硼酸盐晶体Li4CaB2O6的从头计算研究

本文通过总能赝势方法理论研究了八面体晶体材料Li4CaB2O6的晶体和电子结构以及Mulliken布居数；本文使用的总能赝势方法包括局域密度近似和广义梯度近似两种密度泛涵理论.所得的结果与实验提供的数据吻合较好.通过分析电子能带结构，可以推断多晶材料Li4CaB2O6 适用于半导体光学材料.     

The structure of the high-energy spin excitations in a high-transition-temperature superconductor

In conventional superconductors, lattice vibrations (phonons) mediate the attraction between electrons that is responsible for superconductivity. The high transition temperatures (high-T(c)) of the copper oxide superconductors has led to collective spin excitations being proposed as the mediating excitations in these materials. The mediating excitations must be strongly coupled to the conduction electrons, have energy greater than the pairing energy, and be present at T(c). The most obvious feature in the magnetic excitations of high-T(c) superconductors such as YBa2Cu3O6+x is the so-called 'resonance'. Although the resonance may be strongly coupled to the superconductivity, it is unlikely to be the main cause, because it has not been found in the La2-x(Ba,Sr)(x)CuO4 family and is not universally present in Bi2Sr2CaCu2O8+delta (ref. 9). Here we use inelastic neutron scattering to characterize possible mediating excitations at higher energies in YBa2Cu3O6.6. We observe a square-shaped continuum of excitations peaked at incommensurate positions. These excitations have energies greater than the superconducting pairing energy, are present at T(c), and have spectral weight far exceeding that of the 'resonance'. The discovery of similar excitations in La2-xBa(x)CuO4 (ref. 10) suggests that they are a general property of the copper oxides, and a candidate for mediating the electron pairing.     

ZnO电子结构及高压相变的第一性原理研究

基于屏蔽交换的LDA方法研究了高压下B4及B1相ZnO的能带结构和态密度特性;使用GGA WC交换关联泛函,计算了B4,B3,B2和B1相结构ZnO的基态能量、晶格常数、体模量及其对压力的导数.计算结果表明：ZnO在从纤锌矿（B4）转变为岩盐（B1）结构的过程中,存在着一个亚稳平衡过渡相,即闪锌矿结构（B3）.计算得到的相变压Ptr表明：随着外压的增加,ZnO将依照B4→B3→B1→B2的路径发生一系列的结构相变,相变压依次为Ptr（B4→B3）=3.156 GPa,Ptr（B3→B1）=7.996 GPa,Ptr（B4→B1）=9.855 GPa,Ptr（B1→B2）=253.605 GPa.     

金属Ti热学性质第一原理研究

应用基于密度泛函与密度泛函微扰理论的平面波赝势方法计算一组不同晶格常数下六角密堆积(hcp)结构金属Ti的声子谱及相应的静态总能,由此得到不同晶格常数下的自由能,由准谐近似及自由能极小判据得到自由能与温度的关系,进而计算热膨胀系数、定容摩尔热容及定压摩尔热容与温度的关系,对热膨胀系数及定容摩尔热容的第一原理计算值与德拜理论计算值进行比较。结果表明:295 K下声子谱理论值与实验值除在[001]方向上的光学纵模有少量偏差外,其余部分符合得很好;hcp结构金属Ti有一定程度的各向异性热膨胀,沿c轴方向与a轴方向的热膨胀系数比值为1.5左右;热膨胀系数、定容摩尔热容及定压摩尔热容第一原理计算值在较宽的温度范围内与已有的实验数据相符;热膨胀系数的德拜理论值仅在室温以下温区与实验结果相符;定容摩尔热容的第一原理计算值与德拜理论值在中温区有少量偏差,在低温及高温区非常接近。     

