Semiclassical Approximation Method Research Articles

The condensation of ideal Bose gas in a gravitational field in the framework of Dunkl-statistic

In the framework of the theory of Dunkl-deformed bosons, Bose-Einstein condensation of two and three-dimensional Dunkl-boson gases confined in the one-dimensional gravitational field is investigated. Using the semi-classical approximation method, we calculate the expressions of the Dunkl-critical temperature $T_{c}^{D}$, the ground state population $\frac{N_{0}^{D}}{N}$ and the Dunkl-mean energy and Dunkl-specific heat functions. Further numerical calculation shows that the condensation temperature ratio $\frac{T_{c}^{D}}{T_{c}^{B}}$ increases with the increasing Wigner parameter.

Bound state solutions, Fisher information measures, expectation values, and transmission coefficient of the Varshni potential

The eigensolutions of the Schrödinger equation under the Varshni potential function are studied with two eigensolution techniques such as the Nikiforov–Uvarov and the semi-classical WKB approximation methods. We extended the work to investigate the analytical and numerical Fisher information measure of complexities and also the expectations values using the Hellmann–Feynman theorem. We determined the transmission coefficient using the WKB method. The WKB energy levels and mean values fluctuate with the potential range compared with the NU derived values. Our results for the Fisher information measure obey the uncertainty relation and the Cramer–Rao inequality for position space (). The mean values conform to the ones reported in existing literature.

Black hole entropy and boundary conditions

It is well-known that in order to make the action well defined, one may employ different kinds of boundary conditions (BCs) accompanied by the appropriate Gibbons-Hawking-York (GHY) terms. In this paper we investigate the role of the selected BC and the corresponding GHY terms on the black hole (BH) entropy. Our result shows, regardless of the kind of BC, the BH entropy in all cases is the same as one obtained under Dirichlet BC from Wald formula or semi-classical approximation method. We considered the Schwarzschild solution for $f(R)$-gravity and general relativity (GR) in standard dimensions as special models.

WKB Energy Expression for the Radial Schrödinger Equation with a Generalized Pseudoharmonic Potential

In this paper, we applied the semi-classical quantization approximation method to solve the radial Schrödinger equation with a generalized Pseudoharmonic potential. The four turning points problem within the framework of the Wentzel-Kramers-Brillouin (WKB) method was transformed into two turning points and subsequently, the energy spectrum was obtained. Some special cases of the generalized Pseudoharmonic potential are presented. The WKB approximation approach reproduces the exact energy expression obtained with several analytical methods in the literature. The values of the energy levels for some selected diatomic molecules (N2, CO, NO, CH) obtained numerically are in excellent agreement with those from previous works in the literature.

Modified Fermions Tunneling Radiation from Nonstationary, Axially Symmetric Kerr Black Hole

In this paper, by applying the deformed dispersion relation in quantum gravity theory, we study the correction of fermions’ tunneling radiation from nonstationary symmetric black holes. Firstly, the motion equation of fermions is modified in the gravitational space-time. Based on the motion equation, the modified Hamilton-Jacobi equation has been obtained by a semiclassical approximation method. Then, the tunneling behavior of fermions at the event horizon of nonstationary symmetric Kerr black hole is investigated. Finally, the results show that, in the nonstationary symmetric background, the correction of Hawking temperature and the tunneling rate are closely related to the angular parameters of the horizon of the black hole background.

Modified fermions tunneling radiation from Kerr-Newman-de Sitter black hole

By using the deformed dispersion relation, we study the modified fermions tunneling for rotating charged black hole in de Sitter spacetime. Firstly, the Rarita-Schwinger equation is modified in the gravitational background, and then the deformed Hamilton-Jacobi equation is derived by a semi-classical approximation method. It is shown that the form of the correctional Hamilton-Jacobi equation does not depend on the spin of the fermions field in the semi-classical approximation, and its correctional term is given by − 2 σ m g t t ( ω − e A t ) 2 . Using the correction, we also investigate the fermion tunneling radiation for Kerr-Newman-de Sitter black hole spacetime, and the results show that the correctional temperature and entropy depend on the angular parameters of the horizon of the rotating black hole background.

Tunneling Glashow-Weinberg-Salam Model Particles from Black Hole Solutions in Rastall Theory

Using the semiclassical WKB approximation and Hamilton-Jacobi method, we solve an equation of motion for the Glashow-Weinberg-Salam model, which is important for understanding the unified gauge-theory of weak and electromagnetic interactions. We calculate the tunneling rate of the massive charged W-bosons in a background of electromagnetic field to investigate the Hawking temperature of black holes surrounded by perfect fluid in Rastall theory. Then, we study the quantum gravity effects on the generalized Proca equation with generalized uncertainty principle (GUP) on this background. We show that quantum gravity effects leave the remnants on the Hawking temperature and the Hawking radiation becomes nonthermal.

