Semiclassical approximation for relativistic potentials

We consider the application of semiclassical approximation to relativistic potentials for massless particles where the kinetic energy is a nontrivial, nonlocal operator. Quantization rules are derived for an arbitrary confining potential and compared to some exact results forS-waves. These results admit of a partial generalization to smalll values.     

Semiclassical matrix model for quantum chaotic transport with time-reversal symmetry

We show that the semiclassical approach to chaotic quantum transport in the presence of time-reversal symmetry can be described by a matrix model. In other words, we construct a matrix integral whose perturbative expansion satisfies the semiclassical diagrammatic rules for the calculation of transport statistics. One of the virtues of this approach is that it leads very naturally to the semiclassical derivation of universal predictions from random matrix theory.     

Matrix Elements of One- and Two-Body Operators in the Unitary Group Approach (I) - Formalism

The tensor algebraic method is used to derive general one- and two-body operator matrix elements within the U_n representations, which are useful in the unitary group approach to the configuration interaction problems of quantum many-body systems.     

Semiclassical anomalies of the quantum mechanical systems and their modifications for the asymptotic matching

JWKB solutions to the Initial Value Problems (IVPs) of the Time Independent Schrodinger’s Equation (TISE) for the Simple Linear Potentials (SLPs) with a turning point parameter have been studied according to the turning points by graphical analysis to test the results of the JWKB solutions and suggested modifications. The anomalies happening in the classically inaccessible region where the SLP function is smaller than zero and the results of the suggested modifications, which are in consistent with the quantum mechanical theories, to remove these anomalies in this region have been presented. The origins of the anomalies and verifications of the suggested modifications showing a great success in the results have also been studied in terms of a suggested matrix elements made up of the JWKB expansion terms, S_i−1,j (where i = 1, 2, 3 and j = 1, 2). The results of the modifications for the IVPs and their application to the Bound State Problems (BSPs) with an example application of the Harmonic Oscillator (HO) have been presented and their generalization for any potential function have been discussed and classified accordingly.     

Analytical Derivations of Single-Particle Matrix Elements in Nuclear Shell Model

We present analytical method to calculate single particle matrix elements used in atomic and nuclear physics. We show seven different formulas of matrix elements of the operator f(r)d_r^m where f(r) = r^μ, r^μ jJ (qr), V (r) corresponding to the Gaussian and the Yukawa potentials used in nuclear shell models and nuclear structure. In addition, we take into account a general integral formula of the matrix element ＜n'l'|f(r) d _r^(m) |n l＞ that covers all seven matrix elements obtained analytically.     

Semiclassical theory of potential scattering for massless Dirac fermions

In this paper we study scattering of two-dimensional massless Dirac fermions by a potential that depends on a single Cartesian variable. Depending on the energy of the incoming particle and its angle of incidence, there are three different regimes of scattering. To find the reflection and transmission coefficients in these regimes, we apply the Wentzel–Kramers–Brillouin (WKB), also called semiclassical, approximation. We use the method of comparison equations to extend our prediction to nearly normal incidence, where the conventional WKB method should be modified due to the degeneracy of turning points. We compare our results to numerical calculations and find good agreement.     

On the Spatial Density Matrix for the Centre of Mass of a One-Dimensional Perfect Gas

We examine the reduced density matrix of the centre of mass on position basis considering a one-dimensional system of Nnoninteracting distinguishable particles in a infinitely deep square potential well. We find a class of pure states of the system for which the off-diagonal elements of the matrix above go to zero as Nincreases. This property holds also for the state vectors which are factorized in the single particle wave functions. In this last case, if the average energy of each particle is less than a common bound, the diagonal elements are distributed according to the normal law with a mean square deviation which becomes smaller and smaller as Nincreases towards infinity. Therefore when the state vectors are of the type considered we cannot experience spatial superpositions of the centre of mass and we may conclude that position is a preferred basis for the collective variable.     

On Higher Order Pyramidal Finite Elements

In this paper we first prove a theorem on the nonexistence of pyramidal polynomial basis functions. Then we present a new symmetric composite pyramidal finite element which yields a better convergence than the nonsymmetric one. It has fourteen degrees of freedom and its basis functions are incomplete piecewise triquadratic polynomials. The space of ansatz functions contains all quadratic functions on each of four sub-tetrahedra that form a given pyramidal element.     

渐变折射率平板波导的逆分析转移矩阵方法

利用分析转移矩阵方法，可精确计算任意折射率分布光波导模式的有效折射率。在此基础上，推出了逆分析转移矩阵方法，根据实验测量的导模有效折射率来拟合光波导的折射率分布，取得了比逆WKB方法更为合理的结果。     

Semiclassical Weyl Formula for a Class of Weakly Regular Elliptic Operators

We investigate the semiclassical Weyl formula describing the asymptotic behaviour of the counting function for the number of eigenvalues in the case of self-adjoint elliptic differential operators satisfying weak regularity hypotheses. We consider symbols with possible critical points and with coefficients which have Hölder continuous derivatives of first order. Mathematics Subject Classification (2000) 35P20.     