几种交换能密度泛函的数值检验

通过对原子和分子体系的密度泛函计算检验了LDA、B88、BR89、B2000、VSX和作者提出的CPX等6种交换能密度泛函的精度。非定域校正使原子的交换能计算值有很大改善,其中用B88和CPX泛函的计算结果最好。对于只含轻元素的分子,除LDA泛函以外,用其他泛函计算的原子化能都比较好,接近或者稍微超过MP2方法的计算精度。对于含重元素的分子,原子化能的计算误差显著增大,B88、CPX和BR89泛函给出的结果比较好一些;VSX泛函的精度还不如不加梯度校正的LDA泛函。非定域校正并不改善第一电离势的计算结果。VSXC泛函虽然用于只含轻元素分子的计算比较成功,用于含重元素体系计算效果很差。作者提出的CPX泛函的表现还比较好,通过仔细优选参数,有可能发展成为一种对含重元素体系计算精度也较高的交换能密度泛函。     

泛函积分与玻色费米子模型中的长波激发

本文采用泛函积分方法研究了高温超导中玻色-费米子模型的长波激发.推导了能隙方程和激发谱方程,并且计算了在长波近似下费米场的玻色能谱,得到了简并和非简并激发模.     

关于系统绝热近似

根据算符的微分性质和分部积分法分别讨论了绝热近似下的形式消去公式,然后用迭代法得出快变量的表达式,继而用一个非线性随机微分系统为例子来说明迭代法的原理和应用方法,最后利用直接求解法处理在乘法噪声驱动下的线性随机微分系统,得到了其绝热近似下的快变量表达式.     

在相对论理论中研究原子核的巨单极态

在相对论的手征对称破缺模型基础上,应用Jocal Lorentz boost和scaling座标方法,首先采用Hartree近似讨论了无限核物质的巨单极共振激发态,但计算结果略大于实验值。进而采用Thomas-Fermi近似处理有限核的表面效应以及核子分布的非均匀性对原子核巨单极共振激发能的影响,自洽计算的结果和实验符合得很好,由此证明对于巨共振态,考虑核子分布的非均匀性以及核的表面效应是十分重要的。     

Using photoemission spectroscopy to probe a strongly interacting Fermi gas

Ultracold atomic gases provide model systems in which to study many-body quantum physics. Recent experiments using Fermi gases have demonstrated a phase transition to a superfluid state with strong interparticle interactions. This system provides a realization of the 'BCS-BEC crossover' connecting the physics of Bardeen-Cooper-Schrieffer (BCS) superconductivity with that of Bose-Einstein condensates (BECs). Although many aspects of this system have been investigated, it has not yet been possible to measure the single-particle excitation spectrum (a fundamental property directly predicted by many-body theories). Here we use photoemission spectroscopy to directly probe the elementary excitations and energy dispersion in a strongly interacting Fermi gas of (40)K atoms. In the experiments, a radio-frequency photon ejects an atom from the strongly interacting system by means of a spin-flip transition to a weakly interacting state. We measure the occupied density of single-particle states at the cusp of the BCS-BEC crossover and on the BEC side of the crossover, and compare these results to that for a nearly ideal Fermi gas. We show that, near the critical temperature, the single-particle spectral function is dramatically altered in a way that is consistent with a large pairing gap. Our results probe the many-body physics in a way that could be compared to data for the high-transition-temperature superconductors. As in photoemission spectroscopy for electronic materials, our measurement technique for ultracold atomic gases directly probes low-energy excitations and thus can reveal excitation gaps and/or pseudogaps. Furthermore, this technique can provide an analogue of angle-resolved photoemission spectroscopy for probing anisotropic systems, such as atoms in optical lattice potentials.     

平均场加邻近轨道相互作用对力模型对超铀区大形变核的应用

利用严格可解的平均场加邻近轨道相互作用对力模型来描述大形变核 .将该模型应用于超铀区的核素 .计算了2 2 6 2 3 4 Th ,2 3 0 2 40 U及2 3 6 2 43 Pu同位素的结合能和对激发能 ,并与实验结果进行比较 .     

