Massive Scalar Field Evolution in the Dyadosphere Spacetime of Charged Black Hole

Scalar field quasinormal modes in the dyadosphere spacetime of charged black hole are studied by using the third-order WKB approximation. From numerical results obtained, we find that the scalar field mass u plays an important role in studying the quasinormal frequencies. With the scalar field mass increases, the real parts increase and the magnitudes of the imaginary parts decrease. Particulary, these change are almost linearly.     

Liouville–Green (WKB) asymptotics for almost-diagonal linear second-order matrix difference equations

A Liouville–Green (or WKB) asymptotic approximation theory is developed for a class of almost-diagonal (‘asymptotically diagonal’) linear second-order matrix difference equations. Rigorous and explicitly computable bounds for the error terms are obtained, the asymptotics being made with respect to both, the index and some parameter affecting the equation. The case of the associated inhomogeneous equations is also considered in detail. Some examples and a number of applications are presented for the purpose of illustration.     

Exact WKB analysis of a Schrödinger equation with a merging triplet of two simple poles and one simple turning point,II — Its relevance to the Mathieu equation and the Legendre equation

We develop the exact WKB analysis of an M2P1T (merging two simple poles and one simple turning point) Schrödinger equation. In Part II, using a WKB-theoretic transformation to the algebraic Mathieu equation constructed in Part I, we calculate the alien derivative of its Borel transformed WKB solutions at each fixed singular point relevant to the simple poles through the analysis of Borel transformed WKB solutions of the Legendre equations. In the course of the calculation of the alien derivative we make full use of microdifferential operators whose symbols are given by the infinite series that appear in the coefficients of the algebraic Mathieu equation and the Legendre equation.     

Quasinormal Modes of a Black Hole with Quintessence-Like Matter and a Deficit Solid Angle for Electromagnetic Perturbation

We investigate the electromagnetic perturbation around a black hole with quintessence-like matter and a deficit solid angle. The complex frequencies of the quasinormal modes of electromagnetic perturbation are evaluated by the third-order WKB approximation. The results show that the electromagnetic perturbation around the black hole damps more slowly owing to the presence of the quintessence-like. The phenomenon can be distinguished from the black hole only with a deficit angle.     

Supersymmetric WKB Approximation of Anharmonic Potential V（r）=ar^2＋br^-4＋cr^-6

This article uses the supersymmetric WKB approximation to obtain the approximate energy levels and wave functions of the anharmonic potential V（r） = ar^2 ＋ br^-4 ＋ cr^-6 in order to tesify the correctness between [Phys. Left. A 170 （1992） 335] and the paper written by M. Landtman [Phys. Left. A 175 （1993） 147].     

改进WKB近似的新方法

利用转移矩阵理论，在考虑层间一次反射和转折点处实际相移的基础上，导出了改进的ＷＫＢ公式，数值计算的结果表明本文所得公式的精度远优于传统的ＷＫＢ近似，而且能适用于接近于截止的模式和变化剧烈的折射率分布。     

Energy for Two-electron Quantum Dots: The Quantization Rule Approach

The energy spectra for two electrons in a parabolic quantum dot are calculated by the quantization rule approach. The numerical results are in excellent agreement with the results by the method of integrating directly the Schr?dinger equation, and better than those by the WKB method and the WKB-DP method.     

Wave equations with time-dependent dissipation I. Non-effective dissipation

The goal of this article is to construct structural representations of the solutions to Cauchy problems for weakly dissipative wave equations below scaling and to deduce estimates of the solution and its energy based on L^q(Rⁿ), q?2. Furthermore, the sharpness of the obtained estimates is discussed.     

Determination of Optical Waveguide Refractive-Index Profiles with the Inverse Analytic Transfer Matrix Method

In this paper, we present an inverse analytic transfer matrix (IATM) method to predict the refractive index profiles from the measurement of mode indices based on the analytic transfer matrix (ATM) method, which can exactly determine the modal characteristics of a planar optical waveguide with arbitrary index profiles. IATM method has been proved to be universally reliable not only in slowly changing profiles but also the profiles changing rapidly in which inverse WKB method would find difficult through numerical analysis for several typical refractive index profiles.     

含双噪声源电路的类WKB法研究

本文首次尝试利用ＷＫＢ方法对双噪声原电路的Ｖａｎｄｅｒ Ｐｏｒ方程进行了讨论，并对倍加ＯＵ噪声和可加白噪声下的系统进行了数值计算，所得结果对调节含噪声源的电路有一定指导意义。