烷基苯的热力学性质与分子拓扑指数的关系研究

此文分析了烷基苯的结构特点，以分子的拓扑指数为结构参数，研究了苯、烷基系列的燃烧热，生成自由能等八种热力学性质与结构参数的关系，提出计算热力学性质的一个通用关系式Ｙ＝ａ·Ｎ＋ｂ·Ｒ＋ｃ·ＮＲ＋ｄ，用计算机处理，得到一系列经验公式，计算结果表明：烷基苯系列的热力学性质与拓扑指数相关性能很好。     

蓖麻油黏度与表面张力系数的关系研究

分别利用落球法和拉脱法测量了蓖麻油在不同温度下的黏度和表面张力系数;根据最速下降法,编制自动调参程序FIT,通过拟合实验测量数据,得到了描述蓖麻油黏度与表面张力系数关系的经验公式.     

Calculated cross sections for the single ionization of atoms (N, Cu, As, Se, Sn, Sb, Te, I, Pb) by electron impact

By correcting some primary parameters in the semi-classical Deutsch--M?rk (DM) formula, this paper calculates the absolute single electron-impact ionization cross sections of atoms N, Cu, As, Se, Sn, Sb, Te, I and Pb from threshold to 10000eV. The calculated cross sections are compared with available experimental data and other theoretical results. An excellent agreement was achieved between the calculated and measured cross sections for these atoms over a wide range of impact energies.     

Correspondence between quantum-optical transform and classical-optical transform explored by developing Dirac’s symbolic method

By virtue of the new technique of performing integration over Dirac’s ket–bra operators, we explore quantum optical version of classical optical transformations such as optical Fresnel transform, Hankel transform, fractional Fourier transform, Wigner transform, wavelet transform and Fresnel–Hadmard combinatorial transform etc. In this way one may gain benefit for developing classical optics theory from the research in quantum optics, or vice-versa. We cannot only find some new quantum mechanical unitary operators which correspond to the known optical transformations, deriving a new theorem for calculating quantum tomogram of density operators, but also can reveal some new classical optical transformations. For examples, we find the generalized Fresnel operator (GFO) to correspond to the generalized Fresnel transform (GFT) in classical optics. We derive GFO’s normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in the context of quantum optics. Especially, the introduction of quantum mechanical entangled state representations opens up a new area in finding new classical optical transformations. The complex wavelet transform and the condition of mother wavelet are studied in the context of quantum optics too. Throughout our discussions, the coherent state, the entangled state representation of the two-mode squeezing operators and the technique of integration within an ordered product (IWOP) of operators are fully used. All these have confirmed Dirac’s assertion: “...for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory”.     

Stationary Dyonic regular and black hole solutions

We consider globally regular and black hole solutions in SU(2) Einstein–Yang–Mills–Higgs theory, coupled to a dilaton field. The basic solutions represent magnetic monopoles, monopole–antimonopole systems or black holes with monopole or dipole hair. When the globally regular solutions carry additionally electric charge, an angular momentum density results, except in the simplest spherically symmetric case. We evaluate the global charges of the solutions and their effective action, and analyze their dependence on the gravitational coupling strength. We show, that in the presence of a dilaton field, the black hole solutions satisfy a generalized Smarr type mass formula. B. Kleihaus gratefully acknowledges support by the German Aerospace Center. F. Navarro-Lérida gratefully acknowledges support by the Ministerio de Educación y Ciencia under grant EX2005-0078.     

Trigonometrical sums connected with the chiral Potts model,Verlinde dimension formula,two-dimensional resistor network,and number theory

We have recently developed methods for obtaining exact two-point resistance of the complete graph minus N$N$ edges. We use these methods to obtain closed formulas of certain trigonometrical sums that arise in connection with one-dimensional lattice, in proving Scott’s conjecture on permanent of Cauchy matrix, and in the perturbative chiral Potts model. The generalized trigonometrical sums of the chiral Potts model are shown to satisfy recursion formulas that are transparent and direct, and differ from those of Gervois and Mehta. By making a change of variables in these recursion formulas, the dimension of the space of conformal blocks of SU(2)$SU\left(2\right)$ and SO(3)$SO\left(3\right)$ WZW models may be computed recursively. Our methods are then extended to compute the corner-to-corner resistance, and the Kirchhoff index of the first non-trivial two-dimensional resistor network, 2×N$2\times N$. Finally, we obtain new closed formulas for variant of trigonometrical sums, some of which appear in connection with number theory.     

Research on the propagation properties of hollow laser beams with three-dimensional trap optical distribution

A new kind of hollow beams - hollow laser beams with three-dimension trap optical distribution - was put forward. With the help of the Collins formula in paraxial optical system, the analytical equation of propagation and transformation of the hollow laser beams was deduced. According to the analytical equation, the propagation properties of the kind of hollow beams that transform in free space were simulated. In the experiment, we obtained the hollow laser beams by means of the combinational optical system of reflecting positive-axis and negative-axis pyramids. The intensity of the vertical loop in different distances was tested, which shows that the analytical equation of propagation and transformation is in agreement with the result.     

Operators’s-parameterized ordering and its classical correspondence in quantum optics theory

In reference to the Weyl ordering xmpn→(1/2)mΣι=0m(ιm)Xm-ιPnXι , where X and P are coordinate and momentum operator, respectively, this paper examines operators’s-parameterized ordering and its classical correspondence, finds the fundamental function-operator correspondence ((1-s)/2)(n+m)/2Hm,n((2/(1-s))～(1/2)α,(2/(1-s))～(1/2)α)→a+man,and its complementary relation αnα*m→(-i)n+m((1-s)/2)(m+n)/2:Hm,n(i(2/(1-s))～(1/2)a+,i((2/(1-s))～(1/2)a):,where H m,n is the two-variable Hermite polynomial, a, a+ are bosonic annihilation and creation operators respectively, s is a complex parameter. The s’-ordered operator power-series expansion of s-ordered operator sa+mans in terms of the two-variable Hermite polynomial is also derived. Application of operators’s-ordering formula in studying displaced-squeezed chaotic field is discussed.