双井中的随机共振现象

用Ｆｏｋｋｅｒ－Ｐｌａｎｃｋ算子法建立了处理分段连续调制下的双井随机共振问题的理论方法，并对方波和锯齿调制情况进行了解算。文中用线性响应理论对结果加以处理，并发现了随机共振现象。分析方法包括了绝热近似下的结果，并适用于非绝热的情况。     

Observation of a roton collective mode in a two-dimensional Fermi liquid

Understanding the dynamics of correlated many-body quantum systems is a challenge for modern physics. Owing to the simplicity of their Hamiltonians, (4)He (bosons) and (3)He (fermions) have served as model systems for strongly interacting quantum fluids, with substantial efforts devoted to their understanding. An important milestone was the direct observation of the collective phonon-roton mode in liquid (4)He by neutron scattering, verifying Landau's prediction and his fruitful concept of elementary excitations. In a Fermi system, collective density fluctuations (known as 'zero-sound' in (3)He, and 'plasmons' in charged systems) and incoherent particle-hole excitations are observed. At small wavevectors and energies, both types of excitation are described by Landau's theory of Fermi liquids. At higher wavevectors, the collective mode enters the particle-hole band, where it is strongly damped. The dynamics of Fermi liquids at high wavevectors was thus believed to be essentially incoherent. Here we report inelastic neutron scattering measurements of a monolayer of liquid (3)He, observing a roton-like excitation. We find that the collective density mode reappears as a well defined excitation at momentum transfers larger than twice the Fermi momentum. We thus observe unexpected collective behaviour of a Fermi many-body system in the regime beyond the scope of Landau's theory. A satisfactory interpretation of the measured spectra is obtained using a dynamic many-body theory.     

Fe_n,Co_n和Ni_n(n=2～4)分子团簇的自旋极化效应

采用密度泛函理论中的交换关联函数B3P86,对Fen,Con和Nin(n=2~4)分子团簇进行了几何结构的优化。对于每一个分子体系,为了能找到具有最低能量的结构,分别考虑多种同分异构体和不同的多重度,最终得到它们的基态结构、键长和键能。结果表明:Fen,Con和Nin(n=2~4)分子的最低能量随着多重性的增加而降低,这种电子自旋的非平衡性显示出自旋极化效应。     

Low-energy acoustic plasmons at metal surfaces

Nearly two-dimensional (2D) metallic systems formed in charge inversion layers and artificial layered materials permit the existence of low-energy collective excitations, called 2D plasmons, which are not found in a three-dimensional (3D) metal. These excitations have caused considerable interest because their low energy allows them to participate in many dynamical processes involving electrons and phonons, and because they might mediate the formation of Cooper pairs in high-transition-temperature superconductors. Metals often support electronic states that are confined to the surface, forming a nearly 2D electron-density layer. However, it was argued that these systems could not support low-energy collective excitations because they would be screened out by the underlying bulk electrons. Rather, metallic surfaces should support only conventional surface plasmons-higher-energy modes that depend only on the electron density. Surface plasmons have important applications in microscopy and sub-wavelength optics, but have no relevance to the low-energy dynamics. Here we show that, in contrast to expectations, a low-energy collective excitation mode can be found on bare metal surfaces. The mode has an acoustic (linear) dispersion, different to the dependence of a 2D plasmon, and was observed on Be(0001) using angle-resolved electron energy loss spectroscopy. First-principles calculations show that it is caused by the coexistence of a partially occupied quasi-2D surface-state band with the underlying 3D bulk electron continuum and also that the non-local character of the dielectric function prevents it from being screened out by the 3D states. The acoustic plasmon reported here has a very general character and should be present on many metal surfaces. Furthermore, its acoustic dispersion allows the confinement of light on small surface areas and in a broad frequency range, which is relevant for nano-optics and photonics applications.     

