Cheng Nan-Pu

Statistical Properties of the Realistic Model Spectra for Doubly-Odd Nuclei

The statistical properties of the energy levels calculated for the doubly-odd nuclei 84Y, 124Cs and 156Tb within the quasiparticle plus axially symmetric rotor model are studied by means of the two standard statistical tests of random-matrix theory, i.e. the distribution function p(s) of the nearest-neighbour level spacings and the spectral rigidity (Δ3 statistics). We also investigate the Brody distribution function pB(s) with a single parameter that describes the chaotic degree of the systematic dynamics and the transition behaviour of the spectral fluctuations between Poisson and Gauss orthogonal ensemble limits.

LiNbO 3 和LiTaO 3 晶体电子结构、平面声波和光折射特性

本研究基于密度泛函理论的第一性原理超软赝势平面方法计算了LiNbO 3 和LiTaO 3 的晶格参数、电子结构和弹性常数, 并利用Christoffel方程研究了二者平面声波特征。结果表明: 两者的理论计算晶格参数和弹性常数与实验值接近, 禁带宽度分别为3.78和3.98 eV, 导带底和价带顶主要由O-2p和Nb-4d(Ta-5d)态电子贡献。化学键理论揭示Li和Nb(Ta)与O原子之间有两种成键类型。 电荷布局分析结果显示有两种相应的重叠布居数, Nb(Ta)–O键呈现强共价键作用, 并且Nb–O(Ta–O)键长小于Li–O键长。LiNbO 3 和LiTaO 3 晶体平面声波有两支横波和一支纵波, 纵波速度大于横波速度, 在 xy 平面呈现六重对称性, 在 xz 和 yz 平面各向异性程度强于 xy 平面, 沿[001]、[00-1]晶向上两支横波振动速度相等。最后利用模守恒赝势(Norm-conserving)计算了介电常数和静态折射率, 计算表明LiNbO3晶体的折射性能和非寻常光(e光)离散程度均强于LiTaO3晶体。本研究基于密度泛函理论的第一性原理超软赝势平面方法计算了LiNbO 3 和LiTaO 3 的晶格参数、电子结构和弹性常数, 并利用Christoffel方程研究了二者平面声波特征。结果表明: 两者的理论计算晶格参数和弹性常数与实验值接近, 禁带宽度分别为3.78和3.98 eV, 导带底和价带顶主要由O-2p和Nb-4d(Ta-5d)态电子贡献。化学键理论揭示Li和Nb(Ta)与O原子之间有两种成键类型。 电荷布局分析结果显示有两种相应的重叠布居数, Nb(Ta)–O键呈现强共价键作用, 并且Nb–O(Ta–O)键长小于Li–O键长。LiNbO 3 和LiTaO 3 晶体平面声波有两支横波和一支纵波, 纵波速度大于横波速度, 在 xy 平面呈现六重对称性, 在 xz 和 yz 平面各向异性程度强于 xy 平面, 沿[001]、[00-1]晶向上两支横波振动速度相等。最后利用模守恒赝势(Norm-conserving)计算了介电常数和静态折射率, 计算表明LiNbO3晶体的折射性能和非寻常光(e光)离散程度均强于LiTaO3晶体。

Electronic Structure, Plane Acoustic Velocities and Refractive Properties of LiNbO

本研究基于密度泛函理论的第一性原理超软赝势平面方法计算了LiNbO 3 和LiTaO 3 的晶格参数、电子结构和弹性常数, 并利用Christoffel方程研究了二者平面声波特征。结果表明: 两者的理论计算晶格参数和弹性常数与实验值接近, 禁带宽度分别为3.78和3.98 eV, 导带底和价带顶主要由O-2p和Nb-4d(Ta-5d)态电子贡献。化学键理论揭示Li和Nb(Ta)与O原子之间有两种成键类型。 电荷布局分析结果显示有两种相应的重叠布居数, Nb(Ta)–O键呈现强共价键作用, 并且Nb–O(Ta–O)键长小于Li–O键长。LiNbO 3 和LiTaO 3 晶体平面声波有两支横波和一支纵波, 纵波速度大于横波速度, 在 xy 平面呈现六重对称性, 在 xz 和 yz 平面各向异性程度强于 xy 平面, 沿[001]、[00-1]晶向上两支横波振动速度相等。最后利用模守恒赝势(Norm-conserving)计算了介电常数和静态折射率, 计算表明LiNbO3晶体的折射性能和非寻常光(e光)离散程度均强于LiTaO3晶体。本研究基于密度泛函理论的第一性原理超软赝势平面方法计算了LiNbO 3 和LiTaO 3 的晶格参数、电子结构和弹性常数, 并利用Christoffel方程研究了二者平面声波特征。结果表明: 两者的理论计算晶格参数和弹性常数与实验值接近, 禁带宽度分别为3.78和3.98 eV, 导带底和价带顶主要由O-2p和Nb-4d(Ta-5d)态电子贡献。化学键理论揭示Li和Nb(Ta)与O原子之间有两种成键类型。 电荷布局分析结果显示有两种相应的重叠布居数, Nb(Ta)–O键呈现强共价键作用, 并且Nb–O(Ta–O)键长小于Li–O键长。LiNbO 3 和LiTaO 3 晶体平面声波有两支横波和一支纵波, 纵波速度大于横波速度, 在 xy 平面呈现六重对称性, 在 xz 和 yz 平面各向异性程度强于 xy 平面, 沿[001]、[00-1]晶向上两支横波振动速度相等。最后利用模守恒赝势(Norm-conserving)计算了介电常数和静态折射率, 计算表明LiNbO3晶体的折射性能和非寻常光(e光)离散程度均强于LiTaO3晶体。

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The thermodynamic properties of an ensemble of metallic nano-particles are affected by the level distribution and the level correlation between the discrete electronic energy levels. We numerically calculate the specific heat of metallic nano-particles in the canonical ensemble with an odd or even number of electrons by considering the effects of the level distribution and the level correlation. The behaviour of the specific heat at low and high temperatures, compared with the average nearest-neighbour level spacing, is also investigated.

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In this paper we introduce an approach in which the random matrices are applied to superconducting nano-particles and obtain the effects of enhancement and attenuation simultaneously. We also explore the influence of magnetic fields on the superconductivity and the condensation energies in nano-particles. Comparisons with other models and some experimental results are given.

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The energy levels of the odd-odd nucleus 86Nb at low spins are calculated by using quasi-particles plus a rotor model. The distribution of the nearest-neighbour spacing and the spectral rigidity are studied. We find that the chaotic degree of the energy spectra increases with the increasing spin and reaches a maximum at I = 10; then it decreases gradually for spins above I = 10. The recoil term in the model Hamiltonian makes the energy spectra slightly regular. The Coriolis force, however, makes the spectra chaotic and plays a major role in the spectral statistics of the odd-odd nucleus 86Nb.