Ground state properties of a Bose－Einstein condensate confined in an anharmonic external potential

In light of the interference experiment of Bose－Einstein condensates, we present an anharmonic external potential model to study ground state properties of Bose－Einstein condensates. The ground state energy and the chemical potential have been analytically obtained, which are lower than those in harmonic trap. Additionally, it is found that the anharmonic strength of the external potential has an important effect on density and velocity distributions of the ground state for the Thomas－Fermi model.     

A GENERATION OF EXACTLY SOLVABLE ANHARMONIC SYMMETRIC OSCILLATORS

Using the ideas of supersymmetric quantum mechanics, we exactly solve a continuous family of anharmonic potentials, which are the supersymmetric partners of the linear harmonic oscillators. The family includes a series of potentials in which the excited-state energy is the same as that of the harmonic oscillators, but the ground-state energy can be any value lower than the excited states. The shape of the potential is variable, which includes the double-well and triple-well potentials. All the potentials obtained in this paper are free of singularities, and the supersymmetry of the solutions is unbroken.     

Critical rotation of an anharmonically trapped Bose--Einstein condensate

We consider rotational motion of an interacting atomic Bose-Einstein condensate (BEC) with both two- and three-body interactions in a quadratic-plus-quartic and harmonic-plus-Gaussian trap. By using the variational method, the influence of the three-body interaction and the anharmonicity of the trap on the lowest energy surface mode excitation and the spontaneous shape deformation (responsible for the vortex formation) in a rotating BEC is discussed in detail. It is found that the repulsive three-body interaction helps the formation of the vortex and reduces the lowest energy surface mode frequency and the critical rotational frequency of the system. Moreover, the critical rotational frequency for the vortex formation in the harmonic-plus-Gaussian potential is lower than that in the quadratic-plus-quartic potential.     

Coulomb effects on the formation of proton halo nuclei

This paper makes some qualitative and quantitative analyses about halo formation rules of some mirror nuclei with the relativistic mean-field (RMF) theory and the Woods--Saxon mean-field model. By analysing two opposite effects of Coulomb interaction on the proton halo formation, it finds that the energy level shift has a larger contribution than that of the Coulomb barrier when the mass number A is small, the hindrance of the Coulomb barrier becomes more obvious with the increase of the mass number A, and the overall effect of the Coulomb interaction almost disappears when A≈39 as its two effects counteract with each other.     

Vibrational spectra of benzophenone conformers

We have used direct quantum DFT methods to calculate the parameters of the adiabatic potential of four benzophenone conformers. According to the data obtained, the existence of only one conformer is possible (C₁ symmetry) for the free benzophenone molecule, for which torsional vibrations of the benzene moieties are reproduced and for which we calculated the vibrational spectrum in the anharmonic approximation of the theory of molecular vibrations. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 5, pp. 561–564, September–October, 2007.     

Unified Method for Dynamical Groups of Some Anharmonic Potentials

Realizations of the creation and annihilation operators for some important anharmonic potentials, such as the Morse potential, the modified Pöschl–Teller potential (MPT), the pseudoharmonic oscillator, and infinitely deep square-well potential, are presented by a factorization method. It is shown that the operators for the Morse potential and the MPT potential satisfy the commutation relations of an SU(2) algebra, but those of the pseudoharmonic oscillator and the infinitely deep square-well potential constitute an SU(1, 1) algebra. The matrix elements of some related operators are analytically obtained. The harmonic limits of the SU(2) operators for the Morse and MPT potentials are studied as the Weyl algebra.     

超流Fermi气体在非简谐势阱中的集体激发

研究了非谐振势中超流Fermi气体的集体激发. 基于一维超流流体动力学模型, 采用变分法获得了体系从分子Bose-Einstein凝聚端渡越到Cooper对凝聚端时系统的两个低能激发模, 即偶极模和呼吸模. 分析发现: 在整个跨越区偶极模和呼吸模都发生了频移现象, 且在BCS端频移更加显著. 进一步研究发现在不同驱动振幅激发下超流Fermi气体质量中心和宽度变化呈现出了复杂动力学特性, 由于非谐振势的贡献,超流Fermi气体两低能模发生耦合, 使宽度变化产生量子拍频现象, 且拍频频率随着驱动振幅的增加而增大. 这种非线性耦合对外部驱动的响应在幺正区尤其显著.关键词：超流Fermi气体非谐振势集体激发     

Thermal properties of cubic metals in anharmonic approximation

Expressions for thermal properties such as thermal expansion, specific heat and melting point are obtained by employing the usual quadratic-quartic form of the potential energy. Computed results for nineteen cubic metals are presented and compared with the experimental values. The model describes the broad features observed in the thermal properties and an estimate of the anharmonicity in cubic metals.     

