances are the most unstable confirming thus existing experimental findings. Furthermore, a Wentzel–Kramers–Brillouin (WKB) analysis is performed to shed light on the asymptotic behavior of these time-dependent flows in the low-frequency limit when the cylinders are slowly oscillating.

Tunneling splittings in the vibrationally excited states of water trimer.

Tunneling splitting (TS) patterns in vibrationally excited states of the water trimer are calculated, taking into account six tunneling pathways that describe the flips of free OH bonds and five bifurcation mechanisms that break and reform hydrogen bonds in the trimer ring. A tunneling matrix (TM) model is used to derive the energy shifts due to tunneling in terms of the six distinct TM elements in symbolic form. TM elements are calculated using the recently-developed modified WKB (Wentzel-Kramers-Brillouin) method in full dimensionality. Convergence was achieved for the lowest six excited vibrational modes. Bifurcation widths of the pseudorotational quartets are shown to be of comparable size to the ground-state widths, obtained using instanton theory, or increased for some particular modes of vibration. The largest increase is obtained for the excited out-of-phase flip of two adjacent water monomers with free OH bonds pointing in opposite directions relative to the ring plane. Bifurcation widths in (D2O)3 are found to be two orders of magnitude smaller than in (H2O)3. Geometrical arguments were used to explain the order of states in some TS multiplets in vibrationally excited water trimers.

Large deviations for trajectory observables of diffusion processes in dimension d > 1 in the double limit of large time and small diffusion coefficient

For diffusion processes in dimension d > 1, the statistics of trajectory observables over the time-window [0,T] can be studied via the Feynman–Kac deformations of the Fokker–Planck generator, which can be interpreted as Euclidean non-Hermitian electromagnetic quantum Hamiltonians. It is interesting to compare the four regimes corresponding to the time T, either finite or large, and to the diffusion coefficient D, either finite or small. (1) For finite T and finite D, one needs to consider the full time-dependent quantum problem that involves the full spectrum of the Hamiltonian. (2) For large time T→+∞ and finite D, one only needs to consider the ground-state properties of the quantum Hamiltonian to obtain the generating function of rescaled cumulants and to construct the corresponding canonical conditioned processes. (3) For finite T and D → 0, one only needs to consider the dominant classical trajectory and its action satisfying the Hamilton–Jacobi equation, as in the semi-classical Wentzel–Kramers–Brillouin (WKB) approximation of quantum mechanics. (4) In the double limit T→+∞ and D → 0, the simplifications in the large deviations in TD of trajectory observables can be analyzed via the two orders of limits, i.e. either from the limit D → 0 of the ground-state properties of the quantum Hamiltonians of (2), or from the limit of long classical trajectories T→+∞ in the semi-classical WKB approximation of (3). This general framework is illustrated in dimension d = 2 with rotational invariance.

Foundations of the Wentzel-Kramers-Brillouin approximation for models of cochlear mechanics in 1- and 2-D.

The Wentzel-Kramers-Brillouin (WKB) approximation is frequently used to explore the mechanics of the cochlea. As opposed to numerical strategies, the WKB approximation facilitates analysis of model results through interpretable closed-form equations and can be implemented with relative ease. As a result, it has maintained relevance in the study of cochlear mechanics for half of a century. Over this time, it has been employed to study a variety of phenomena, including the limits of frequency tuning, active displacement amplification within the organ of Corti, feedforward mechanisms in the cochlea, and otoacoustic emissions. Despite this ubiquity, it is challenging to find rigorous exposition of the WKB approximation's formulation, derivation, and implementation in cochlear mechanics literature. In this tutorial, the foundations of the WKB approximation are discussed in application to models of one- and two-dimensional cochlear macromechanics. This includes mathematical background, rigorous derivation and details of its implementation in software.