Quadratic decomposition of symmetric semi-classical polynomial sequences of even class: an example from the case s = 2

In the present work, we deal with the quadratic decomposition of symmetric semi-classical polynomial sequences of even class. An example from class 2 is settled. We give an integral representation of the considered symmetric form.     

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

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.     

激光驻波场中钠原子沉积图样的理论研究

原子在近共振激光驻波场中受光的作用力汇聚沉积，形成以激光半波长为周期的光栅结构. 利用半经典模型对钠原子束在不饱和驻波场中的运动行为进行了理论研究，用数值方法模拟出在考虑横向温度、纵向速度和自由飞程后钠原子沉积的光栅结构，通过半高宽、对比度对最终沉积图样进行表征，分析了这些因素对沉积的影响，为正在开展的原子光刻实验提供了必要的理论依据. 关键词： 原子沉积 半经典模型 激光驻波场     

Characterization of semi-classical orthogonal polynomials on nonuniform lattices

We state and prove characterization theorem for semi-classical orthogonal polynomials on nonuniform lattices (quadratic lattices of a discrete or q-discrete variable). This theorem proves the equivalence between the four characterization properties, namely, the Pearson type equation for the linear functional, the strictly quasi-orthogonality of the derivatives, the structure relation, and the Riccati equation for the formal Stieltjes function. We give the classification of the semi-classical linear functional of class one on nonuniform lattice. Using the definition and the properties of the associated orthogonal polynomials, we prove that semi-classical orthogonal polynomials satisfy the second-order divided difference equation on nonuniform lattices.     

On Fourth-order Difference Equations for Orthogonal Polynomials of a Discrete Variable: Derivation,Factorization and Solutions

We derive and factorize the fourth-order difference equations satisfied by orthogonal polynomials obtained from some modifications of the recurrence coefficients of classical discrete orthogonal polynomials such as: the associated, the general co-recursive, co-recursive associated, co-dilated and the general co-modified classical orthogonal polynomials. Moreover, we find four linearly independent solutions of these fourth-order difference equations, and show how the results obtained for modified classical discrete orthogonal polynomials can be extended to modified semi-classical discrete orthogonal polynomials. Finally, we extend the validity of the results obtained for the associated classical discrete orthogonal polynomials with integer order of association from integers to reals.     

Measurements and calculations of H2-broadening and shift parameters of water vapour transitions of the ν1 + ν2 + ν3 band

The water vapour line broadening and shifting for 97 lines in the ν₁ + ν₂ + ν₃ band induced by hydrogen pressure are measured with Bruker IFS 125 HR FTIR spectrometer. The measurements were performed at room temperature, at the spectral resolution of 0.01 cm^?1 and in a wide pressure range of H₂. The calculations of the broadening γ and shift δ coefficients were performed in the semi-classical method framework with use of an effective vibrationally depended interaction potential. Two potential parameters were optimised to improve the quality of calculations. Good agreements with measured broadening coefficients were achieved. The comparison of calculated broadening coefficients γ with the previous measurements is discussed. The analytical expressions that reproduce these coefficients for rotational, ν₂, ν₁, and ν₃ vibrational bands are presented.     

Line broadening,shifting and mixing parameters for the ν1 + ν3 band of OCS perturbed by N2 and O2

In this paper, we report measured Rosenkranz N₂- and O₂-broadening, induced pressure-shift and mixing coefficients for OCS in the ν₁ + ν₃ band, using a multi-pressure fitting technique applied to the measured shapes of the lines, including the interference effects caused by the line overlaps. These measurements were made by analysing six laboratory absorption spectra recorded at 0.004 cm^?1 resolution using the Fourier transform spectrometer Bruker IFS125HR located at the Laboratoire Interuniversitaire des Systèmes Atmosphériques, in Créteil. The spectra have been recorded in the 1850–3000 cm^?1 wave number range at 295 K, using a multipass absorption cell with an optical path of 3.249 m. The total sample pressures ranged from 5.97 to 83.28 Torr with OCS volume mixing ratios between 0.001 and 0.013 in nitrogen or oxygen. We have been able to determine the N₂- and O₂-pressure-broadening coefficients of 81 ν₁ + ν₃ transitions with rotational quantum number J up to 50. The measured N₂- and O₂-broadening coefficients range from 0.0815 ± 0.0698 to 0.1169 ± 0.1027 cm^?1 atm^?1 at 295 K, respectively. Most of the measured pressure shifts are positive. The reported N₂- and O₂-induced pressure-shift coefficients vary from about ?0.0103 ± 0.0092 to 0.0097 ± 0.0092 cm^?1 atm^?1, respectively. We have examined the dependence of the measured broadening parameters on the quantum number m (m = ?J for the P branch and m = J + 1 for the R branch) and also developed an empirical expression to describe the broadening coefficients in terms of |m|. On average, this empirical expression reproduces the measured broadening coefficients to within 2%. Using a semi-classical Robert and Bonamy formalism, the theoretical broadening coefficients have been calculated at room temperature and compared with the experimental results. The theoretical results of the broadening coefficients are in very good overall agreement with the experimental data (2%).     

Semi-Classical Calculation of the Particle Production in QED via the Schwinger Dynamical Principle

The Schwinger quantum dynamical principle is used to calculate the free vacuum persistence amplitude in the presence of a prescribed electromagnetic background, and the probability that free pairs are created from the vacuum state. An explicit expression of these amplitudes is obtained in the semi-classical approach, showing that, in this approach, the particle production is a stochastic Poisson process. PACS subject classifications. 02.30.Xx, 11.15.Bt, 12.20.Ds, 12.20.-m.