On the asymptotic analysis of the JWKB method via change of dependent variable in the first-order Bessel’s equation

The first-order Jeffreys–Wentzel–Kramers–Brillouin method (called (JWKB)1) is a conventional semi-classical approximation method used in quantum mechanical systems for accurate solutions. It is known to give accurate energy and wave-function in the classically accessible region of the related quantum mechanical system defined by Schroedinger’s equation whereas the solutions in the classically inaccessible region require special treatment, conventionally known as the asymptotic matching rules. In this work, (JWKB)1 solution of the Bessel differential equation of the first order (called (BDE)1), chosen as a mathematical model, is studied by being transformed into the normal form via the change of dependent variable. General JWKB solution of the initial value problem where appropriately chosen initial values are applied is studied in both normal and standard form representations to be analyzed by the generalized JWKB asymptotic matching rules regarding the Sij matrix elements defined in the literature. Consequently, regions requiring first-order and zeroth-order JWKB approximations are determined successfully.

The effect of the GUP on massive vector and scalar particles tunneling from a warped DGP gravity black hole

This paper discusses the effects of the mass and the angular momentum of massive vector and scalar particles on the Hawking temperature manifested under the effects of the generalized uncertainty principle (GUP). In particular, we calculate the Hawking temperature of a black hole in a warped DGP gravity model in the framework of the quantum tunneling method. We use the modified Proca and Klein-Gordon equations previously determined from the GUP Lagrangian in the spacetime background of a warped Dvali-Gabadadze-Porrati (DGP) metric, with the help of Hamilton-Jacobi (HJ) and semiclassical (WKB) approximation methods. We find that as a special case of a warped DGP black hole solution, the Hawking temperature of a Schwarzschild-de Sitter (SdS) black hole can be determined. Furthermore, the Hawking temperature is influenced by the mass and the angular momentum of vector and scalar particles and depends on which of those types of particles is being emitted by the black hole. We conclude that the nonthermal nature of the Hawking spectrum leads to Planck-scale nonthermal correlations, shedding light on the information paradox in black hole evaporation.

A Normal and Standard Form Analysis of the JWKB Asymptotic Matching Rule via the First Order Bessel’s Equation

Traditional first order JWKB method ( = : ( J W K B ) 1 ) is a conventional semiclassical approximation method mainly used in quantum mechanical systems for accurate solutions. ( J W K B ) 1 general solution of the Time Independent Schrodinger’s Equation (TISE) involves application of the conventional asymptotic matching rules to give the accurate wavefunction in the Classically Inaccessible Region (CIR) of the related quantum mechanical system. In this work, Bessel Differential Equation of the first order ( = : ( B D E ) 1 ) is chosen as a mathematical model and its ( J W K B ) 1 solution is obtained by first transforming into the normal form via the change of independent variable. The ( J W K B ) 1 general solution for appropriately chosen initial values in both normal and standard form representations is analyzed via the generalized ( J W K B ) 1 asymptotic matching rules regarding the S ˜ i j matrix elements given in the literature. Instead of applying the common ( J W K B ) 1 asymptotic matching rules relying on the physical nature of the quantum mechanical system, i.e., a physically acceptable (normalizable) wavefunction, a pure semiclassical analysis is studied via the ( B D E ) 1 model mathematically. Finally, an application to a specific case of the exponential potential decorated quantum mechanical bound state problem is presented.

On The Exact and JWKB Solution of 1D Quantum Harmonic Oscillator by Mathematica

Although being the fundamental semiclassical approximation method mainly used in quantum mechanics and optical waveguides, JWKB method along with the application of the associated JWKB asymptotic matching rules is known to give exact solutions for the Quantum Harmonic Oscillator (QHO). Asymptotically matched JWKB solutions are typically accurate or exact in the entire domain except for a narrow domain around the classical turning points where potential energy equals the total energy of the related quantum mechanical system. So, one has to cope with this diverging behavior at the classical turning points since it prohibits us from using continuity relations at the related boundaries to determine the required JWKB coefficients. Here, a computational diagram and related mathematica codes to surmount the problem by applying parity matching for even and odd JWKB solutions rather than boundary continuities are being presented. In effect, JWKB coefficients as well as the conversion factor for the dimensionless form of the Schrodingers equation, which is common to both exact and JWKB solutions, is being successfully obtained.

Lorentz Invariance Violation and Modified Hawking Fermions Tunneling Radiation

Recently the modified Dirac equation with Lorentz invariance violation has been proposed, which would be helpful to resolve some issues in quantum gravity theory and high energy physics. In this paper, the modified Dirac equation has been generalized in curved spacetime, and then fermion tunneling of black holes is researched under this correctional Dirac field theory. We also use semiclassical approximation method to get correctional Hamilton-Jacobi equation, so that the correctional Hawking temperature and correctional black hole’s entropy are derived.

