WKB Regime Research Articles

Quasinormal modes and greybody factors of symmergent black hole

Symmergent gravity is an emergent gravity framework in which gravity emerges guided by gauge invariance, accompanied by new particles, and reconciled with quantum fields. In this paper, we perform a detailed study of the quasinormal modes and greybody factors of the black holes in symmergent gravity. Its relevant parameters are the quadratic curvature term cO and the vacuum energy parameter α. In our analyses, effects of the both parameters are investigated. Our findings suggest that, in both positive and negative direction, large |cO| values of the parameter on the quasinormal modes parallel the Schwarzschild black hole. Moreover, the quasinormal model spectrum is found to be sensitive to the symmergent parameter α. We contrast the asymptotic iteration and WKB methods in regard to their predictions for the quasinormal frequencies, and find that they differ (agree) slightly at small (large) multipole moments. We analyze time-domain profiles of the perturbations, and determine the greybody factor of the symmergent black hole in the WKB regime. The symmergent parameter α and the quadratic curvature term cO are shown to impact the greybody factors significantly. We provide also rigorous limits on greybody factors for scalar perturbations, and reaffirm the impact of model parameters.

Uniform Airy Approximation for Nonadiabatic Transitions in a Curve-Crossing Weak-Coupling Case

Abstract This work suggests a connection between Landau-Zener transition probabilities between two crossing potentials in the classically accessible WKB regime and Landau-Lifshitz transition probabilities in the classically inaccessible WKB regime. It is based on the uniform Airy (UAi) approximation which represents a generalization of quantum transition probabilities for linear crossing potentials with constant coupling. The performance of the UAi approximation is tested by comparison with distorted-wave probabilities for an exponential potential model and illustrated for potentials that determine the intersection of two ab initio vibronic potential surfaces of the NO-Ar system.

Quasinormal resonances of a charged scalar field in a charged Reissner–Nordström black-hole spacetime: A WKB analysis

The fundamental quasinormal resonances of charged Reissner–Nordström black holes due to charged scalar perturbations are derived analytically. In the WKB regime, qQ≫ℏ, we obtain a simple expression for the fundamental quasinormal resonances: ω=qQ/r+−i2πTBH(n+12), where TBH and Q are the temperature and electric charge of the black hole and q is the electric charge of the field. Remarkably, our results show that the relaxation dynamics of a perturbed Reissner–Nordström black hole may saturate the recently proposed universal relaxation bound.

Predictions from an anisotropic inflationary era

This paper investigates the predictions of an inflationary phasestarting from a homogeneous and anisotropic universe of theBianchi I type. After discussing the evolution of the background spacetime, focusing on the number ofe-folds and the isotropization, we solve the perturbation equations and predict the powerspectra of the curvature perturbations and gravity waves at the end of inflation.The main features of the early anisotropic phase is (1) a dependence of the spectra onthe direction of the modes, (2) a coupling between curvature perturbations andgravity waves and (3) the fact that the two gravity wave polarizations do not sharethe same spectrum on large scales. All these effects are significant only on largescales and die out on small scales where isotropy is recovered. They depend on acharacteristic scale that can, but a priori must not, be tuned to some observable scale.To fix the initial conditions, we propose a procedure that generalizes the one standardlyused in inflation but that takes into account the fact that the WKB regime is violated atearly times when the shear dominates. We stress that there exist modes that do not satisfythe WKB condition during the shear-dominated regime and for which the amplitude at theend of inflation depends on unknown initial conditions. On such scales, inflation loses itspredictability.This study paves the way for the determination of the cosmological signature of a primordial shear, whateverthe Bianchi I spacetime. It thus stresses the importance of the WKB regime to drawinflationary predictions and demonstrates that, when the number ofe-folds is large enough, the predictions converge toward those of inflation in a Friedmann–Lemaîtrespacetime but that they are less robust in the case of an inflationary era with a small number ofe-folds.

SCATTERING PHASE SHIFTS IN QUASI-ONE-DIMENSION

Scattering of an electron in quasi-one-dimensional quantum wires have many unusual features, not found in one, two or three-dimensions. In this work we analyze the scattering phase shifts due to an impurity in a multi-channel quantum wire with special emphasis on negative slopes in the scattering phase shift versus incident energy curves and the Wigner delay time. Although at first sight, the large number of scattering matrix elements show phase shifts of different character and nature, it is possible to see some pattern and understand these features. The behavior of scattering phase shifts in one-dimension can be seen as a special case of these features observed in quasi-one-dimensions. The negative slopes can occur at any arbitrary energy and Friedel sum rule is completely violated in quasi-one-dimension at any arbitrary energy and any arbitrary regime. This is in contrast to one, two or three dimensions where such negative slopes and violation of Friedel sum rule happen only at low energy where the incident electron feels the potential very strongly (i.e. there is a very well defined regime, the WKB regime, where FSR works very well). There are some novel behavior of scattering phase shifts at the critical energies where S-matrix changes dimension.

Intense laser interacting with a two-level atom: WKB expressions for dipole transitions and population inversion

In a previous paper, we have already considered the system composed by a two-level atom interacting with a coherent external electromagnetic field. No application whatsoever has been made of the rotating wave approximation. Being especially interested in the problem of higher harmonic generations for the case of very intense laser fields, we have developed in this Letter a much more efficient way to obtain these solutions as well as to carry out some calculations in a range in which the parameters take extreme values. Also the formalism allows us now to provide analytic expressions in the WKB regime for the electric dipole moment and the population inversion. The spectrum can be decomposed in periodic and non-periodic contributions. Only the latter depends upon the Floquet exponent and can be responsible of the main complexities of the observed Rabi revivals and the hyper-Raman shift.

Wave effects in gravitational lensing of electromagnetic radiation.

Wave effects in the gravitational lensing of electromagnetic radiation by compact objects in astrophysics are treated. In the regime where the influence of diffraction is severe, solutions of the wave equation appropriate for lensing in astrophysics (which is of the form of the Schroumldinger equation for Coulomb scattering) are obtained. In the WKB regime, previous formulations are refined and extended to the case in which a part of the source is directly behind the lensing mass. Wave effects tend to be largest for this geometry which requires that radiation at a caustic be treated. The autocorrelation function of the electric field and the related frequency dependence of the radiation are emphasized, in addition to the diffraction pattern, to measure the deviations from the solutions obtained in the approximation of geometrical optics. In contrast, gravitational lensing is independent of frequency in the usual treatment which is based upon geometrical optics. Numerical computations are performed to indicate how the wave effects depend upon the relevant parameters including especially the size of the source. Wave effects are most significant at radio frequencies and for lensing by stellar and planetary masses. The importance of wave effects is governed by the ratio of the Schwarzschild radius of the lensing mass to the wavelength of the radiation.

Classical analog of cosmological particle creation

A classical, minimally coupled scalar field in a given background cosmology is discussed. Far from the initial singularity a WKB approximation is valid so that a semiclassical particle number can be defined as an adiabatic invariant. This number is then compared to scalar field parameters near the singularity. Generalization of work by Misner can be used for a nonparticle singularity description. Alternatively, "freezing" of the cosmology at some time ${t}_{0}$ after the singularity is required to obtain a particle description there. This procedure is shown to be valid if a WKB regime does exist at ${t}_{0}$. It gives unphysical results if a WKB regime does not exist at ${t}_{0}$. These classical methods are shown to reproduce the results of the quantum treatment except for zero-point energy terms. It is further shown that the "freezing" procedure is not conformally invariant for a conformally coupled massless scalar field. Grishchuk's result on gravitational wave amplification is reproduced and discussed.