流体PVTX性质测试虚拟仪器系统的研制

在对国内外现有流体PVTx性质测量实验系统的分析研究基础上,结合现有温度、压力及计算机自动化测试等技术,研制了有关的温度、压力等测量系统,同时利用Visual C++6.0开发了一套完整的流体PVTx性质测试软件,实现了PVTx性质测量的自动化,基本形成了一套较为完整的流体PVTx性质测试虚拟仪器系统。     

Raman spectroscopic study of ceramic Sr2Bi4Ti5O18

Raman spectra of ceramic Sr2Bi4Ti5O18 （SBTi5） are reported to consist of four different Raman bands. Temperature-dependent spectra reveal the relationship between the lattice vibration and the material＇s structure. There appears a relatively large change in structure of the material at about 273K, The anharmonic potential of the material has a great influence on its phonon mode full width at half maximum （FWHM）, which can be expressed by a function of temperature. Theoretical fittings of the FWHMs for the two modes at around 312 cm^-1 and 464cm^-1 indicate that the latter phonon mode is more anharmonic than the former one.     

细胞骨架微管管壁的赝自旋模型

本文利用赝自旋模型描述细胞骨架微管管壁上的非束缚电子的动力学行为。基于微管的固有的对称结构及其电学性质，将其处理为一维铁电系统，用双阱势描述组成微管管壁的单个蛋白丝上的电偶极子的非线性动力学行为，进而，将此物理问题影射到赝自旋系统，并且通过采用平均场近似得到了一些物理结果。     

三势阱中玻色-爱因斯坦凝聚的开关特性

应用平均场近似的方法,研究了弱耦合的三势阱中玻色-爱因斯坦凝聚的开关效应.当粒子置于左阱时,可以通过在中间势阱中加入少量粒子控制左阱粒子向右阱的隧穿,从而呈现出明显的导通与截止行为.对中间势阱的深度和相对相位的影响也进行了讨论,并指出了该理论模型的一些潜在应用前景.关键词：玻色-爱因斯坦凝聚开关效应三势阱平均场近似     

The representation of thermodynamic properties at high pressures

It is sometimes advantageous to have an expression for the Gibbs energy, G_m(T,P), from which one can analytically derive an expression for the Heimholtz energy, F_m(T, V_m). Such an expression is suggested for solid substances and it is shown how expressions for other physical properties can be derived from it.     

Temperature variation of higher-order elastic constants of MgO

An effort has been made for obtaining higher-order elastic constants for MgO starting from basic parameters, viz. nearest-neighbor distance and hardness parameter using Coulomb and Börn-Mayer potentials. These are calculated in a wide temperature range (100–1000 K) and compared with available theoretical and experimental results.     

An analytic equation of state based on analytic mean-field potential approach and application to three phases of metallic Zirconium

The analytic mean-field approach (AMFP) was applied to study the thermodynamic properties of Zirconium (Zr). The analytic expressions for the Helmholtz free energy, internal energy and equation of state have been derived. The formalism for the case of the Morse potential is used in this work. The four potential parameters are determined by fitting the molar volume of the three phases of Zr. The calculated molar volume of α, β and ω Zr are in fairly good agreement with the available experimental data. The results presented in this paper verify that the AMFP is a useful approach to study the thermodynamic properties of Zr. Furthermore, we predict the variation of the relationship of free energy and internal energy versus the molar volume at various temperatures and the dependence of the bulk modulus, the thermal expansion coefficient and the heat capacity on temperature at zero pressure of α, β and ω Zr.      

多元混合工质泡点和露点的推算研究

本文在对二元和三元混合液的泡点和露点研究基础上,导出了理想混合物的泡点压力和露点压力与组分的关系式,并通过对R401(A/B/C)、R407(A/B/C/D/E)、R409(A/B)等系列三元混合物的研究,推荐了多元混合物泡点压力和露点压力与对比温度的关联式,上述算法和推算式通过多种混合工质的实验值或文献推荐值比较检验,平均偏差在1%以内,个别点的最大偏差也就在2%左右,满足工程使用精度。