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.     

Matrix Elements in Fermion Dynamical Symmetry Model

In a neutron-proton system, the matrix elements of the generators for SO(8) × SO(8) symmetry areconstructed explicitly, and with these matrix elements the low-lying excitation spectra obtained by diagonalization arepresented. The excitation spectra for SO(7) nuclei Pd and Ru isotopes and SO(6) r-soft rotational nuclei Xe, Ba, andCe isotopes are calculated, and comparison with the experimental results is carried out.     

Analytical Expressions of Matrix Elements of Physical Quantities for Dirac Oscillator

The analytical expressions of the matrix elements for physical quantities are obtained for the Dirac oscillator in two and three spatial dimensions. Their behaviour for the case of operator's square is discussed in details. The two-dimensional Dirac oscillator has similar behavior to that for three-dimensional one.     

Matrix Elements in Fermion Dynamical Symmetry Model

In a neutron-proton system, the matrix elements of the generators for SO(8)×SO(8) symmetry are constructed explicitly, and with these matrix elements the low-lying excitation spectra obtained by diagonalization are presented. The excitation spectra for SO(7) nuclei Pd and Ru isotopes and SO(6) r-soft rotational nuclei Xe, Ba, and Ce isotopes are calculated, and comparison with the experimental results is carried out.     

Analytic Calculation of Arbitrary Matrix Elements for Boson Exponential Quadratic Operators

By means of the transformation relation between the ordinary form of boson exponential quadratic operators (BEQO) and its anti-normal product form, we present an effective method to conveniently calculate arbitrary matrix elements of BEQO. By this method, many important matrix elements can be calculated analytically. As a direct application, we obtain the exact solutions of the density matrix and partition function for general boson quadratic Hamiltonian without any information about the energy level.     

Zn Belavin模型的反射矩阵

本文得到了Zⁿ Belavin模型反射矩阵的矩阵元表达式,在退化到三角极限后,得到了非对角的三角统计模型的反射矩阵.     

基体干扰对ICP-AES分析土壤样品中主、次量元素的影响研究

为了研究分析方法中的干扰因素对于分析结果的影响程度,针对地球化学中常用的分析手段ICP-AES法,选择土壤标准物质采用与被测样品相同消解方法,作为工作校准曲线来抵消基体影响因素。比较了在土壤基体和无土壤基体条件下测得的土壤样品中各主、次量元素结果的相对偏差,分析了其中联系和规律。发现无土壤基体干扰的结果RE值均在0左右浮动,正负偏移比例基本一致,若排除谱线干扰因素的话,基体匹配方法能有效消除土壤中基体干扰影响。而土壤基体干扰对Al,Ca,Fe,Mg,P,Ti和Ba元素分析结果有较大负偏差影响,最大偏离差Mg 279.5 nm谱线达-14.49%,影响程度排序为Ti,Mg＞P,Fe＞Ca,Ba＞Al,对其他元素Na,Cr,Cu,V,Li,Mn,Ni和Sr则无明显影响。与原本设想的结果相反,基体干扰对我们视作基体的高含量元素测试结果影响十分大,反而对次量元素影响表现并不显著。在综合基体干扰中,Ca和Mg两元素自身组分含量影响权重明显,表现为自身组分含量与分析结果相对偏差值有明显线性相关性。其他元素自身组分与基体影响结果无线性趋势,自身含量的影响权重很小。谱线的选择,干扰因素的排除对结果的确定十分重要。干扰影响的因素和规律一直是ICP光谱学者致力研究探索的课题。这些研究结果对ICP-AES分析土壤样品时谱线的选择及结果准确度的判定有很好的指导意义。     

Semiclassical calculation of ionization rate for Rydberg hydrogen atoms near a metal surface

The ionization of Rydberg hydrogen atoms near a metal surface at different scaled energies above the classical saddle point energy has been discussed by using the semiclassical method. The results show that the atoms ionize by emitting a train of electron pulses. In order to reveal the chaotic and escape dynamical properties of this system in detail, the sensitive dependence of the ionization rate upon the scaled energy is discussed. As the scaled energy is close to the saddle point energy, the ionization process of the hydrogen atom is nearly the same as the case of hydrogen atom in an electric field. There is only a single pulse of electrons, with an exponentially decaying tail. With the increase of the scaled energy, the ionization rates are similar to the case of the hydrogen atom in parallel electric and magnetic field, a series of electron pulses appear in the ionization process. This is caused by classical chaos, which occurs for the metal surface. Our studies also suggest that the metal surface can play the role of both the electric and the magnetic fields. Our theoretical analysis will be useful for guiding experimental studies of the ionization of atoms near the metal surface.