Functional Integrals and Collective Excitations in Boson-Fermion Model

In this paper, collective excitations in the boson-fermion model are investigated by means of functional integration method. The equations of energy gap and excitation spectrum are derived. Moreover, the Bose energy spectrum of zero wave vector Fermi fields is also calculated.     

Functional Integrals and Excitation Energy in Three-Band Hubbard Model

The normal and anomalous Green＇s functions of antiferromagnetie state in three-band Hubbard model are studied by using functional integrals and temperature Green＇s function method. The equations of energy spectrum are derived. In addition, excitation energy of Fermi fields are calculated under long wave approximation.     

The Binding Energy, Spin-Excitation Gap, and Charged Gap in the Boson-Fermion Model

In this paper, by applying a simplified version of Lieb ‘s spin-refleetion-positivity method, which was recentlydeveloped by one of us [G.S. Tian and J.G. Wang, J. Phys. A: Math. Gen. 35 (2002) 941], we investigate some generalproperties of the boson-fermion Hamiltonian, which has been widely used as a phenomenological model to describe thereal-space pairing of electrons. On a mathematically rigorous basis, we prove that for either negative or positive couplingV, which represents the spontaneous decay and recombination process between boson and fermion in the model, thepairing energy of electrons is nonzero. Furthermore, we also show that the spin-excitation gap of the boson-fermionHamiltonian is always larger than its charged gap, as predicted by the pre-paired electron theory.     

Functional Integrals and Variational-Cumulant Expansion in sine-Gordon-Thirring Model

The free energy in 1D sine-Gordon-Thirring model with impurity coupling is studied by means of functional integrals and variational-cumulant expansion methods. Two variational parameters are introduced to evaluate free energy and statistical averages. It is shown that the non-perturbation method of functional integrals can be applied to strong-coupling range of fermion systems.     

Functional Integrals and Variational-Cumulant Expansion in sine-Gordon-Thirring Model

The free energy in 1D sine-Gordon- Thirring model with impurity coupling is studied by means of functional integrals and variational-cumulant expansion methods. Two variational parameters are introduced to evaluate free energy and statistical averages. It is shown that the non-perturbation method of functional integrals can be applied to strongcoupling range of fcrmion systems.     

The Binding Energy, Spin－Excitation Gap, and Charged Gap in the Boson－Fermion Model

In this paper, by applying a simplified version of Lieb‘s spin-reflection-positivity method, which was recently developed by one of us [G.S. Tian and J.G. Wang, J. Phys. A: Math. Gen. 35 (2002) 941], we investigate some general properties of the boeon-fermion Hamiltonlan, which has been widely used as a phenomenological model to describe the real-space pairing of electrons. On a mathematically rigorous basis, we prove that for either negative or positive couping V, which represents the spontaneous decay and recombination process between boson and fermion in the model, the pairing energy of electrons is nonzero. Furthermore, we also show that the spin-excitation gap of the boson-fermion Hamiltonian is always larger than its charged gap, as predicted by the pre-palred electron theory.     

Functional Integrals and Free Energy in sine-Gordon-Thirring Model with Impurity Coupling

The free energy at low temperature in 1D sine-Gordon-Thirring model with impurity coupling is studied by means of functional integrals method. For massive free sine-Gordon-Thirring model, free energy is obtained from perturbation expansion of functional determinant. Moreover, the free energy of massive model is calculated by use of an auxiliary Bose field method.     

Functional Integrals and Quantum Fluctuations on Two-DimensionalNoncommutative Space-Time

The generalized Thirring model with impurity coupling is defined ontwo-dimensional noncommutative space-time, a modified propagator and freeenergy are derived by means of functional integrals method. Moreover,quantum fluctuations and excitation energies are calculated on two-dimensional black hole and soliton background.     

Functional Integrals and Quantum Fluctuations on Two-Dimensional Noncommutative Space-Time

The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutative space-time, a modified propagator and free energy are derived by means of functional integrals method. Moreover, quantum fluctuations and excitation energies are calculated on two-dimensional black hole and soliton background.     

Collective Excitations of Low Dimensional Trapped Bose-Condensed Gas

In this paper, we investigate excited characteristic of the weakly interacting quasi-one-dimensional (1D) and quasi-two-dimensional (2D) Bose-Einstein condensation (BEC) in harmonic potential trap. The energy spectrum and the analytical expression of the sound velocity are obtained and analyzed. Compared with 3-Dimensional homogeneous Bose-condensed gas occasion, the sound velocity of 2D Bose-Einstein condensation in harmonic potential trap is smaller.     

Collective Excitations of Low Dimensional Trapped Bose-Condensed Gas

In this paper, we investigate excited characteristic of the weakly interacting quasi-one-dimensional （11）） and quasi-two-dimensional （2D） Bose-Einstein condensation （BEC） in harmonic potential trap. The energ3, spectrum and the analytical expression of the sound velocity are obtained and analyzed. Compared with 3-Dimensional homogeneous Bose-condensed gas occasion, the sound velocity of 21） Bose-Einstein condensation in harmonic potential trap is smaller.     

Nucleon—Pair Shell Model：Magnetic Excitations for Ba Isotopes

Magnetic excitations for Ba isotopes are discussed within the nucleon-pair shell model truncated in the SD subspace.With the SD pair determined by a surface-δ interaction,M1 transitions for ^134Ba are well fitted.The M1 and M3 transitions for ^132Ba and ^130Ba are also predicted.It is shown that the statement,the collective magnetic properties are due to the orbital motion of nucleons,is approximately valid.     