The condensation of ideal Bose gas in a gravitational field

Bose–Einstein condensation of two- and three-dimensional boson gases confined in the one-dimensional gravitational field is investigated. Using the semiclassical approximation method, the expressions for the BEC transition temperature, condensate fraction, heat capacity and the entropy of the system are obtained. The heat capacities of the systems with D =1, 2, 3 ( D is the dimension) at the critical temperature are discussed. We find that for the 1-D and 2-D boson systems, the heat capacities are continuous, but for the 3-D case there is a gap at the critical temperature T c . The entropies of the systems with D =1, 2, 3 are also studied in detail. It is found that the entropies increase with the increasing of the temperature T .

BOSE–EINSTEIN CONDENSATION OF A RELATIVISTIC IDEAL BOSE GAS IN RANDOM BOX

Using semi-classical approximation method, the Bose–Einstein condensation (BEC) of a relativistic ideal boson gas (RIBG) in random box is studied. The exact BEC transition temperature Tc and Helmholtz free energy at Tc are derived. The phase diagrams in the (Δ, T) plane are obtained, where Δ is the fluctuation of the box length and T is the temperature of the system. We find that Tc is lowered by the presence of the quenched disorder caused by the random boundary conditions. The effects of antibosons on the RIBG are also studied and it is found that the Helmholtz free energy of the system with antibosons at Tc is lower than that of the system without antibosons. This implies that the omission of antibosons always leads to a metastable state.

Quantum tunnelling of higher-dimensional Kerr-anti-de Sitter black holes beyond semi-classical approximation

Based on the theory of Klein-Gordon scalar field particles, the Hawking radiation of a higher-dimensional Kerr-anti-de Sitter black hole with one rotational parameter is investigated using the beyond semi-classical approximation method. The corrections of quantum tunnelling probability, Hawking temperature and Bekenstein-Hawking entropy are also included.

Influence of Homogeneous Weak Electric Field on the Chemical Potential and Heat Capacity of Charged Fermion System

In light of the semiclassical (Thomas-Fermi) approximation method, the thermo- dynamic properties of the charged fermion system in homogeneous weak electric field are studied. After deriving the relationship of chemical potential and heat capacity of charged fermion system changed with the external electric field, then the analytic formula of the chemical potential and heat capacity of charged fermion system in the high and low tem- perature approximation condition is desired. Moreover, the influence of the homogeneous weak electric field on the chemical potential and heat capacity are analyzed.

Fermion tunnels at cosmological horizon of higher dimensional de Sitter space time

Using semiclassical approximation method, the fermion tunnels at cosmological horizon of higher dimensional de Sitter and Schwarzschild de Sitter space-times are researched in this paper. In our work, the Dirac equation, which describes the property of 1/2 spin particles, is simplified, and then the semiclassical Hamilton-Jacobi equation is obtained via the condition that there are non-trivial solutions of Dirac equation. The research has been simplified greatly, and the Hawking temperature and tunneling rate at cosmological horizon of static higher dimensional de Sitter space time is gotten finally.

Elastic scattering and breakup effect analysis ofBe11+C12at 38.4 MeV/nucleon

{sup 11}Be+{sup 12}C elastic-scattering data at 38.4 MeV/nucleon has been analyzed using the optical model. The optical potential is calculated in the framework of the double folding model using M3Y effective nucleon-nucleon interaction. Different models of {sup 11}Be density are tested and the model that does not include the halo structure gives poor fitting with data. The breakup effect is studied by introducing a complex dynamical polarization potential (DPP) that is added to the ''bare'' potential. The DPP is taken in different forms that have been obtained from simple phenomenological, semiclassical approximation, and microscopic methods. The simple phenomenological DPP is related to the semiclassical approximation method. The sensitivity of the differential and reaction cross sections to these polarization potentials is tested. The microscopic DPP that has been constructed from the derivative of the folding potential describes the breakup effect well. It gives an explicit justification for the long range of the polarization potential.

Fermion tunneling from higher-dimensional black holes

Via the semiclassical approximation method, we study the $1/2$-spin fermion tunneling from a higher-dimensional black hole. In our work, the Dirac equations are transformed into a simple form, and then we simplify the fermion tunneling research to the study of the Hamilton-Jacobi equation in curved space-time. Finally, we get the fermion tunneling rates and the Hawking temperatures at the event horizon of higher-dimensional black holes. We study fermion tunneling of a higher-dimensional Schwarzschild black hole and a higher-dimensional spherically symmetric quintessence black hole. In fact, this method is also applicable to the study of fermion tunneling from four-dimensional or lower-dimensional black holes, and we will take the rainbow-Finsler black hole as an example in order to make the fact explicit.

Fermions tunneling of higher-dimensional Kerr–Anti-de Sitter black hole with one rotational parameter

The 1/2 spin fermions tunneling at the horizon of n-dimensional Kerr–Anti-de Sitter black hole with one rotational parameter is researched via semi-classical approximation method, and the Hawking temperature and fermions tunneling rate are obtained in this Letter. Using a new method, the semi-classical Hamilton–Jacobi equation is gotten from the Dirac equation in this Letter, and the work makes several quantum tunneling theories more harmonious.