手征对称破缺理论对原子核巨单极和巨四极共振态的研究

在相对论手征对称及其自发破缺模型下,研究了有限核的巨单极和巨四极共振激发态．采用ＴｈｏｒｍａｓＦｅｒｍｉ近似和Ｓｃａｌｉｎｇ坐标方法,讨论了原子核的表面效应及核子分布不均匀性对原子核巨单极和巨四极共振激发态的影响．通过对巨单极和巨四极共振激发能的自洽计算,得到了与实验数据符合得较好的理论计算值．     

三维转动神经网络的研究：（1）能量函数

简述了三维转动神经网络模型，通过对能量函数的研究，证明了网络当神经元个数远大于存贮图象数时，存贮图象为能量空间中的极小值．引入了绝热近似，有效局域场能正确迭代的几率，等于方向角和旋转角分别能正确选代的几率的乘积．     

关于复模态分析法的推广

把复模态分析法推广到刚度矩阵可以奇导且质量矩阵、阻尼矩阵和刚度矩阵均不必为对称的情形。利用常微分方程组理论在较一般条件下求出了线性有阻尼多自由度振动系统对任意外激励的精确响应。在较特殊的条件下，与复模态分析法的结果是一致。     

一类具有无穷分布时滞的反应扩散神经网络的全局渐近稳定性

针对一类具有无穷分布时滞的反应扩散神经网络模型,在Dirichlet边界条件下应用Lyapunov稳定性理论,通过构造适当的Lyapunov-Krasovskii泛函获得了该系统的全局渐近稳定性判据,数值模拟说明了所得理论判据的可行性.     

Generation of Fock states in a superconducting quantum circuit

Spin systems and harmonic oscillators comprise two archetypes in quantum mechanics. The spin-1/2 system, with two quantum energy levels, is essentially the most nonlinear system found in nature, whereas the harmonic oscillator represents the most linear, with an infinite number of evenly spaced quantum levels. A significant difference between these systems is that a two-level spin can be prepared in an arbitrary quantum state using classical excitations, whereas classical excitations applied to an oscillator generate a coherent state, nearly indistinguishable from a classical state. Quantum behaviour in an oscillator is most obvious in Fock states, which are states with specific numbers of energy quanta, but such states are hard to create. Here we demonstrate the controlled generation of multi-photon Fock states in a solid-state system. We use a superconducting phase qubit, which is a close approximation to a two-level spin system, coupled to a microwave resonator, which acts as a harmonic oscillator, to prepare and analyse pure Fock states with up to six photons. We contrast the Fock states with coherent states generated using classical pulses applied directly to the resonator.     

How Cooper pairs vanish approaching the Mott insulator in Bi2Sr2CaCu2O8+delta

The antiferromagnetic ground state of copper oxide Mott insulators is achieved by localizing an electron at each copper atom in real space (r-space). Removing a small fraction of these electrons (hole doping) transforms this system into a superconducting fluid of delocalized Cooper pairs in momentum space (k-space). During this transformation, two distinctive classes of electronic excitations appear. At high energies, the mysterious 'pseudogap' excitations are found, whereas, at lower energies, Bogoliubov quasi-particles-the excitations resulting from the breaking of Cooper pairs-should exist. To explore this transformation, and to identify the two excitation types, we have imaged the electronic structure of Bi(2)Sr(2)CaCu(2)O(8+delta) in r-space and k-space simultaneously. We find that although the low-energy excitations are indeed Bogoliubov quasi-particles, they occupy only a restricted region of k-space that shrinks rapidly with diminishing hole density. Concomitantly, spectral weight is transferred to higher energy r-space states that lack the characteristics of excitations from delocalized Cooper pairs. Instead, these states break translational and rotational symmetries locally at the atomic scale in an energy-independent way. We demonstrate that these unusual r-space excitations are, in fact, the pseudogap states. Thus, as the Mott insulating state is approached by decreasing the hole density, the delocalized Cooper pairs vanish from k-space, to be replaced by locally translational- and rotational-symmetry-breaking pseudogap states in r-space.