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1.
A general algorithm is proposed for calculating the Θ series of SiC polytypes. The obtained Θ series of the main SiC polytypes can be useful in calculating lattice sums, in particular when using the Mellin transform of the Θ series. By expanding the Θ series in the Jacobi parameter, one obtains sequences of coordination numbers for crystallographically nonequivalent atomic sites in the main SiC polytypes. A nontrivial interrelationship is demonstrated between these numerical sequences and the local symmetry of the nonequivalent sites. Fiz. Tverd. Tela (St. Petersburg) 41, 183–186 (February 1999)  相似文献   

2.
A correction is derived to the expression for the radius of convergence of the Laplace series for the “internal” potential of a homogenous circular torus. A spherical shell is found inside which the problem of expansion of the torus potential into a power series should be specially solved.  相似文献   

3.
A two dimensional gauge theory is canonically associated to every Drinfeld double. For particular doubles, the theory turns out to be e.g. the ordinary Yang–Mills theory, the G/G gauged WZNW model or the Poisson σ-model that underlies the Kontsevich quantization formula. We calculate the arbitrary genus partition function of the latter. The result is the q-deformation of the ordinary Yang–Mills partition function in the sense that the series over the weights is replaced by the same series over the q-weights. For q equal to a root of unity the series acquires the affine Weyl symmetry and its truncation to the alcove coincides with the Verlinde formula. Received: 10 December 1999 / Accepted: 8 October 2000  相似文献   

4.
Exciton absorption spectra in high-quality β-ZnP2 single crystals have been investigated at T=1.7 K for various directions of the wave vector and various polarization states of the radiation. It has been unambiguously established that the additional high-energy A series, which in some works has been called a D series and ascribed to ZnP2 crystals, of so-called “rhombic” symmetry,1,8,10,11 is an intrinsic exciton of the β-ZnP2 series. A mixed mode has been detected for the first time, and the energy of the longitudinal exciton has been determined. The selection rules for the exciton transitions have been analyzed by a group-theoretical approach, and the symmetry of the nS states of the single exciton has been established on the basis of the experimental data — Γ 2 (z). Fiz. Tverd. Tela (St. Petersburg) 41, 193–202 (February 1999)  相似文献   

5.
The behavior of excitation cross sections of the strontium atom was studied experimentally in the spectral series 5s4d1D2-5snf1F 3 o in the range n = 4–26, and also the optical excitation functions for lines in the same series in the range n = 4–12. It was established that the beginning of the series is perturbed. The effect of the perturbation is manifested both in the irregular course of the dependence of the absolute values of the cross sections on n, and in the difference between the shapes of the optical excitation functions for different terms of the series. The results obtained are compared with available experimental data. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 5, pp. 557–560, September–October, 2007.  相似文献   

6.
The completeness of the quasinormal modes of the wave equation with P?schl–Teller potential is investigated. A main result is that after a large enough time t 0, the solutions of this equation corresponding to &C -data with compact support can be expanded uniformly in time with respect to the quasinormal modes, thereby leading to absolutely convergent series. Explicit estimates for t 0 depending on both the support of the data and the point of observation are given. For the particular case of an “early” time and zero distance between the support of the data and observational point, it is shown that the corresponding series is not absolutely convergent, and hence that there is no associated sum which is independent of the order of summation. Received: 10 March 1998 / Accepted: 1 February 1999  相似文献   

7.
Calculations of the excited-state structure and of the absorption and radiation spectra of trans-β-methylstyrene are performed by the parametric method for models of the first and second approximations. Only three of the parameters, being constant in a series of related compounds, are used for molecular fragments. In the calculation, the main regularities observed in electronic spectra are reproduced, and an analysis and interpretation of their fine vibrational structure are carried out. The use of the model of the second approximation with a single additional parameter allows more accurate reproduction of angular deformations of the molecule under excitation and of the characteristic changes observed in the low-frequency spectral region in the series of diphenyl polyenes, stilbene, styrene, and methylstyrene molecules. It is shown that the parameters of the second approximation (just as of the first one) possess the transference property in the homological series of molecules. In modeling complex molecules in excited states and their vibronic spectra, the parametric method is more efficient than the ab initio one. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 2, pp. 148–153, March–April, 2000.  相似文献   

8.
Using the imaginary time method, we study the structure of the perturbation series for the hydrogen atom in electric ℰ and magnetic ℋ fields. It is shown that there is a “critical” value of the ratio γ=ℋ|ℰ at which the perturbation series for the ground state changes from having a fixed sign (for γ<γ c ) to having a variable sign (for γ>γ c ). This conclusion is confirmed by direct higher-order perturbation calculations. The change in the asymptotic regime is explained by competition among the contributions of the various complex trajectories that describe the subbarrier motion of the electrons. Here the parameter γ c depends on the angle θ between the electric and magnetic fields. Zh. éksp. Teor. Fiz. 113, 2047–2055 (June 1998)  相似文献   

9.
Self-consistent calculations of electron density distribution from first principles for a series of semi-infinite metals show that the electron density almost drops to zero at 8.5 a.u. away from a metal surface. The electron densities in a series of bimetallic-electrode systems with a distance between the two electrodes of 21.7 a.u. are further investigated. Spin-polarized calculations of electron density for nonmagnetic and magnetic bimetallic-electrode systems are compared. Our work is helpful for first principles investigation of spin-dependent metal–molecule–metal tunneling junctions.  相似文献   

10.
Let Γ be a Fuchsian group of the first kind acting on the hyperbolic upper half plane \mathbbH{\mathbb{H}}, and let M = G\\mathbbH{M = \Gamma\backslash \mathbb{H}} be the associated finite volume hyperbolic Riemann surface. If γ is a primitive parabolic, hyperbolic, resp. elliptic element of Γ, there is an associated parabolic, hyperbolic, resp. elliptic Eisenstein series. In this article, we study the limiting behavior of these Eisenstein series on an elliptically degenerating family of finite volume hyperbolic Riemann surfaces. In particular, we prove the following result. The elliptic Eisenstein series associated to a degenerating elliptic element converges up to a factor to the parabolic Eisenstein series associated to the parabolic element which fixes the newly developed cusp on the limit surface.  相似文献   

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