泛函积分方法于Dicke模型中的临界温度和集体激发谱

采用泛积分方法研究了Ｄｉｃｋｅ模型中的临界温度和能隙方程,计算了模型中的零温度能隙;此外,还推导了Ｄｉｃｋｅ模型中的玻色型激发谱,讨论子粒子的能量了振动频率的依赖关系。     

奇特核结构与激发的微观研究

原子核是一个从少体到多体过渡的量子体系,展现了很多有趣的集体现象。随着国际上若干大型放射性核束流实验装置的发展,极不稳定奇特核的结构与激发的研究成为当前核物理的前沿热点问题。本工作以形变弱束缚核40Mg为例,基于格点空间连续谱能量密度泛函和自洽的FAM-QRPA对奇特核的基态与激发态跃迁进行了研究。发现弥散的表面密度分布与连续谱对低能共振有很大影响。通过对同位旋矢量偶极激发的研究,说明低能矮共振与巨共振的微观机制有很大差异。此外还进行了大规模拟合,发展针对丰中子核,超重核的新的高精度有效相互作用,以期为相关学科如核天体物理、核裂变能等提供更为可靠的核理论模型。Nuclei are quantum systems in the evolution from few-body to many-body systems, and can exhibit many amazing collective phenomena. With the development of several advanced radioactive-beam facilities, the study of structures and excitations of extreme unstable exotic nuclei has become a hot issue. In this work, we solve the self-consistent FAM-QRPA in large deformed coordinate-spaces to treat continuum effects. We study properties of structures and collective excitations in deformed drip-line nuclei. We found that in weakly bound nuclei 40Mg, the diffuse surface density and pairing density play an important role in low-lying resonance. Through analysis of deformation-induced K-splitting in isovector dipole modes, we see that pygmy resonances have very different mechanism compared to giant resonances. In addition, large-scale fittings are performed to develop highprecision effective interactions, which will provide more reliable theoretical model for related subjects, such as nuclear astrophysics and nuclear fission energy.     

Energy Level Statistics of SO（5） Limit of Super-symmetry U（6/4） in Interacting Boson-Fermion Model

We study the energy level statistics of the SO（5） limit of super-symmetry U（6/4） in odd-A nucleus using the interacting boson-fermion model. The nearest neighbor spacing distribution （NSD） and the spectral rigidity （Δ3） are investigated, and the factors that affect the properties of level statistics are also discussed. The results show that the boson number N is a dominant factor. If N is small, both the interaction strengths of subgroups SO^B（5） and SO^BF （5） and the spin play important roles in the energy level statistics, however, along with the increase of N, the statistics distribution would tend to be in Poisson form.     

Energy Level Statistics of SO(5) Limit of Super-symmetry U(6/4) in Interacting Boson-Fermion Model

We study the energy level statistics of the SO(5) limit of super-symmetry U(6/4) in odd-A nucleus using the interacting boson-fermion model. The nearest neighbor spacing distribution (NSD) and the spectral rigidity (△3)are investigated, and the factors that affect the properties of level statistics are also discussed. The results show that the boson number N is a dominant factor. If N is small, both the interaction strengths of subgroups SOB(5) and SOBF(5)and the spin play important roles in the energy level statistics, however, along with the increase of N, the statistics distribution would tend to be in Poisson form.     

Charged Shear-Free Fluids and Complexity in First Integrals

The equation yxx=f(x)y2+g(x)y3 is the charged generalization of the Emden-Fowler equation that is crucial in the study of spherically symmetric shear-free spacetimes. This version arises from the Einstein–Maxwell system for a charged shear-free matter distribution. We integrate this equation and find a new first integral. For this solution to exist, two integral equations arise as integrability conditions. The integrability conditions can be transformed to nonlinear differential equations, which give explicit forms for f(x) and g(x) in terms of elementary and special functions. The explicit forms and arise as repeated roots of a fourth order polynomial. This is a new solution to the Einstein-Maxwell equations. Our result complements earlier work in neutral and charged matter showing that the complexity of a charged self-gravitating fluid is connected to the existence of a first integral.     

Collective Excitations in Spin-2 Bose-Einstein Condensates

The Green＇s functions and the correlation functions in spin-2 Bose-Einstein condensates at finite temperature are defined and the generalized Dyson-Beliaev equations are introduced. We discuss the spin conservation in z direction and decouple the Green＇s functions and the generalized Dyson-Beliaev equations according to different spin conservations in z direction. The anomalous vertex functions are introduced and the self-energies are separated into the proper self-energies and the improper self-energies. The generalized Dyson-Beliaev equations are decoupled according to separation of the self-energies. We calculate the Green＇s functions step by step in the Bogoliubov approximation and discuss the collective excitations in spin-2 Bose-Einstein condensates in the polar, ferromagnetic, and cyclic cases, respectively.     

Functional integrals in the statistical theory of turbulence and the burgers model equation

The functional integrals appearing in master equations for turbulent flow of an incompressible fluid and for the Burgers model equation are treated. A possible way is described to define the integration properly and related problems are discussed. For the simple example of the Burgers model equation of turbulence some results are presented.     

Spin-Wave Excitations in Anisotropic Kondo Lattice Model

The spin-wave excitations in anisotropic Kondo lattice model are studied using the spin Green's function. Both the ferromagnetic and antiferromagnetic cases are considered. The equations to determine the spectrum of low-energy excitations are given. The anisotropy gaps are obtained, and the long-wavelength and strong-coupling limits are analyzed.